PCUSIM
Version 1.1
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Table of Contents Requirements........................................................................................................................................... 1 Relationship to the Process Control Unit .............................................................................................. 2 Quick Demonstration of Main Features .................................................................................................... 3 Manual Control. ............................................................................................................................ 3 Flow Control ................................................................................................................................. 4 Temperature Control ..................................................................................................................... 5 Batch Volume Control .................................................................................................................. 6 Fluid Level Control ....................................................................................................................... 6 Open Loop Control ....................................................................................................................... 6 Saving and Retrieval of Trends ..................................................................................................... 7 Software Facilities Reference.................................................................................................................... 7 File Menu ...................................................................................................................................... 7 Control Menu ................................................................................................................................ 8 Setup Menu ................................................................................................................................... 8 Help Menu..................................................................................................................................... 8 Initialisation of the Software ......................................................................................................... 9 Definition of Terms used in the Subsequent Sections................................................................... 9 Manual Control ........................................................................................................................... 12 Flow Control ............................................................................................................................... 12 Temperature Control ................................................................................................................... 12 Batch Volume Control ................................................................................................................ 13 Fluid Level Control ..................................................................................................................... 13 Open Loop Control ..................................................................................................................... 13 Saving.......................................................................................................................................... 14 Printing........................................................................................................................................ 14 Trend Updating ........................................................................................................................... 14 Courseware Suggestions ....................................................................................................................... 16 Exercise 1: Proportional Control............................................................................................................. 16 Exercise 2: Proportional and Integral Control......................................................................................... 18 Exercise 3: Saturation and Integral Windup............................................................................................ 21 Exercise 4: Three Term or PID Control .................................................................................................. 23 Exercise 5: Ziegler / Nichols Tuning ...................................................................................................... 24 Exercise 6: Temperature Control ............................................................................................................ 28 Exercise 7: Batch Volume Control ......................................................................................................... 30 Exercise 8: Fluid Level Control .............................................................................................................. 31 Exercise 9: Open Loop Control............................................................................................................... 34 Exercise 10: Bode Plots .......................................................................................................................... 36 Glossary of Terms ................................................................................................................................. 38
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PCUSIM User Manual
Requirements PCUSIM requires the following minimum PC configuration. Pentium Processor 8Mb free system RAM 4Mb HDD space VGA Graphics Display Windows 95 or later Parallel Port or USB Port for dongle It is recommended that PCUSIM be viewed with a screen resolution of 800 x 600 pixels and 256 colours.
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Relationship to the Process Control Unit PCUSIM is a package designed for teaching ‘three term’ (PID) process control concepts and techniques. It is based upon the design of the Bytronic Process Control Unit (PCU) that has been widely sold to colleges and universities for more than twelve years.
The PCU is supplied with Windows 95, 98, NT4 and 2000 compatible PID software that allows the following main areas to be studied: • • • • •
Control of the rate of flow of water from the sump (bottom tank) to the process tank (top). Control of the temperature of the body of water in the process tank. Batch volume control, i.e. the ‘supply’ (from the process tank) of a specified volume of water at a specified temperature over a specified period of time. Control of the water level in the process tank. Open loop investigations.
PCUSIM simulates the same processes that are implemented on the physical PCU and it provides facilities for studying all of the areas bulleted above. The software is intending to be used to support the use of an actual Bytronic International Ltd.
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PCU in the control-teaching laboratory. Many institutions might only have one PCU in the lab. but perhaps ten or more students who need to learn about PID control. Traditionally the students might be circulated around a set of lab. experiments to ensure that they all have equal opportunities to learn. PCUSIM now makes it possible for all students to learn about PID concepts and to practice the techniques simultaneously, even though there might only be one piece of hardware available. Ideally all students would still take a turn on the hardware but with the introduction of PCUSIM they can now all be taught the same subject at the same time.
Quick Demonstration of Main Features This section provides you with a brief ‘tour’ of the main areas of experimentation provided by PCUSIM. It is not intended to be a comprehensive guide to all aspects of the software but rather to convey the ‘flavour’ of the package.
Manual Control Select System Mimic (Control, System Mimic) and experiment by clicking upon the stirrer motor, cooler fan, diverter valve and drain valve. Click, hold down and slide the Pump Output controls and observe the effects. This manual control facility is provided to help familiarise users with the operations available on the Process Control Unit simulated within PCUSIM in the event that the actual hardware is not available. It also illustrates the concept of Supervisory Control and Data Acquisition (SCADA) that is widely used in the process industry. In the real world SCADA is implemented within a specialised software package running on a computer which is used to supervise the control actions applied by one or more programmable logic controllers (PLCs). The PLC obtains feedback from the process and generates control outputs that depend upon the logic and algorithms programmed into its memory. Communication between the PLC and the supervising computer allows the latter to display a real-time graphical representation of the process. The computer may also acquire and store data such as the values of the process variables etc. for later off-line examination. The SCADA computer also provides a convenient facility for human intervention such as changing the set point or PID values for a process control loop. This is a much better way to change parameters than editing the ladder program within the PLC memory!
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If you experiment with the various System Mimic features you will see that the simulated system behaves in the same way as a physical unit would. For example, when the process tank drain valve is closed (blue) and the pump is turned on the water level indicator rises until the process tank is full then the overflow pipe turns blue to represent the flow of water back to the sump. Also the flow rate display increases and decreases in accordance with the Pump Output control and the blue ‘wetted pipe’ indication varies with the valve settings.
Flow Control Select Flow Control (Control, Flow) and click START to see a simulation using the default PI controller. This represents automatic control of the rate of flow of water through the impeller type flow meter in the centre of the PCU. Click STOP once the traces have settled down to the 1.5 litres/minute set point value. Now click the ticked boxes adjacent to the legends; Flow SP (i.e. set point), Flow MV (i.e. measured value) and Pump Output. You will see that the traces may be hidden or revealed as required to help in your evaluation of the response. Move the slider near the top right hand side of the screen across to the left to magnify the traces and position the tip of your mouse pointer at various positions on the traces to pop up the values recorded at specific times. Move the slider back and start the simulation again, this time click the SP value after about ten seconds and change the set point to say 1 litre/minute and then increase it to 1.8 litres/minute after a further ten seconds. You will see that whilst a little oscillatory the response is reasonable, i.e. the measured value reaches the set point quickly and without massive overshoot for the first two SP values. When the SP is 1.8 litres/minute however the simulation produces the effect of saturation, i.e. even with 100% controller output (white trace at the very top) the measured value does not reach the set point. In the real world this effect might occur because the actuator (pump) is not powerful enough or the pipes are too small or accumulated detritus has reduced the effective diameter of the pipe at some point in the circuit. Change the SP to 1 litre/minute and the integral term in the controller to 999 seconds and then run the simulation again. (An integral action time of 999 seconds more or less eliminates any integral effect that means that we are now left with a proportional only controller. The proportional and integral terms etc. will be defined later in this manual). Once the proportional offset has been clearly established, i.e. the steady state gap between the set point and the flow measured value of about 0.5 litre/minute, reduce the integral action time to 1 second and observe how Bytronic International Ltd.
