EEIB413 Chapter 1_Student

Chapter 1 Introduction to Process Control

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Introduction to Process Control • The term control means methods to force parameters in the environment to have specific values. • In general, all the elements necessary to accomplish the control objective are described by the term control system. • Control system exist in nature. • This can be as simple as – Making the temperature in a room stay at 21˚C. – Move large equipment with precision. – Elevator system.

• Motor provides the power, control systems regulate the position and speed. 2

Self Regulated System • Liquid is flowing into a tank at some rate Qin. • The liquid in the tank has some height or level h. • so the higher the level, the faster the liquid flows out. • If the output flow rate is not exactly equal to the input flow rate, the level will either rise or drop. • A self regulating system does not provide regulation, if the input flow rate changed, then the level would change also, so it is not regulated to a reference value. 3

A Human Aided Control System • • • •

• • •

Artificial regulation of the level by a human, so that it maintains the value h. This can be achieved by a sensor (sight tube, S) to measure the level. The actual liquid level is called the controlled variable. A valve has been added so that the output flow rate can be changed by the human. The output flow rate is called the manipulated variable or controlling variable. The level of height in the sight tube is compared to the set-point value. If the measured value is larger, the human opens the valve wider to increase the output flow rate If the level lowers toward the setpoint. If the measured value is smaller than the set-point, the human closes the valve a little to decrease the output flow rate and allow the level to rise toward the 4 set-point.

An Automatic Control System • Machines, electronics, or computers replace the operation of the human. • Sensor is used to measure the value of the level and convert it into a proportional signal, s. • This signal is used as input to the controller which performs the function of evaluating the measurement and providing an output signal, u. • This control signal used to change the valve setting via an actuator connected to the valve by a mechanical linkage. • When automatic control is applied to systems like the example to regulate the value of some variable to a specific reference, it is called process control. 5

Servo-Mechanism • The objective is to force some parameter to vary in a specific manner • In stead of regulating a variable to a specific reference, the servomechanism forces the controlled variable value to follow variation of the reference value • Servo mechanisms force the robot arm to follow a path form point A to point B, this done by controlling the speed of motors driving the arm and the angles of the arm parts 6

Discrete State Control Systems • This is a type of control system concerned with controlling a sequence of events rather than regulation or variation of individual variables. • Example: the manufacture of paint. • This sequence is described in terms of events that are timed to be started and stopped on a specific schedule. • These discrete state control systems are often implemented using specialized computer based equipment called programmable logic controllers (PLCs). 7

Tank A (Red 30%)

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Tank B (White 70%)

Objective: To produce pink color paint.

Stir 1

Valve A

Valve B

Mixing Tank (Pink 100%)

2

4

3

Heater

Step1 – Turn on Valve A and turn it off after obtained 30% of the red paint. Step2 – Turn on Valve B and turn it off after obtained 70% of the red paint. Step3 – Turn on Stir and Heater for 10 minutes. Step4 – Turn on Valve C

Valve C Tank A Tank B Tank C Tank D

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Process Control Block Diagram • To provide a practical, working description of process control. • Model may be constructed using blocks to represent each distinctive element. • The characteristics of control operation then may be developed from a consideration of the properties and interfacing of these elements. 9

Process (Plant) • A process (plant) can consist of a complex assembly of phenomena that relate to some manufacturing sequence. • Many variables may be involved in such a process and it may be desirable to control all these variables at the same time. • There are single variable processes, in which only one variable is to be controlled, as well as multivariable process, in which many variables, perhaps interrelated, may require regulation.

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Measurement • To effectively control a variable in a process, we must have information about the variable itself. Such information is found by measuring the variable. • A measurement refers to the conversion of the variable into some corresponding analog of the variable. Ex: pressure, voltage, current. • A sensor or transducer is a device that performs the initial measurement and energy conversion of a variable into analogous electrical or pneumatic information. Ex: pressure, distance, motion. • Transducer: converts voltage to current. • The result of the measurement is a representation of the variable value in some form required by the other elements in the process control operation. 11

Error Detector • The difference between the actual level, h, and the set-point level, H, and deduced an error. • Error determination must be made before any control action is taken by the controller. 12

Controller

• It is also known as compensator or filter. • Depending upon the difference of the measurement and the controlled variable, the controller evaluates and determines the effort required to drive the process toward the setpoint value

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Control Element • It provides those required changes in the controlled variable to bring it to the setpoint. • This element accepts an input from the controller, which is then transformed into some appropriate action performed on the process. • Ex: the control valve that adjusts the output flow rate of liquid from the tank.

