Lab Manual

Faculty of Engineering Department of Chemical and Biochemical Engineering

Laboratory Note CBE 3310

Feedback control of liquid level in a surge tank

Instructor: Dr. Sohrab Rohani

Winter 2011

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1. Objectives: •

To become familiar with the hardware and software used in a control system.

•

To determine the process and load transfer functions.

•

To control the level of the liquid in the tank using a PC.

2. Introduction In this experiment, the process and load transfer functions will be determined by an open loop step test. Also the liquid level in the tank will be controlled using a PC.

2.1. Process Identification Figure 1 shows the experimental setup and Figure 2 a block diagram of the closed loop control system. By introducing a step change in the liquid flow rate into the tank and monitoring the response in the liquid level in the tank, a combined load (or disturbance) transfer function and the measuring element transfer function will be obtained. Assuming negligible dynamics for the measuring element, the load transfer function dynamics can be determined. The gain of the measuring element can be obtained from the calibration curve. H ( s) Gmeasuring element ( s ) = m = K m H ( s) where Hm and H are the measured and actual liquid level in the tank, respectively. A second step change in the actuating pressure to the control valve 2 results in combined transfer function of the valve, measuring element and the process. The valve has negligible dynamics because its time constant is much smaller than the process time constant. The gain of the valve can be calculated by: Gvalve ( s ) =

X ( s) = Kv ∆Pc ( s )

(1)

where: ∆X = Change in the valve stem position ∆Pc = Change in actuating pressure to the control valve 2 In this way the process transfer function is obtained from the above tests, because the observed transfer function is the product of the valve, process and the measuring element:

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Gobserved ( s ) =

H m ( s) = Gvalve ( s )* G process ( s )* Gmeasuring element ( s ) ∆Pc ( s ) =

X ( s) H ( s) H m ( s) * * ∆Pc ( s ) X ( s ) H ( s )

Due to the non-linear dependency of the outlet flow rate from the tank on the liquid level, it is important to carry out all experiments around a fixed steady-state liquid level.

Flow Transmitter

Cold Water F Control Valve 1

Manual Valve 1

Tank Control Station

Level Transmitter

To Drain

L Control Valve 2

Manual Valve 2

Figure 1. Piping and instrumentation diagram (P&ID) of the surge tank

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Figure 2. Process Block Diagram

2.2. Feedback Control The feedback controller used for digital control is a PID controller given by: Pc(t) = Pc + Kc e(t) + {Kc /τI} ∫e(t)dt + { Kc τD }de/dt

(2)

where

P(t) = Controller Output e(t) = Error (Set point – Process Variable) = hsp – h(t) Kc = the Controller Gain Pc = Controller Bias that is the controller output when e(t) = 0 τI = Integral Time (min/repeat) τD = Derivative time (min) In this part of the experiment the computer will be used to control the level of the liquid in the tank. The differential pressure transmitter will output a 4-20 mA signal proportional to the hydrostatic pressure acting on it. Electrical signal is sent to an Analog to Digital (A/D) converter. The converter samples the analog signal at a specified rate producing a digital signal that the computer can process. The control program then compares this signal to the set-point value and calculates the difference (error). This error term is manipulated through the PID algorithm and a command signal is calculated. This output signal is sent through the D/A converter and is converted to an analog signal. This signal is in the form of a voltage, which will be between 0-10 VDC. Between the sampling/control interval, this voltage is held at a constant value using a zero-order-hold device (ZOH). The output voltage from the ZOH device is then passed through a signal conditioner, which converts it to a current signal within the range of 4-20 mA. The current signal passes through an I/P transducer, which converts the 4-20 ma signal to an air pressure signal between 3-15 psi. The air pressure will change the position of the control valve.