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the integrating action, which takes account of the historical aspect of the error, brings the measured value smartly up to the set point! With the default PI controller and a set point of 1 litre/minute run the simulation. Once the traces have settled down click the “-” button near the legend; Gate Valve: 100%, (bottom right hand corner of screen) to partially close the gate valve that is in line with the flow meter. Experiment with opening (“+”) and closing (“-”) this valve to see the way that the controller responds. In essence the controller output (white trace) will always change in opposition to the flow-measured value (cyan trace) as it seeks to bring it back to the set point.
Temperature Control Select Temperature Control (Control, Temperature) and click START to see a simulation using the default PI controller. This represents automatic control of the heat input to the process (top) tank on the PCU. Click STOP after about three minutes, enter “0” in the Start Time box at the top left hand side of the graph and move the slider near the top right hand side of the graph across to the right to show the whole trace. Position the tip of your mouse pointer at various positions on the traces to pop up the values recorded at specific times. Now click the ticked boxes adjacent to the legends; Temp SP (i.e. set point), Temp MV (i.e. measured value) and Temp Output. You will see that again the traces may be hidden or revealed as required to help in your evaluation of the response. Reset the process tank temperature to 20ºC by clicking the Initial Value box (bottom left of screen) and change the set point to a much higher temperature say 60ºC by clicking on the Set Point box. Run the simulation and observe how much longer the measured value takes to reach the set point when the initial error is so large. Clearly the temperature control loop on the simulated (and the actual) PCU has much larger time constants that the flow control loop. The temperature control is in fact a very different matter since you cannot really allow the temperature to go above the set point because the only way to then cool the specific body of water in the process tank is via natural methods i.e. mainly by evaporation. With the very short time constants of the flow loop it is quite acceptable, even desirable to allow the flow to overshoot the set point once or twice in order to achieve the optimum settling time.
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Batch Volume Control In this section two PID control algorithms are applied in order to deliver a specific quantity of water at a fixed temperature over a particular period of time. The water is ‘delivered’ at the point where it overflows from the process tank. Batch volume control is of necessity rather more complex than the control of separate flow and temperature loops. The procedure involves pre-heating the water in the process tank (top) to within a few degrees of the set point and then driving the pump at an appropriate rate to ensure that, over the specified period, exactly the volume of water required will be displaced through the overflow from the top of the tank. The task is complicated by the need to keep the temperature of the water being ‘delivered’ at or in reality, as close as possible to, the set point. Select Batch Volume Control (Control, Batch Volume) and make the volume and temperature set points 3 litres and 60ºC respectively. Click START to see a simulation using the default PI controllers. Many of the comments about the way the graphs can be manipulated made in the above paragraphs also apply to the batch volume section.
Fluid Level Control Select Fluid Level Control (Control, Fluid Level) and click START to see a simulation of level control in the process tank, using the default controller. Over the 120 second duration of the experiment vary the set point several times by clicking the SP box and observe the effects. In this simulation the process tank drain valve is normally closed and the controller opens it every time the set point is changed to a value that is lower than the current level. If the set point is increased however, the pump is turned on fully to drive water into the process tank as quickly as possible. As the water level approaches the new set point the control algorithm is used to progressively reduce the pump output so that there is no overshoot. The resulting graph may be manipulated as those looked at previously.
Open Loop Control This section provides the facility to study the open loop response of the flow loop to manually selected step, ramp and sinusoidal inputs etc. Select Open Loop Control (Control, Open Loop) and click the sine wave input option. Start the simulation and once a full wavelength of the traces has been drawn, experiment by changing the Max, Min and Period parameters Bytronic International Ltd.
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to see how the input signal may be manipulated. In this open loop section the sinusoidal input function may be used to examine the frequency response of the flow loop by running several simulations with the same Max and Min values with a range of different Periods.
Saving and Retrieval of Trends On completion of any open or closed loop control experiment the graph that is produced may be saved onto the hard disk. As an example select Flow Control (Control, Flow) and click START to see the default simulation then click File, Save to save the graph to the hard disk. Now close down PCUSIM then restart it and click File, Open to retrieve this ‘trend’. Over a period of time a family of informative trends can be built up to illustrate key features such as ‘proportional offset’, the benefits of integral action, integral windup and the advantages and disadvantages of derivative action etc.
Software Facilities Reference PCUSIM is very straightforward to use with a graphical interface that is similar to the software included with the PCU itself. It has four main menus named File, Control, Setup and Help.
File Menu The File menu provides five choices as follows: New begins a new simulation. Open opens and displays a trend file (previously saved to disk) produced by an earlier simulation. (See section headed ‘Saving and retrieval of trends’ above). Save saves the current simulation trend to disk for later retrieval. Print prints the current simulation trend. Exit exits from PCUSIM.
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Control Menu The Control menu provides six choices as follows: System Mimic gives manual control of the main PCU features, illustrating the concept of SCADA. Flow allows control of the rate of flow of water from the sump to the process tank in litres/minute. Temperature allows control of the temperature of the body of water in the process tank. Batch Volume allows control of the supply (volume/temperature) of heated water from the process tank overflow. Fluid Level allows control of the level of the water in the process tank. Open Loop allows open loop control of the rate of flow of water from the sump to the process tank.
Setup menu The Setup menu provides three choices as follows: Toolbar turns on the toolbar to reveal graphical command icons. Easy Menu pops up a diagram of the PCU with buttons for control options and trend retrieval below it. Preferences opens a window in which certain start up preferences may be specified. (See section headed ‘Initialisation of the software’ below).
Help Menu The Help menu provides two options: Contents gives entry to the help information for all features of the software, (also accessible by hitting F1). About gives software version number.
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Initialisation of the software Before using PCUSIM the start up preferences should be specified by selecting Preferences from the Setup menu. The ‘Program Interface’ field allows the user to set whether PCUSIM is always maximised and whether the toolbar and/or ‘easy menu’ are displayed at start up. Language selection can also be made on this window.
Definitions of Terms used in Subsequent Sections Start/Stop starts or stops the simulated process. Once the process has begun, the data will be captured and displayed on the trend. Viewing stored data is mouse controlled and highly intuitive. Once stopped, data can be saved or printed. Control Mode may be PID Control or Manual Control. PID Control uses ‘three term control’ to calculate the output signal which is used to drive the pump or heating element. Essentially a three-term controller takes a measured value from the sensor (flow meter, temperature probe or level sensor) and compares it against the set point (desired value). The discrepancy between the measured and desired values, called the error, is used to determine the control output signal. This is all represented in the following block diagram, labelled for the flow loop, though do note that the same basic ‘closed loop’ arrangement applies to the control of flow rate, temperature, batch volume and level within PCUSIM.
