process reaction curve

JWBK093-WOR July 4, 2006 13:55 Char Count= 0

Workshop 5 Controller tuning for capacity anddead time processes

A little experience often upsets a lot of theory.

Samuel Parks Cadman

Introduction

Prior to attempting this workshop, you should review Chapter 5 in the book.

This workshop will illustrate that HYSYS may be used to determine the appropriateparameters for a PI controller that is controlling a capacitive process with significantdead time. You will learn that controller tuning is determined by the desired load or set-point response as well as the type of process and the values of the process parameters,which include process gain, time constant, and dead time. A review of the three tuningtechniques that are used in this workshop is provided below.

Process reaction curve tuning technique

In the process reaction curve method, a process reaction curve is generated in responseto a disturbance. This process curve is then used to calculate the controller gain, integraltime and derivative time. The method is performed in open loop so that no control actionoccurs and the process response can be isolated.

To generate a process reaction curve, the process is allowed to reach steady stateor as close to steady state as possible. Then, in open loop, so that there is no controlaction, a small step disturbance is introduced and the reaction of the process variable isrecorded. Figure W5.1 shows a typical process reaction curve for the process variable(PV) generated using the above method for a generic self-regulating process. The termself-regulating refers to a process where the controlled variable eventually returns to astable value or levels out without external intervention.

A Real-Time Approach to Process Control, Second Edition W. Y. Svrcek, D. P. Mahoney and B. R. Young© 2006 John Wiley & Sons, Ltd. ISBN: 978-0-470-02533-8


292 WORKSHOP 5 CONTROLLER TUNING

t

TL

ΔCpPV

Figure W5.1 Process reaction curve

The process parameters that may be obtained from this process reaction curve are asfollows:

L (min) lag timeT (min) time constant estimateP (%) initial step disturbance�Cp(%) change in PV in response to step disturbance,

(change in PV)/(PV span) ×100

N = �Cp

T(% min−1) reaction rate

R = L

T= NL

�Cp

(dimensionless) lag ratio

The Ziegler–Nichols process reaction curve tuning method for a PI controller is asfollows:

1 Determine a reasonable value for the step valve change P . This value isarbitrarily chosen, but typically 5 per cent is reasonable.

2 With the controller in manual mode, manually move the valve ‘P’ per cent.

3 Wait until the PV lines out to the new steady-state value.

4 Determine N and R from the process reaction curve.

5 Perform the following calculations:

controller gain Kc = 0.9P/NL

controller integral time Ti = 3.33 L

6 Implement these recommendations for the controller settings in the controller.

7 Close the control loop by placing the controller in automatic mode.

8 Test thoroughly, fine-tuning the parameters to obtain the QDR.


WORKSHOP 5 CONTROLLER TUNING 293

Auto-tune variation tuning technique

The auto-tune variation or ATV technique of Astrom is one of a number of techniquesused to determine two important system constants called the ultimate period and theultimate gain. Tuning values for proportional, integral and derivative controller param-eters may be determined from these two constants. All methods for determining theultimate period and ultimate gain involve disturbing the system and using the distur-bance response to extract the values of these constants.

In the case of the ATV technique, a small limit-cycle disturbance is set up between themanipulated variable (controller output) and the controlled variable (process variable).Figure W5.2 shows the typical ATV response plot with critical parameters defined. Itis important to note that the ATV technique is applicable only to processes with deadtime. The ultimate period will just equal the sampling period if the dead time is notsignificant.

The general ATV tuning method for a PI controller is as follows:

1 Determine a reasonable value for the valve change h. This value is arbitrarilychosen, but typically 0.05 is reasonable, i.e. 5 per cent.

2 With the controller in the off position, manually move the valve ‘+h’ units.

3 Wait until the process variable PV starts to move and then move the valve‘−2h’ units.

4 When the process variable crosses the set point, move the valve ‘+2h’ units.

5 Repeat until a limit cycle is established, as illustrated in Figure W5.2.

ControllerOutput

ProcessVariable

a

h

Ultimate PeriodPu

Ultimate Gain

Ku 3.14a

4h=

Figure W5.2 ATV critical parameters



6 Record the value of the amplitude a by picking it off the response graph.


ultimate period Pu = period taken from the limit cycle

ultimate gain Ku = 4h/3.14a

controller gain Kc = Ku/3.2

controller integral time Ti = 2.2Pu.