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Actuator

• Often an intermediate operation is required between the controller and the final control element. • It uses the controller signal to actuate the final control element. • The actuator translates the small energy signal of the controller into a larger energy action on the process. 15

Ex: Physical diagram of a process control loop

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Block diagram of the process control loop

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Problem 1.3 (Pg. 45) • Construct a block diagram of a refrigerator control system. Define each block in terms of the refrigerator components.

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Problem 1.3 (Pg. 45) Solution

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Control System Evaluation • A process control system is used to regulate the value of some process variable • The variable used to measure the performance of the control system is the errors, e(t), which is the difference between the reference value, r(t), and the controlled (actual) variable, c(t). Mathematically, the relationship can be expressed as:

e(t ) = r (t ) − c(t ) • A real control system is evaluated based on the following requirements. (1) Stability. (2) Transient response. (3) Steady state performance. 20

• A practical statement of control system objective is represented by three requirement: – The system should be stable. – The system should provide the best possible steady-state regulation. – The system should provide the best possible transient regulation.

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Stability • The necessary correct action should taken on the process to eliminate the error. • The process can become unstable if the action is done wrongly. • The control system must be designed and adjusted so that the system is stable. 22

Steady-State Regulation (SSE) • SSE should be minimum in any process system. • But, there some deviation error value occur about the setpoint. • This range of deviation is expected and acceptable. • If the error drift out of the range, the control system will correct it. • Ex: 150°C ±2°C, allowable temp range is 148°C to 152°C 23

Transient Response • Transient error occur when sudden change of setpoint (Ex: temperature change from 20°C to 22°C) or some other process variable value (fluctuation of the surrounding temperature). • Transient regulation specifies how the control system reacts to bring the temperature to the new setpoint value for the purpose to minimize the bad effect on the process. 24

Damped Response • Setpoint is changed to a new value. • Controlled variable increases to the new setpoint in duration of tD. • Some overshoot, emax occur during the rising period of the controlled variable. • The duration tD is often define as the time from the start of the disturbance until the controlled variable to go from 10% to 90% of the changed. • Different tuning gives different values of emax and tD, either larger duration with smaller peak error or vice verse. 25

Cyclic/Underdamped Response • When setpoint changed, the controlled variable oscillates about the setpoint. • emax and tD (also called settling time) be measured as well. • The duration is measured from the time when the allowable error is first exceeded to the time when it falls within the allowable error and stays. • emax and tD can be varied by tuning the minimum area or quarter 26 amplitude.

• For minimum area, tuning is adjusted until the net area under the error-time is minimum. • For quarter amplitude, adjust the amplitude of each peak of the cyclic response be a quarter of the preceding peak, a2 = a1/4, a3 = a2/4 and so on.

A = ∫ e(t ) dt = minimum 27

• Transient Response – Elevator system: a slow transient response makes passengers impatient, excessively rapid response makes them uncomfortable. – Too fast a transient response could cause permanent physical damage.

• Steady-State Response – This response resembles the input and remains after the transient have decayed to zero. – Elevator system: stopped near the desired floor for the passengers to exit. 28

Problem 1.4 (Pg. 46) • A process control loop has a setpoint of 175˚C and an allowable deviation of ±5˚C. A transient cause the response shown. Specify the maximum error and settling time.

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Solution Problem 1.4 (Pg. 46)

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Problem 1.5 (Pg. 46) • Two different tunings of a process-control loop result in the transient response shown. Estimate which would be preferred to satisfy the minimum area criteria.

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Problem 1.5 (Pg. 46) Solution

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Problem 1.6 (Pg. 46) • The second cyclic transient error peak of a response test measure 4.4 %. For the quarter-amplitude criteria, what error should be the third peak value?

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Problem 1.6 (Pg. 46) Solution

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Problem 1.7 (Pg. 46) • Does the response satisfy the quarter-amplitude criterion?

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Solution Problem 1.7 (Pg. 46)

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Problem 1.8 (Pg. 46) • An analog sensor converts flow linearly so that flow from 0 to 300 m3/h becomes a current from 0 to 50mA. Calculate the current for a flow of 225 m3/h.

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Problem 1.8 (Pg. 46) Solution

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Analog and Digital Processing • Analog processing – Data are represented by the magnitude of voltages and currents.