The line running from the block labelled ‘Flow Measurement’ to the circular ‘summing junction’ in the diagram is known as the feedback signal and any process that contains such a signal is a closed loop system. The three components of a three-term controller each behaves in a different way but when combined they can provide a very accurate degree of control. The three elements of the controller are the Proportional term, the Integral term and the Derivative term, hence the other name by which this type of algorithm is known, ‘PID control’. The proportional term produces an output (Q) that is directly proportional to the error between
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the desired setpoint (SP) and the measured value (MV). All of these variables are functions of time, hence:
error (t ) = SP(t ) − MV (t ) Proportional action can be defined by either the Proportional Gain (PG) or the Proportional Band (PB), described below. Controllers that use only proportional action are possible however they can suffer from the effects of steady state errors i.e. a constant discrepancy between the desired and measured values. This constant error is commonly known as ‘proportional offset’. The proportional gain (PG) is a constant supplied by the user that is multiplied by the error to give the control output:
Q(t ) = PG * error (t ) In proportional mode there is a saturation value of error when the control output reaches 100%. Thereafter further increases in error do not produce any further increase in the control output. The error band where the output is between 0 and 100% is called the proportional band. To describe the proportional control in terms of this band, the output is generated from the constant proportional band (PB) supplied by the user according to the following equation:
Q(t ) =
100 * error (t ) PB
Integral action is used to determine a component of control output based upon the history of the error. It is calculated by finding the net area under the error curve against time and then dividing this value by a constant called the Integral Action Time (I) and multiplying it by the proportional gain (PG). The controller equation is:
Q(t ) =
PG error (t )dt I ∫
The integral action time I, sets the time taken for the integral action to duplicate the proportional action of the controller, if the error was to remain constant during this period. Integral action is most commonly used to remove any steady state error (proportional offset) incurred when using a proportional only controller. Derivative action is based upon the time rate of change of error multiplied by a constant called the Derivative Action Time (D). The controller equation is:
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Q(t ) = PG * D
de dt
The derivative action time D, sets the time taken for the proportional action of the controller to duplicate the instantaneous output of the derivative element. The derivative control mode is never used alone as there is no controller output corresponding to zero rate of change. Derivative action is the final refinement of a three-term controller and is often used to reduce the response time of the system. However it is important to note that it can exaggerate high frequency noise in the system. The three basic control methods described above may be mixed in any measure to provide a P(roportional) plus I(ntegral) plus D(erivative) controller. Sample Time is an important factor that affects the performance of a three-term controller. It is the time interval between successive measured values. A long period between samples reduces the need for rapid analogue to digital conversion and reduces the computational load, but as the sample time is increased a number of degrading effects become significant. If the sampling frequency is too low then important high frequency information will be lost. As the time between consecutive samples is effectively a dead time, the closed loop stability of the system may be reduced. Experiment Time for the batch volume simulation may be varied between 60 and 600 seconds. This is the period over which the target volume (set point) of water should be ‘delivered’ at the overflow outlet of the process tank. Set Point is the process variable desired value that the controller is trying to achieve and maintain. It can either be a fixed value or a square, saw tooth, ramp or sinusoidal waveform for the flow and fluid level simulations. For the temperature and batch volume simulations fixed value set points only are available, for obvious reasons. Traffic Light displays are used in PCUSIM to show the real-time state of the system. When red the process has been halted. When green the process is running in real-time. When amber the process is running slow – heavy processing of some sort is taking place e.g. moving windows, other programs, or processing by Windows, and the system is catching up a fraction each sample cycle. Recurrent amber can be solved by closing other programs, increasing the processing capacity of the computer or increasing the sample time.
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Trends show the results from the simulation session. To display more data on the screen the user may adjust the slider to the top right of the trend. This slider varies the time base of the trend. The arrows to the left of the trend allow the data to be scrolled left or right. Direct numerical input equivalents for these two features are also provided. Auto Drain is a function that automatically steps the drain valve open and closed in a repeating cycle if the measured level is greater than the set point in the fluid level simulation.
Manual Control To switch any of the actuators on, simply hover over the item until the cursor changes to a pointing hand and then click the left mouse button. To switch the actuators off, repeat this action. The pump is controlled by means of the Pump Output slider and the Flow Rate display near the centre of the PCU will show a number of litres/minute depending upon the setting of this control. Three strategically positioned temperature probes give immediate readouts on the displays labelled Flow Temperature, Sump Tank Temperature and Process Tank Temperature.
Flow Control Control of the flow rate may be achieved either manually using the simulated gate valve on the PCU (“+” and “-” buttons) to adjust the flow rate or automatically using a P, PI or PID controller. In the case of manual control the pump is operated at its maximum speed, producing a constant output of approximately 1.75 litres/minute. By switching between manual and automatic control the user is able to compare his performance to that of the computer. The flow rate is measured by the flow meter and this value is used to draw the cyan trace on the graph.
Temperature Control Control of the temperature of the body of water in the process tank may be achieved using a P, PI or PID controller. The temperature is measured by a platinum resistance temperature probe (PRT) in the process tank and this value is used to draw the red trace on the graph.
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Batch Volume Control In many industrial processes it is necessary to supply a volume (batch) of liquid at a prescribed temperature to some secondary process. This can be demonstrated within PCUSIM by combining both the flow and temperature control cycles. The batch volume simulation requires that set points for both the fluid volume in litres and temperature in °C are specified by the user. The batch volume simulation assumes that the process tank is initially filled with water at the desired temperature. During the batch control cycle the water is heated and pumped simultaneously in order to supply the specified volume of water at the prescribed temperature over the required period and the system’s response is displayed. Batch volume control may be achieved using pairs of P, PI or PID controllers.
Fluid Level Control The level sensor provides an analogue feedback value that represents the level of water in the process tank. Control of the water level may be achieved using a P, PI or PID controller to control the flow of water being pumped into the process tank.
Open Loop Control Open loop control allows a user-determined function, either a step, ramp or sine wave etc. to be applied to the pump. The system’s open loop response is then drawn on the screen. A block diagram of the control loop is shown below:
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Saving PCUSIM can save the trend data recorded during a simulation session to a comma-delimited file suitable for importing into many different statistical packages such as Microsoft Excel or Mathworks MATLAB. You must complete a simulation session before you can to save the data. The data can be analysed online by opening the file and examining the trends on the screen.
Printing When printing from PCUSIM the package automatically selects the default printer and default settings. To change this click on the change button next to the printer name. You can print all of the traces at once or single traces by selecting from the available choice. You can select to print the whole diagram or just a portion of it. The default range is that displayed in the upper trend window on the control screen. Selection between black and white and colour style of printing is available. Traces will automatically have different colours on a colour printer. Black and white style varies line thickness and dashing to provide distinction on black and white printers. On colour printers, it is recommended that this option be turned off.
Trend Updating PCUSIM can display trends saved to disk from physical experiments carried out on an actual PCU. File upgrade for trends saved under old (DOS) versions of PCU software is provided via the PCU Trend Update utility. This is available from the Bytronic program group in the Start menu, along with PCUSIM. To update a saved trend, run the utility and select the File menu and from that select Convert. Follow the graphical prompts to select the data file to be updated, moving up and down the directory tree as necessary. Use the drop-down box toward the base of the screen to select between Flow, Temperature etc. files. When ready click Open, there will be a short delay and then a message box will appear. If the conversion worked this will say ‘Conversion OK’. If there were any problems, e.g. the format of the selected file was inappropriate, some form of error message will appear and the program will halt. Following a successful conversion click OK and you will be prompted to give a new file name to store the data.