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The PID equation on Labtech is:

O(t) = P.e(t) + I.∫e(t)dt + D.de/dt

(3)

where: O(t) = Output

P = Proportional Constant I = Integral Constant = ∆t Kc /τi D = Derivative Constant = KcτD/∆t e(t) = Error Signal = hsp – h(t) τI = Integral Time (sec) τD = Derivative time (sec) ∆t = sampling/control interval (sec) The discrete version of a digital PID, in general, is:

Vn = Vo + Kc[en + ∆t/τi∑ek + (τD/∆t)(en-en-1)] where:

(4)

Vn = Computer output at nth sampling interval (Volts) En = Error at nth sampling interval (Volts) V0 = Computer bias when en = 0 (Volts) ∆t = Sampling interval (sec)

Equation (4) is known as the ‘position’ form of the discrete version of the PID action. The problem with this equation is that one must know V0, the steady state value of the computer output signal. For a non-linear process this means that V0 must be changed for each new set-point. This is solved by using the ‘velocity’ form of the discrete version of the PID action. This form is obtained by writing equation (4) for the (n-1)st sampling interval and subtracting it from equation (4).

∆Vn = Kc[en – en-1 + (∆t/τI)en + (τD/∆t)(en – 2en-1 + en-2)]

(5)

This is the ‘velocity’ form of the discrete PID, where ∆Vn is the change in the computer output signal at the nth sampling interval relative to its value at the (n-1)st interval. Therefore:

Vn = ∆Vn + Vn-1

(6)

3. Experimental Procedure 3.1. Process Identification • Open the air and water supply valves. Make sure the manual valve before and after both control valves are open and their bypass valves are closed. 5

• Turn on the computer and start Labtech by double clicking on the icon on the screen. • Click File>Open, Go to the directory called 410_07. Open the file called “LEVEOPEN.ltc”. (see Figure 3) • Double click on the file icon and enter a path and a filename where your data will be stored. Labtech c:\ 410_07\run1. Your filename should be no more than eight characters long. • Run the program by clicking on the “RUN” button. • Set the water inlet at 0.83V which corresponds to 4.0 psig and outlet valves at 6.00V which corresponds to 10 psig. • Allow the water level in the tank to reach steady state. Record the water level and the pressure signal to the Control Valve. • Now increase the water inlet valve signal from 0.83V to 1.75V (which corresponds to 5.0 psig). • Allow the water level to reach a new steady state value. Record this value and the pressure signal to the Control Valve.

Figure 3. Labtech interface for open loop experiment

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Figure 4. Labtech interface for closed loop experiment

3.2. Feedback Control a) In Labtech Click File>Open, go to the directory called 410_07. Open the file called “CLOSEDSA.LTC” (See Figure 4). b) Double click on the file icon and enter a path and a filename where your data will be stored. Eg. c:\ 410_07\run1. Your filename should be no more than eight characters long. c) Double click on the PID Control Icon to set the adjustable parameters P, I, and D for the closed-loop experiment to control level at 4 V (54.3 cm ≈). Note that in Labtech: P=Kc , I=Kc/τI , and D=KcτD. d) Set the water outlet valve at 6.0V which sends 10.0 psig to the control valves. e) Run the program by clicking on the “RUN” button. f) Allow the water level in the tank to reach steady state. g) Find the responses of the designed controller to a step change in set point (4 V → 5 V). Record the time of step change and allow the system to go to steady state. h) Then find the responses of the designed controller to an impulse change (disturbance) by adding 2 liters of water as quickly as possible. Record the time of adding water and allow the system to reach a steady state i) Increase only Kc by 50%, recalculate the adjustable parameters, and then repeat steps c-h.

3.3. Process Identification Use a first order lag transfer function for the process. The valve and the measuring element should be approximated by pure gains.

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Attach the process open loop response to a step change in the inlet flow rate and in the valve actuating signal to your report. What are the values of Kp, τp, Kv, Km?

3.4. Feedback Control Attach the process closed loop response for step change and impulse change. Explain the effect of increasing Kc on the liquid level responses.

Report The report should be formal including abstract, table of contents, introduction, apparatus, theory of controllers, experimental, results, discussion, conclusions and references.

Final report must be submitted to TA within 2 weeks from the date of experiment. Late submission will be penalised.

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