• Digital processing – For modern control system. – Data are represented as binary bits.

• Data represented the physical variable in a process, ex: thermal sensor produces the output voltage which magnitude is proportional to the measured temperature in the control loop. 39

Analog and Digital Data • Output analog data b represent by a smooth and continuous curve which varies according to the measured variable c. • The output is nonlinear because the same δc does not result in the same δb. 40

• Digital data only have two values, 1’s and 0’s. • When analog data converted to digitally, some range of analog numbers is encoded by a fixed number of binary digitals. • This will cause loss information because a fixed number of binary digitals has a limitation resolution. Ex: 4.25 V and 4.75 V both are represented by 01002. • Also lost of smooth and continuous data representation between the output values and the measured variable values. Only in discrete representation.

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Data Conversions

• Analog-to-Digital converters (ADCs) – Convert analog voltages into a digital representation. – Interface between the o/p of sensor and the i/p of digital computer.

• Digital-to-Analog converters (DACs) – Convert digital voltages into a analog representation. – Interface between the o/p of digital computer and the i/p of the final control element (Ex: relay, valve, etc)

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Problem 1.10 (Pg. 46) • Suppose each bit change in a 4-bit ADC represents a level of 0.15 m. – a) What would the 4 bits be for a level of 1.7 m? – b) Suppose the 4 bits were 10002. What is the range of possible levels?

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Solution Problem 1.10 (Pg. 46)

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NO/OFF Control • Most elementary control. • Controller output only produces two digital representation binary signals: 1 and 0. • The final control element only has two stages: ON and OFF.

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Ve = K (Vref − V )

• • • • • • •

Objective: to maintain the temp. in a system at some reference value, Tref. A sensor converts temp. values into a resistance values in an analog way. R varies smoothly and continuously with T. Signal conditioning converts the variable R into an analog voltage V. The differential amplifier multiplies the difference between V and Vref by a gain K to produce an error voltage Ve. Relays will either be open or closed so that the heater or cooler will either be on or off. 46 This system exhibits a deadband, where the behavior of the system is different at the same value of temperature.

Programmable Logic Controllers (PLC)

• Most of the manufacturing operations are ON/OFF in nature (Ex: conveyor, heater, valve, motor etc). • These discrete controls can be done by hard wiring relay refer as relay logic controller. • It replaced by PLC. • Thermal-limit switches are used instead of sensor to indicate when the temperature has risen above or fallen below the limit temperatures.

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Problem 1.11 (Pg. 47) • For the process control shown, suppose that the relays close at 1.5V and open at 1.1 V. This means that as the voltage on the relay reaches ±1.5V, it closes, and does not open again until the voltage drops to 1.1V (i.e. there is a deadband). The amplifier has a gain of 10, the reference is 3V, and the sensor outputs is 150mV/°C. Calculate the temperature at which the heater turns on and off and at which the cooler turns on and off.

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Solution Problem 1.11 (Pg. 47)

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Analog Data Representation • In control process, if the process variables involve a range of variation, the controller should able to produce the control signals which proportion to the range of the process variable changing. • The common used analog representation is: – Electric system: electric current in wires, 4 to 20 mA. – Pneumatic system: gas pressure in pipes, 3 to 15 psi.

• These signals are used primarily to transmit variable information over some distance, ex: between control room and the plant.

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• Current is used to transmit measurement data about the controlled variable to the control room. • Gas pressure in pipes is used to transmit a feedback signal to a valve to change flow as the controlling variable.

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Transfer Function

• Describes the relationship between the input and output for the block. • Described into two parts: static and dynamic. • Static TF: describes the input/output relationship when the input is not changing in time (constant). It presented in the form of equation, tables or graph. • Dynamic TF: describes the input/output relationship when the input is changing in time (time response). It presented by a differential equation in time 52

Linearity • In signal conditioning, for each value of the input variable, there exists one unique value of the output variable. • The relationship between the input and output can be represented by linear equation (straightline):

cm = mc + c0 • • • •

c = variable to be measured m = slop of straight line c0 = offset of intercept of straight line cm = output of measurement 53

Example 1.7 (Pg. 25) • Suppose the temperature range 20 °C to 120 °C is linearly converted to the standard current range of 4mA to 20 mA. – a) What current will result from 66 °C? – b) What temperature does 6.5 mA represent?