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By default the data will be saved into a new file in the same directory with the same name but new file extension .psm, although you can save the file in any location or with any name or extension by changing these here. Finally click Save and all will be saved ready to load into PCUSIM.
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Courseware Suggestions Exercise 1: Proportional Control Run flow loop simulations using ‘proportional only control’ with the following pairs of SP and PG values. Record the eventual ‘steady state’ flow rate values in litres/minute in the table below, once the initial oscillations have decayed. SP (l/min) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
PG Steady State 0.5 1.0 1.5 2.0 4.0 6.0 8.0 10
SP (l/min) 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
PG Steady State 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
What conclusions about the nature of ‘proportional only control’ may be drawn from your observations? You should be able to see that for a given SP the final ‘steady state’ value increases as PG is increased. However there is no value of PG for which the steady state value is exactly equal to the SP because with proportional control there must always be some error in order for there to be a controller output. As PG is increased there is also an increase in the magnitude and duration of the initial oscillations and if PG is too high many systems will oscillate continuously and never settle to a steady state. The second set of eight simulations suggested in this exercise reveal another important point. For a proportional only controller with a given PG value although the set point is never reached, the resulting steady state value increases as the set point is increased. This shows that it is possible to use simpler and cheaper proportional only control by setting SP a suitable amount higher than the truly desired value, effectively ‘deceiving’ the controller.
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This strategy might be acceptable in a situation where the set point is not going to change at all or where external disturbances are minimal but if either of these conditions is not true then a more sophisticated controller is generally required. To prove this run a simulation with PG = 1 and SP = 2 which means that we should actually obtain a steady state value of 1 litre/minute and if this is the truly desired value, and there are no disturbances, then all will be fine. When the flow has settled down adjust the manual gate valve by clicking the buttons marked “-” and “+”. If you partially close the valve by clicking one, two or three times on the “-” button you will see that the flow rate immediately drops and then climbs back up towards the value of 1 litre/minute but does not reach it. You should also observe that the control output trace (white) is nowhere near the maximum value so there is plenty of capacity for the control output to be increased but the simple proportional only controller is not capable of doing this. If you reopen the valve by clicking one, two or three times on the “+“ button you will see that the flow rate climbs quickly back up to the value of 1 litre/minute. A few minutes spent experimenting in this manner will convince you that a proportional only controller is very deficient when external disturbances affect the process! The following diagram illustrates the ‘proportional offset’ that is often (although not always) encountered when proportional only controllers are used. (See exercise 8 on fluid level control for an example where this is not true).
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Exercise 2: Proportional and Integral Control Run a flow loop simulation using only proportional control initially and then adding in an element of integral action after about ten seconds. Repeat this process several times and each time increases the amount of integral action according to the following table. In order to turn off the integral action completely you can either remove the tick from the white box to the left of the I term or you can leave this in and set the I term to 999. (Note that the amount of integral action is inversely proportional to the integral action time as it is specified in PCUSIM and on the table below). Record the final steady state flow value (if the flow actually does settle) and your main observations as to the nature of the response. SP (l/min) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
PG 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
I 999 100 50 10 5 1 0.5 0.2 0.1
Steady State
Observations
What conclusions about the effects of integral action upon the nature of a ‘PI controller’ may be drawn from your observations? As in exercise 1, a controller with no integral action (I = 999) is characterised by a response that exhibits a constant offset between the SP and the steady state of the process variable. This is referred to as the ‘proportional offset’. When a relatively small amount of integral action is added (I = 100, 50, 10) the flow rate increases gently and produces a trace that is similar to a capacitor-charging curve. Clearly the integral action takes account of the recent history of the error whereas the proportional action only reacts to the current value of the error. PI control can be very effective if the terms are chosen appropriately and with I =1, the response is rapid with little or no oscillation. However it is possible to ‘have too much of a good thing’ as the last simulation reveals. Increasing the integral action above that which is suitable for a given system can lead to instability and the possibility of gross oscillations in the value of the process variable. With the integral action time set to 0.3 seconds the response is ‘lightly damped’ which means that whilst the control loop is not unstable, (i.e. continuous large amplitude and/or growing oscillations), the controller is not optimally ‘tuned’ for critical or near critical damping. Bytronic International Ltd.
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Optimal tuning of the PI controller in this case requires an integral action time of about 1 second if PG = 1. The lightly damped response is an interesting study and it is important because some real world systems are deliberately designed to be lightly damped. (A classic example is the suspension on an American car, on British vehicles the suspension is normally tuned for near critical damping). The following diagram illustrates several important terms that are routinely used to describe system response curves.
The definitions that follow may equally be applied to open or closed loop systems. The Overshoot is the maximum amount by which the response exceeds the final steady state value of the process variable. It is sometimes expressed as a percentage of the final steady state value. The Rise Time is the time taken for the response to increase from 10% of its final steady state value to 90% of its final steady state value.
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The Settling Time is the time taken for the response to reach its final steady state value, within some specified tolerance. The diagram above shows the settling time for a 5% tolerance. The Periodic Time or Period is the duration of one complete cycle of oscillation. It can therefore be measured as the interval between alternate crossings of the final steady state value or the interval between successive peaks or successive troughs on the response curve. The Frequency is the reciprocal of the period, i.e. the number of cycles per second that is expressed in Hertz (Hz). Sometimes the frequency is expressed in radians per second and the relationship between the two units is that radians per second equals 2π times the frequency in Hertz. The Transport Delay is the period during which there is no change in the process variable after a step change has been made to the set point. (In an open loop situation the set point is obviously meaningless, it is the manual control output which is stepped up or down in this case).
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Exercise 3: Saturation and Integral Windup Run a flow loop simulation using PI control with P = 1 and I = 1. These are close to the optimum settings and if you make changes to SP, both up and down, you will see that the response is rapid and without excessive oscillation. Once you have the flow running smoothly with a set point of 1 litre/minute, experiment with opening and closing the manual gate valve (positioned just before the flow meter on the physical PCU) by clicking the buttons marked “-” and “+”. You should see that the PI controller brings the flow smartly back to the set point without much overshoot in each case. Now restrict the flow by closing the gate valve with six rapid clicks on the “-” button. The controller output (white trace) will shoot up to 100% as it tries to compensate but even with this maximum control effort the restriction is such that the flow rate is held below the SP. The system is now seen as ‘saturated’. Allow this to continue for say twenty-five seconds and then suddenly open the valve by clicking repeatedly on the “+” button. You will see that the flow rate immediately increases to a value well above the SP and stays there for between five and ten seconds before falling back to the SP. The following diagram summarises the nature of these changes.
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Why does this effect occur? This phenomenon, which is called ‘integral windup’ (or ‘reset windup’), is due to the fact that the integral term within the PI controller generates a component of the control output that is based upon the recent history of the error. If you look closely at the graph you will see that the area between the cyan trace and SP (measured from when the valve was closed to when it was opened) is equal to the area between the cyan trace and SP (measured from when the valve was opened until the flow rate once again reached the SP). In more elaborate industrial controllers there is often a feature called ‘anti reset windup’ which can be used to eliminate this problem so that after a saturation episode the process variable will be returned to the SP as soon as the physics of the hardware allows.
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Exercise 4: Three Term or PID Control In this exercise you will learn about the effect of derivative action. Run a flow simulation with SP = 1, PG = 1 and the I and D terms turned off. After a few seconds set I = 0.15. The result will be similar to that seen in exercise 2, a proportional offset whilst there is no integral term followed by permanent oscillations once the integral term is added. Clearly too much integral action was added to the controller! To eliminate the oscillation we could simply reduce the integral action by increasing the I term to say 1 but it would be useful if we could retain the rapid response which the higher integral action confers without pushing the system into unstable oscillations. Whilst this is not always possible with a PI controller, a PID controller is usually capable of eliminating instability and providing a fast response. Run another simulation with the same initial settings and after a few seconds add the same integral term of 0.15 and a derivative term of 0.1 second. You will see that after the initial sudden rise the flow trace does oscillate about six or seven times but there is a smooth decay of the amplitude and it soon settles at the SP. A little more derivative action will improve the response, try D = 0.35 second to prove this. The following diagram summarises the phenomena that you should have observed.
Beware that despite the benefits, derivative action may give rise to detrimental effects in some situations, particularly if there is a significant amount of high frequency ‘noise’ in the measured, and hence error, value. Derivative action can dramatically amplify this noise and degrade the performance of the controller. Bytronic International Ltd.
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Exercise 5: Ziegler / Nichols Tuning How does one select appropriate proportional, integral and derivative values for any given process? Simply plucking numbers out of the air and trying them in a PID controller might be acceptable for very small systems but if you were trying to establish a control algorithm for a full sized industrial process then this would not be a very good strategy! First of all this method could well be quite time consuming which might bring about financial losses due to the plant downtime. This approach might also risk causing damage to actuators or sensors - if it was to drive them beyond their intended range of operating values for instance. A more scientific approach to finding a reasonable set of PID terms is required. Ziegler/Nichols tuning is a popular semi-empirical method of obtaining approximate PID values that can be applied successfully to many different types of processes. The method provides a reasonable starting point and the experienced control engineer might wish to adjust the calculated PID terms slightly to improve the nature of the response. There are two techniques the first called the ‘continuous cycling method’ assumes that the closed loop system can be made to oscillate permanently with a proportional only controller, as illustrated by the following graph.
The continuous cycling method requires that the gain of a proportional only controller be increased little by little until the onset of permanent
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oscillations occurs. At this point the value of the gain (kp) together with the period of the resultant oscillation (T) are noted. The recommended two and three term controllers are then given by: PI: PID:
PG = 0.45kp PG = 0.6kp
IAT = 0.83T IAT = 0.5T
DAT = 0.125T
Run some flow simulations similar to those of exercise 1 with SP=1. Increase the PG value from 1.0 to about 3.5, initially in increments of 0.5 or so. Try to estimate the lowest PG value that produces permanent oscillations in the flow rate. (You might need to adjust the PG value by 0.1 or 0.2 when you get close to this ‘ultimate proportional gain’). Record the PG value (kp) together with the period of the oscillation (T) and use them in the expressions quoted above for PI and PID algorithms. Apply these control algorithms to the flow simulation and note your observations in the table below. Algorithm PI
Observations
PID
Of course many systems cannot be made unstable (i.e. caused to oscillate) by means of a proportional only controller and for some industrial systems it might be undesirable to do this anyway because of the risk of damage referred to above. The second Ziegler/Nichols tuning technique called the ‘process reaction curve method’ requires that an open loop step response curve be produced showing a measurable ‘transport delay’ or ‘dead time’. (Transport delay is the period during which there is no change in the process variable after the controller output has been stepped up or down).
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The following graph shows a typical process reaction curve.
The process reaction curve method requires that an open loop step response of the system is obtained as shown above. From this graph the maximum slope (R) and the transport delay (L) are noted. The step input expressed as a fraction of the total range of the input (∆ ∆u) is also required. (In the open loop section of PCUSIM the step input fraction ∆u is calculated very easily since the step input to the pump is specified as a percentage. When the input is 50%, ∆u = 0.5, when the input is 70%, ∆u = 0.7 and so on). The recommended two and three term controllers are then given by: PI: PID:
PG = 0.9∆ ∆u/RL IAT = 3.3L PG = 1.2∆ ∆u/RL IAT = 2L
DAT = 0.5L
Select the Open Loop option from the PCUSIM Control menu and run an open loop simulation with a step input to the pump of 80%. Estimate the values of R and L from the resultant graph and record them with the ∆u value (0.8 in this case). Use these values in the expressions quoted above for PI and PID algorithms.
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Apply these control algorithms to the flow simulation and note your observations in the table below. Algorithm PI
Observations
PID
Do you think that the PI and PID algorithms derived from the continuous cycling method or those derived from the process reaction curve method gave the best results? In real world processes there are sometimes recommendations as to whether you should start off with one technique or the other. Sometimes this will be because of concerns about safety, risk of damage and downtime as mentioned before but often it is down to the personal choice of the senior engineer!
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Exercise 6: Temperature Control Run several temperature loop simulations using PI control with the following parameters. In order to turn off the integral action completely you can either remove the tick from the white box to the left of the I term or you can leave this in and set the I term to 999. (Note that the amount of integral action is inversely proportional to the integral action time as it is specified in PCUSIM and on the table below). Record the eventual ‘steady state’ temperatures of the water in the process tank and your main observations as to the nature of the response in the table below. You will need to allow the traces to be drawn for about three minutes in some cases. Starting Point 20°C 20°C 20°C 20°C 20°C 20°C 20°C 20°C
SP
PG
I
30°C 30°C 30°C 30°C 30°C 30°C 30°C 30°C
10 10 10 10 100 100 100 100
999 100 10 1 999 100 10 1
Steady State
Observations
What conclusions may be drawn about the nature of the temperature control loop and the responses produced? Clearly the temperature loop presents a radically different scenario to the flow loop. It has a much larger lag, i.e. it is a much ‘slower’ process and its requirement for an integral component within the controller is also quite different from the flow loop. This temperature control loop has an element of ‘built in’ integral action by virtue of the heat capacity of the water in the process tank. This is why the temperature does eventually reach the set point, even without an integral term in the controller! To gain an understanding of this, consider the following argument. What happens to the flow rate when the pump is turned off? Obviously the flow rate drops to zero straight away. What happens to the temperature of the water when the heater is switched off? Clearly its temperature does not immediately drop to zero; in fact the temperature of the water only reduces very slowly due to natural processes such as evaporation. (This is why it’s not acceptable to allow any initial overshoot - once overheated; the water in the process tank cannot be forcibly cooled).