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Example 1.7 (Pg. 25) Solution Using linear equation to solve :

a) When T = 66°C

I m = mT + I o

I m = (0.16mA / °C )(66°C ) + 0.8mA = 11.36mA

4mA = m(20°C ) + I o 20mA = m(120°C ) + I o Solve for m : 16mA = (100°C )m m = 0.16mA / °C Then, solve for I o :

b) When I = 6.5mA I − 0.8mA T= m 0.16mA / °C (6.5 − 0.8)mA = 0.16mA / °C = 35.6°C

4mA = 0.16mA / °C (20°C ) + I o 4mA = 3.2mA + I o I o = 0.8mA ∴ I m = (0.16mA / °C )T + 0.8mA 55

Example 1.14 (Pg. 32) • A sensor resistance changes linearly form 100 Ω to 180 Ω as temperature changes from 20 ˚C to 120 ˚C. Find a linear equation relating resistance and temperature.

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Example 1.14 (Pg. 32) Solution Using Linear Equation R = mT + R 0 Form the equation

:

as :

100 = m ( 20 ) + R 0 180 = m (120 ) + R 0 Temp. Range: Solve for m :

20˚C ~ 120 ˚C Sensor: R = 0.8T+84

Resistance Range: 100Ω ~ 180Ω

180 − 100 = 0 .8 Ω / ° C m = 120 − 20 Solve for R 0 : 100 = 0 . 8 ( 20 ) + R 0 R 0 = 100 − 16 = 84 Ω The linear equation R = 0 . 8T + 84

relating resistance

and temperatu re is : 57

Problem 1.17 (Pg. 47) • Suppose a liquid level ranging from 5.5 m to 8.6 m is linearly converted to pneumatic pressure ranging from 3 psi to 15 psi. – a) What pressure will result from a level of 7.2 m? – b) What level does a pressure of 4.7 psi represent?

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Problem 1.17 (Pg. 47) Solution

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Problem 1.24 (pg. 48) • A level sensor inputs a range from 4.50 ft to 10.6 ft and outputs a pressure range from 3 psi to 15 psi. – a) Find an equation between level and pressure. – b) What is the pressure for the level of 9.2 ft?

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Problem 1.24 (pg. 48) Solution

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Sensor Time Response

• Sensor produces output b(t) as a function of input c(t). • If the input is changed from ci to cf, the output should be produced according to the range of input variation instantaneously (ideally). • Practically, all sensor exhibit some lag between the output and input and some characteristic variation in time before settling on the final value. 62

First-Order Response

• The output change in time following a step input. • The time response is determined by the solution of a first-order differential equation as shown: b(t ) = bi + (b f − bi )[1 − e

− t /τ

] 63

• Bi = initial sensor output from static transfer function and initial input • Bf = final sensor output from static transfer function and final input • τ = sensor time constant • The sensor output start to change at t = 0 and reach constant after 5 time constants. • The sensor output is exponentially increase from bi to bf. • This equation is used to predict a finite starting slope. 64

• The sensor output function is expressed in term of time constant:

b(t ) − bi = (b f − bi )[1 − e − t /τ ] • The sensor output for the first time constant can be found by substitute t = τ • The output function becomes:

b(t ) − bi = (b f − bi )[1 − e −τ /τ ] b(t ) − bi = 0.6321(b f − bi ) • One time constant represents the time at which the output value has changed by approximately 63% of the total change. • The output approximately reached its final value after five time constants. 65

Example 1.15 (Pg. 38) • A sensor measures temperature linearly with a static transfer function of 33 mV/˚C and has a 1.5 s time constant. – a) Find the output 0.75 after the input changes from 20 ˚C to 41 ˚C. – b) Find the error in temperature this represents.

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Example 1.15 (Pg. 38) Solution bi = 33mV ( 20 ) = 660 mV b f = 33mV ( 41) = 1353 mV

τ = 1 .5 s 5τ = 5(1.5) = 7.5 s

Temp. Range: Output Voltage (V) 20˚C ~ 41˚C Sensor: 33mv/˚C,т=0.75s

When t = 0.75s, the output of the sensor is : b (t ) = bi + (b f − bi )[1 − e −t / τ ]

41˚C b (0.75) = 660 + (1353 − 660 )[1 − e − 0.75 / 1.5 ] = 660 + 693 (1 − 0.6065 ) 20˚C = 660 + 272 .6955 = 932 .69 mV The corespondi ng temperatu re for this value of output is : 932 .69 °C T= = 28 .26 °C Output at 0.75s 33mV / °C 0.75s The actual temperatu re is 41 °C, so the error is : 41 °C - 28.26 °C = 12.74 °C The output of the sensor wil l achieved 1353mv after 5τ which is represent 41 °C.