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The heat capacity of the liquid in a real world process tank will also provide a ‘free’ integral effect but you usually need to add some integral action to the controller to achieve the optimum response. (If the tank was poorly insulated and the temperature SP was very high then you would need more integral action than if the tank was well insulated and the SP was lower).
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Exercise 7: Batch Volume Control Run a batch volume simulation with volume SP = ‘3 litres in 3 minutes’ and temperature SP = 40°C using the default PID terms for the volume and temperature controllers. This will produce a graph with six traces the most important of which are the red and dark green ones. The red trace represents the measured temperature and this should follow the light green temperature SP line reasonably well. The dark green trace represents the volume of liquid that has been displaced from the process tank rather than the flow rate. This trace should meet the blue volume SP line at the 3minute mark. (The flow rate is the gradient of the dark green line and you should see that this averages 1 litre per minute, i.e. 3 litres on the y-axis divided by 3 minutes on the x-axis). With the default PI controllers the results are acceptable both for temperature and volume control although you might be able to improve the response a little (particularly in the case of the temperature) by adjusting the parameters. Experiment with different combinations of volume and temperature set points and try different sets of PI and PID controllers. Make observations and note down any comments in the table below. Observations
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Exercise 8: Fluid Level Control Run a set of fluid level control simulations beginning with an empty process tank and using the following parameters. Ensure that the Auto Drain feature is turned off in each case. In order to turn off the integral action completely you can either remove the tick from the white box to the left of the I term or you can leave this in and set the I term to 100,000. (Note that the amount of integral action is inversely proportional to the integral action time as it is specified in PCUSIM and on the table below). You will need to allow the simulation to run for at least two minutes in the case where I = 100,000. Record the eventual ‘steady state’ level of the water in the process tank and your main observations as to the nature of the response in the table below. SP 30% 30% 30% 30% 30% 30% 30% 30% 30%
PG 5 5 5 5 5 5 5 5 5
I 100,000 20,000 10,000 4,000 2,000 1,400 1,000 700 500
Steady State
Observations
What conclusions about the nature of these fluid level experiments may be drawn from your observations? The best response was achieved by the proportional only controller (i.e. the one with I = 100,000) and this fact seems to militate against what you learned from studying flow rate control in the earlier exercises. Normally we might expect to see a ‘proportional offset’ when using a proportional only controller, so why is there no such offset seen in this particular example? Also, why is there apparently no need of an integral term within the algorithm that controls the pump being used to raise the liquid to the desired level? These questions can lead us to an insight into the fundamental nature of level control when it is implemented by pumping liquid into a closed tank. (Incidentally the word ‘closed’ in this context simply means that the level set point is never specified to be above any overflows or other outlets, it does not imply that the tank should actually have a lid on top of it!).
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This type of approach to level control is not unique to the Bytronic PCU of course! Many industrial and other processes including the ubiquitous toilet cistern regulate level by controlling the rate at which liquid flows into a closed container. You can see the effectiveness of a simple proportional level controller at any time by lifting the cover off any convenient toilet cistern. The rate at which the water under mains pressure flows into the tank is determined by the choking action of the ball cock valve. The valve is progressively closed by the action of the rising water as the floating ball lifts the lever connected to it. The valve’s ‘degree of openness’ is proportional to the difference between the desired level and the actual level. No one would argue that once the inrush of water has come to an end the cistern is full to the desired level, (defined by the geometry of the ball/lever assembly) which should obviously be below the emergency overflow. This is similar to what you see with PCUSIM, the proportional controller brings the level up to the set point smoothly and then the pump cuts off altogether. (What is the effect of increasing PG in the proportional only controller?).
The graph above shows several fluid level responses taken from PCUSIM simulations (with PG = 5 in each case), drawn on the same axes. It is clear that there is a progressive increase in what we might call an integral offset effect as the magnitude of the integral action is increased. How can we account for this phenomenon? The questions to answer then are: why is there no proportional offset, why is an integral term in the controller unnecessary and why do integral terms give rise to offsets in this kind of level control?
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The explanation is that by its very nature the process itself provides an element of integral action due to the volumetric capacity of the tank. (It is said to have a ‘free integrator’ in transfer function parlance, i.e. a 1/s term in its Laplace Transform). Consider for a moment the case of flow control, here some output to the pump is required if there is to be any fluid flow at all, if the pump is off then there can definitely be no flow. With the level control however there is always a certain level of water when the pump is off, and if the pump is running then the level will always be rising. Integral action in a PI (or PID) controller takes account of the recent history of the error by adding up the errors for a fixed number of ‘recent’ samples and contributing a component of controller output which is proportional to this sum. With the level control situation the volumetric capacity of the tank continuously ‘integrates’ the incoming flow rate that results in an increasing depth of liquid. This intrinsic characteristic is analogous to the familiar integration of velocity to obtain displacement thus:
In the level control experiment the actual water level is the integral of the flow rate into the tank. Therefore even with a proportional only flow rate controller, both proportional and integrating actions are present within the closed loop formed by the controller and the process. As a result of this intrinsic integral effect there will never be a proportional offset and an explicit integral term in the control algorithm would be entirely redundant. Any integral term that is added either produces no visible effect (if it is very small) or the aforementioned integral offset effect because it keeps the control output to the pump higher for longer than is required. There is one other point that needs to be borne in mind. This level control scenario is non-linear in that the water level may be increased by controlling the pump but, irrespective of the algorithm, the level cannot be lowered through any use of the pump. Once a particular level has been reached, even with the pump turned off completely it cannot be lowered. The only means of lowering the level is to open one of the drain valves. (If you think about it, this again is exactly true of the toilet cistern that was discussed above). Bytronic International Ltd.
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Exercise 9: Open Loop Control Run a set of open loop simulations using a sinusoidal input signal with Min = 30% and Max = 80% to drive the pump. Vary the Period between 0.5 and 20 seconds. Record your main observations as to the nature of the response in the table below. Period (s) 0.5 1 2 3 4 5 7.5 10 15 20
Observations
What conclusions may be drawn about the nature of the open loop responses produced? Firstly you should see that the output from the system, i.e. the flow measured value (cyan trace) is a sine wave which always has the same period as the input to the system, i.e. the signal driving the pump (white trace). One of the characteristics of any linear system is that the resulting (output) signal always has the same waveform as the driving (input) signal. If, for the same period, the amplitude of the input was say doubled (or halved) then the amplitude of the output would be doubled (or halved) accordingly. [As an analogy, consider an alternating voltage applied across a resistor. An alternating current will pass through the resistor that will have exactly the same frequency (and hence period) as the voltage waveform. The amplitude of this alternating current will, in general, be different from that of the voltage but they will always have the same waveform and frequency. The waveforms will also be ‘in phase’, i.e. their peaks and troughs will always coincide. If the resistor was replaced by a capacitor then the alternating current would have the same waveform and frequency but this time it would be ‘out of phase’ with the alternating voltage as well as having a different amplitude. If the capacitor was replaced by a non-linear device such as a diode bridge, then the current would no longer match the voltage in terms of its waveform or frequency. (i.e. in the case of full wave rectification).]. Bytronic International Ltd.
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You should also see that the ratio of the amplitude of the input to the amplitude of the output (which is referred to as the ‘gain’), varies between the simulations and that the peaks and troughs of the two traces never coincide exactly. The traces are ‘out of phase’ or separated by a ‘phase angle’. At lower frequencies the peaks and troughs tend towards coincidence but at higher frequencies they separate dramatically. At the higher frequencies (~ 1 Hertz) the input and output traces can be seen to be in ‘antiphase’, i.e. the peaks of the input occur at roughly the same time as the troughs of the output and vice versa. These observations lead us naturally to the concept of ‘frequency response’. The frequency response of a system is usually summarised in the form of specialised graphs of gain versus frequency and phase angle versus frequency (often plotted logarithmically) called ‘Bode gain and phase plots’.
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Exercise 10: Bode Plots Repeat the set of open loop simulations from exercise 9 but this time estimate the gain and phase angle in each case and record the results in the table below. Period (s) 0.5 1 2 3 4 5 7.5 10 15 20 100
Frequency (Hz)
Gain
Gain ÷ by max. Gain
Phase Angle (°)
2 1 0.5 0.333 0.25 0.2 0.133 0.1 0.067 0.05 0.01
You will need to minimise the period shown on the graph (using the slider at the top right) after the higher frequency simulations, in order to magnify the trace to estimate the phase angle. The gain can be calculated very easily in each case by obtaining the maximum and minimum flow values from the cyan trace, using the digitising cursor. The gain may then be calculated from the following equation: Gain = (Maximum Flow Rate - Minimum Flow Rate) / 50% Here the 50% represents the peak-to-peak value of the input, i.e. 80% 30%. (The peak-to-peak ratio is identical to the amplitude ratio for the input and output signals of course). The only problem with this is that the input signal is quoted as a percentage and the output signal is measured in litres per minute. In order to normalise the calculated gain values in this situation we can divide all of the gain values by the maximum magnitude of the gain; which will be when the period is very large. For practical purposes it will be sufficient to estimate the gain when the period is 100 seconds or more and to divide all of the gain values by this figure. This explains the presence of the second gain column above.
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The phase angle may be estimated in each case by observing how much time passes from the moment the input reaches a peak (or trough) until the output reaches the corresponding peak (or trough). If this time interval is called ∆T then the phase angle (in degrees) may be calculated from the following equation: Phase Angle = (∆ ∆T/Period) * 360° Estimates of the gain and phase angle will of necessity be fairly inaccurate at the highest frequencies due to the difficulty of acquiring accurate data from the traces. Once the table above has been completed use the data in the second, forth and fifth columns to draw Bode Gain and Bode Phase plots for the flow loop. The graph below shows the sort of results you should achieve.
The open loop section within PCUSIM gives us an opportunity to introduce the subject of ‘system frequency response’ and the Bode plot method of representing it but this concept is more usually applied to servo control systems (as found in robotics, aero-engineering, vehicle suspension etc., etc.) rather than fluid process control systems. Normally Bode plots are drawn with a logarithmic frequency scale and the frequency is plotted in radians per second rather than hertz.
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Glossary of Terms Actuator Adc Algorithm Amplitude Analogue to digital conversion Anti reset windup Antiphase Automatic control
Batch volume control Block diagram
Bode plots Closed loop Comma delineated file Continuous cycling method Control algorithm Control cycle Control loop
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Device by means of which control output effects process variable, e.g. pump, valve or heater. Analogue to digital converter. see control algorithm. For a sinusoidal waveform, half the peak-to-peak value. Operation by which analogue measurement values from real world processes are converted electronically to a digital format that can be manipulated by a microprocessor based controller. Feature available on many industrial controllers that eliminates reset windup (integral windup). Situation in which the maxima of an input signal occur simultaneously with the minima of the output signal and vice versa Regulation of a process variable by means of an algorithm implemented by a controller that is usually microprocessor based, e.g. computer or PLC. Control of supply of a specific volume of liquid at a specific temperature over a specific period of time. Visual method of describing a control loop based upon process, controller and feedback blocks together with signal paths and (a) summing junction(s). Graphs showing system response in terms of gain and phase angle plotted against frequency. Any control loop in which the error value is used by the controller algorithm to determine the control output. File format compatible with software packages such as Microsoft’s Excel and Mathworks’ MATLAB. Ziegler/Nichols tuning method that requires that a closed control loop can be made unstable by a proportional only controller. Rule or set of rules by which controller generates control output(s), based upon the error signal in a closed loop system. Phrase sometimes used to refer to execution of a real world control experiment or a PCUSIM simulation. System comprising process, sensor(s), error feedback and source of control output signal. If error feedback is used to calculate control output then it is a closed loop, alternatively it is an open loop.
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Control output Controller Critical damping
D Damping Decay Derivative, Derivative action Derivative term Error Feedback Flat Flow control Flowmeter
Free integrator
Frequency
Frequency response
Gain I In phase
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Signal generated by controller. Calculated from the error according to control algorithm in a closed loop. Device or software routine which applies a control algorithm to determine a control output from the error signal in a closed loop. Damping such that measured value reaches setpoint as quickly as possible without any overshoot. (Damping ratio = 1. Usually the optimum situation is when damping ratio is about 0.7 that gives a single overshoot). see derivative, derivative action, derivative term. Force(s) that oppose the tendency of a system or control loop to oscillate, e.g. friction, air resistance or the effect of controller. Successive reduction in amplitude of control loop oscillations due to damping force(s). Third component in a PID or three-term control algorithm that takes account of the time rate of change of error. Derivative action is based upon the time rate of change of error multiplied by a constant called the derivative action time D. Function of time defined as the difference between setpoint (SP) and measured value (MV). Technique of using error signal to determine control output signal that causes error to be minimised in a well tuned system. Description of setpoint that remains at a certain fixed value until changed by human intervention. Control of rate of flow of a fluid through an open or closed channel. Device for measuring rate of flow of fluid, the miniature turbine type used on the PCU produces a pulsed signal which is processed electronically to determine flow rate in litres/minute. A concept from Laplace transform/transfer function theory that refers to the way certain devices integrate an input with respect to time thus obviating the requirement for integral action within any associated controller. E.g. a tank integrates net inward fluid flow to produce fluid level. The rate of repetition of any periodic waveform, i.e. the number of cycles of that waveform that occur in a unit of time. Usually quoted in cycles per second, hertz (Hz) or radians per second. Overview of the way a system responds to input signals across the complete range of expected frequencies. Input signals include setpoint, noise and external perturbations. Often displayed as Bode graphs, i.e. gain and phase angle plotted against frequency. The ratio of the amplitude of the output signal to the amplitude of the input signal, i.e. output amplitude divided by input amplitude. see integral, integral action, integral term. Situation in which maxima of input and output signals occur simultaneously and minima of input and output signals occur simultaneously.