5т

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Problem 1.27 (Pg. 48) • A pressure sensor measures 44 psi just before a sudden change to 70 psi. The sensor measures 52 psi at a time 4.5 s after the change. What is the sensor time constant?

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Problem 1.27 (Pg. 48) Solution

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Problem 1.28 (Pg. 48) • A photocell with a 35-ms time constant is used to measure light flashes. How long after a sudden dark-to-light flash before the cell output is 80% of the final value?

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Problem 1.28 (Pg. 48) Solution

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Problem 1.29 (Pg. 48) • An alarm light goes ON when a pressure sensor voltage rises above 4.00 V. The pressure sensor outputs 20 mV/kPa and has a time constant of 4.9 s. How long after the pressure rises suddenly from 100 kPa to 400 kPa does the light go ON?

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Problem 1.29 (Pg. 48) Solution

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Problem 1.30 (Pg. 48) • A pressure sensor has resistance that change with pressure according to R = (0.15 kΩ/psi)p + 2.5 kΩ. This resistance is then converted to a voltage with the transfer function

10 R V= volts R + 10k • The sensor time constant is 350 ms. At t = 0, the pressure changes suddenly from 40 psi to 150 psi. – a) What is the voltage output at 0.5 s? – b) What is the indicated pressure at this time? – c) At what time does the output reach 5.0 V? 74

Problem 1.30 (Pg. 48) Solution

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Problem 1.30 (Pg. 48) Solution

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Problem 1.31 (Pg. 48) • At t = 0, a temperature sensor was suddenly changed from 25 ˚C to 100 ˚C . The sensor outputs voltage given by the expression V = (0.06V/˚C)[T – 20 ˚C]. The following table gives the voltages measured and the times. Determine the average time constant of the sensor. t(second) V(volts)

0

0.1

0.2

0.3

0.4

0.5

0.3

1.8

2.8

3.4

3.9

4.2

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Solution Problem 1.31 (Pg. 48)

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S. Problem 1.5 (Pg. 50) •

Figure bellow shows a simple level-control system in which a closed relay opens the valve and an open relay closes the valve. Input flow is not controlled. The relay closes at 6.0 V and opens again at 4.8 V. The level sensor has a transfer function of Vh = 0.8h + 0.4 V. – – –

a) Find the value of amplifier gain, K, required to open the valve when the level reaches 1.5 m. b) At what level does the valve close? c) Suppose Q1 = 5 m3/min, Q2 = 2 m3/min and Qout = 9 m3/min (when open). What is the period of the level oscillation?

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S. Problem 1.5 (Pg. 50) Solution

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S. Problem 1.6 (Pg. 51) • A pressure-measurement system uses a sensor that converts pressure into voltage according to the transfer function, Vp = 0.5(p)1/2. This voltge is then converted into a current. As the pressure varies from 0 psi to 100 psi, the current varies from 4 mA to 20 mA. – a) Find the transfer function equation for the conversion of voltage to current. – b) What pressure change, ∆p, will cause the current to change by 1 mA from 19 mA to 20 mA? – c) What pressure change, ∆p, will cause the current to change by 1 mA from 4 mA to 5 mA? – d) Why is the pressure change not the same as in b) and c) even though the current changed by 1 mA in both cases?

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S. Problem 1.6 (Pg. 51) Solution

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S. Problem 1.7 (Pg. 51) •

Figure bellow shows a system for measuring the pressure of exploding gases inside a steel chamber. A computer is used to measure the pressure. The pressure sensor has a transfer function of Vp = 0.05(p + 500)1/2 and a first-order time constant of τ = 2.0 s. When an explosion occurs, the pressure rises virtually instantaneously from 0 to some maximum, pmax. At t = 0, the explosion occurs, and the computer must take a reading at t = 1 s, and determine the pressure pmax. This is before the sensor signal has stabilized. – – – –

a) Explain how pmax can be determine from a measurement taken at t = 1.0 s. b) Suppose the sensor signal at t = 1.0 s is 1.45 V. What is the value of pmax. c) Suppose pmax = 2500 psi; what value will the sensor voltage have at 1.0 s? d) What equation will the computer be programmed to use in order to find pmax from the sensor voltage taken at 1.0 s.

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S. Problem 1.7 (Pg. 51) Solution

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