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Instability Integral, Integral action, Integral term Integral windup Ladder program Laplace transform
Level control Lightly damped
Linearity
Logic
Manual control
Measured value Mv Noise
Non linearity
Normalise
Off-line Open loop control
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Characteristic of control loop that continues to oscillate with constant or increasing amplitude. Second component in a PI, PID or three-term control algorithm that takes account of the recent history of the error. Integral action is calculated by dividing the net area under the error curve against time by the integral action time I. see reset windup Control program written in a PLC language known as ‘ladder logic’. Result of a mathematical operation that converts functions of time e.g. input and output signals, to functions of the Laplace variable that is universally assigned the letter ‘s’. This allows more convenient mathematical manipulation for advanced work on control theory. Control of level of a fluid in a particular vessel. Description of a system where the damping forces are less than they would be for critical damping. Lightly damped systems all oscillate and the lighter the damping the more cycles of oscillation which are produced. Characteristic of a system that exhibits increases in its output that is proportional to increases in its input. E.g. sinusoidal input and output amplitudes in an open loop flow cycle. Relationships between digital (i.e. on/off) inputs and the required output signals programmed into the memory of a PLC or control computer. Situation in which a human operator determines the control output(s) based upon the required value and current measured value of the process variable Function of time returned by the sensor and signal conditioning which represents the value of the process variable. See measured value Normally random non-periodic signal superimposed upon one or more of the signals in a control loop, having an amplitude which is small in comparison to the magnitude of the signals of interest. Characteristic of a system that does not exhibit increases in its output that is proportional to increases in its input. E.g. flow of current through a diode as voltage is increased from -ve. To +ve. Process of dividing all elements in a set of data by a chosen value, (sometimes the value of one particular element, perhaps the largest) in order to render the whole set more convenient for assimilation or for comparison with other data sets. Beyond the particular time period pertaining to real-time control of a system or process. Any control loop in which the error value is not used by the controller to determine the control output.
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Open loop response
Optimal tuning Oscillation, Oscillatory Overshoot
Pb Pcu Pcu trend update utility Period, Periodic time Pg Phase angle PID control
Plc Process control Process control unit Process reaction curve method Process variable Programmable logic controller Proportional, Proportional term Proportional band Proportional gain
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A description of the way a system responds to certain input signals such as sine waves, step changes or square waves etc. These input signals may originate from manual/human intervention or from an open loop control output. Obtaining an open loop response to a series of well-chosen sine waves may be used to determine the frequency response in the form of Bode graphs. Tuning of the PID controller to produce the best possible results for a given control system. Periodic pattern, almost always sinusoidal, observed in the response of a system. Maximum amount by which measured value exceeds final steady state value of process variable. Often expressed as percentage of final steady state value. see proportional band. see Process Control Unit. Software utility for converting old DOS based PCU trend files to PCUSIM compatible format. Duration of one complete cycle of oscillation i.e. interval between alternate crossings of the final steady state value. see proportional gain. In the context of sinusoidal input and output signals, the amount by which the input leads the output expressed in degrees or radians. Automatic control based upon an algorithm that includes proportional, integral and derivative contributions to the final control output. see Programmable Logic Controller Phrase often (though not always) assigned to control of fluid flow rate, temperature, level, batch volume, acidity, pressure etc. Bytronic hardware system for illustrating and teaching PID control upon which all PCUSIM simulations are based. Ziegler/Nichols tuning method that requires that data from an open loop response to a step change be acquired. The feature of a process loop which is actually being controlled, e.g. temperature, flow rate, level etc. Microprocessor based device used widely in industry to control digital and analogue processes. Essentially a specialised ‘hardened’ computer with its own (often idiosyncratic) programming language. First component in a PI, PID or three-term control algorithm that generates a component of the control output which is directly proportional to the magnitude of the error. The error band where the control output is between 0% and 100%. Proportional band equals 100 divided by the proportional gain. A constant multiplied by the error value to give a control output.
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Proportional offset
Ramp Rate of flow Real-time
Reset windup
Response, Response curve Rise time Sample time Sampling frequency Saturation Sawtooth Scada Servo control Setpoint Setpoint options Settling time Sp Stability Steady state
Step, Step change Summing junction
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Steady state discrepancy between setpoint and measured value that is characteristic of all systems which use proportional only control and which do not have an intrinsic ‘free integrator’. Description of setpoint which changes up or down gradually at a fixed rate. Velocity at which fluid moves along an open or closed channel, usually expressed in litres per minute. Description applied to computerised operation that occurs in step with some real world process. E.g. display of process reaction curves on remote SCADA computer. Used to make a distinction from off-line presentation. Accumulation of controller integral action ‘debt’ after a saturation episode. This offsets measured value from setpoint for longer than the physics of the process would strictly require. Shape of the trace produced by plotting process variable measured value against time. Time taken for the response to increase from 10% of its final steady state value to 90% of its final steady state value. Period between successive samples of measured value digitised by ADC. Rate at which samples of measured value are digitised by ADC. Description for the situation when, even with 100% control output, the measured value cannot be brought to the setpoint. Description of setpoint which changes up and/or down periodically, gradually and at a fixed rate. see Supervisory Control and Data Acquisition Control of motor and solenoid actuated apparatus etc. Used to make a distinction from fluid process control. Desired value of the process variable. PCUSIM facility to change the type of setpoints available accessed via preferences menu. Time taken for the process variable measured value to reach its final steady state value within some specified tolerance. see setpoint. Characteristic of control loop in which all oscillations ultimately decay completely after a step change. The condition of a control loop once all transients have decayed completely, after a step change. The steady state might be a fixed measured value or an oscillation with a fixed amplitude. Description of setpoint which changes up and/or down instantaneously. Point in a control loop block diagram symbolised by a crossed circle where the measured value feedback is subtracted from the setpoint to provide an error signal input for the controller.
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Supervisory Control and Data Acquisition
System frequency response Temperature control Three term control Time constant Trace Transfer function
Transport delay
Trend
Tuning Waveform Wavelength Ziegler/Nichols tuning
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Use of (possibly remote) computer(s) to supervise one or more PLCs that are controlling a local process. The computer can acquire data from the PLC and display it as a real-time graph or store it for off-line processing. It can also send new setpoint and/or PID values to the PLC. see frequency response. Control of temperature of a fixed body of fluid in a vessel. Automatic control by means of a PID control algorithm. Parameter that characterises the speed of response of a control loop or an element within a control loop. Graph of process variable measured value, plotted against time. Mathematical model (or description) of control loop block (e.g. process or controller). Specifically the ratio of Laplace transform of output signal to Laplace transform of test input signal. Period during which there is no change in the process variable after a step change has been made to the set point (in closed loop) or the open loop control output. Graph of process variable measured value plotted against time in PCUSIM. This term is used to refer to complete graph once simulation has stopped, or when retrieving from hard disk. Selection of PID terms to be used within control algorithm. The shape of one cycle of a periodic signal. The length of one cycle of a periodic signal. A pair of techniques for estimating appropriate PID values for a given control loop. See continuous cycling method and process reaction curve method.
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