Ziegler−Nichols closed-loop tuning technique

The closed-loop technique of Ziegler and Nichols is another technique that is commonlyused to determine the two important system constants, i.e. ultimate period and ultimategain. Historically speaking, it was one of the first tuning techniques to be widelyadopted.

In Ziegler–Nichols closed-loop tuning, as for the ATV technique, tuning values forproportional, integral and derivative controller parameters may be determined from theultimate period and ultimate gain. However, Ziegler–Nichols closed-loop tuning is doneby disturbing the closed-loop system and using the disturbance response to extract thevalues of these constants.

The Ziegler–Nichols closed-loop tuning method for a PI controller is as follows:

1 Attach a proportional-only controller with a low gain (no integral or derivativeaction).

2 Place the controller in automatic.

3 Increase proportional gain until a constant-amplitude limit cycle occurs.


ultimate period Pu = period taken from limit cycle

ultimate gain Ku = controller gain that produces the limit cycle

controller gain Kc = Ku/2.2

controller integral time Ti = Pu/1.2.

Key learning objectives

1 Controller tuning is determined by the desired controller response.

2 Controller tuning is determined by the type of process.


WORKSHOP 5 CONTROLLER TUNING 295

3 Controller tuning is affected by the value of the process gain.

4 Controller tuning is affected by the value of the time constant.

5 Controller tuning is affected by the value of the dead time.

6 The ATV tuning technique is a powerful method for many loops.

7 The Ziegler–Nichols closed-loop technique is also useful, but more aggressivethan ATV.

8 The Ziegler–Nichols process reaction curve technique is also useful, as itprovides estimates for the key process parameters.

9 HYSYS can be used to find appropriate tuning parameters for a PI controller

Tasks

1 Tuning Controllers

The process used for this workshop is shown in Figure W5.3. A 50/50 feed mixture ofwater and ethanol (T = 5◦C, P = 200 kPa, F = 100 kmol h−1) is heated in a steamheater to approximately 70◦C. The hot stream passes through a dead-time leg beforebeing stored in a tank for future use. Use a PFR unit operation to simulate the deadtime with a volume of 3 m3 and a length of 2 m. This was the process you worked onin the latter part of Workshop 3.

Set the tank level to 50 per cent with no incoming disturbances. With the temperaturecontroller in manual, adjust the steam valve to get a tank temperature of approximately70◦C. Bring up the temperature controller faceplate.

First use the Ziegler–Nichols process reaction curve technique to determine thecontroller settings at 50 per cent tank level. Determine the controller settings at twomore tank levels (5 and 95 per cent).

to tank

product

steam

feed

TC

Heater

Tankhot feed

PFR

TT

Figure W5.3 Illustrative capacity plus dead time process



Second, use the ATV technique to determine the controller settings as follows. Setthe mode to auto-tune. The controller will bring the process into a limit cycle.� Determine the period of this limit cycle in minutes. Use this limit cycle to determine

the amplitude of the temperature cycle of the stream exiting the tank and make thisdimensionless by dividing by the temperature transmitter span.� Now determine the fractional amplitude of the controller output h.� Calculate the ultimate gain and use this with the ultimate period to compute thecontroller settings.� Determine the controller settings at two more tank levels (5 and 95 per cent).

Now use the Ziegler–Nichols closed-loop tuning technique to determine the controllersettings at the three tank levels.� Compare the results of using both the ATV and Ziegler–Nichols tuning techniques.

2 Controller contributions to attenuation

We have seen in Workshop 3 that the process itself is able to attenuate with no control,i.e. open loop. We have just tuned our feedback controller for various levels of capac-itance and can now determine what the process plus control (closed loop) is able toattenuate. By subtracting the open loop attenuation from the total attenuation we candetermine what the controller itself contributes to the overall process attenuation.� Determine the total closed-loop attenuation of the tank operating at the 50 per cent

level for sinusoidal disturbances of periods 10, 20, 30, 40, and 100 min with anamplitude of 25◦C.� Compute the controller contribution to attenuation for these disturbances.� At the 5 per cent level determine the controller attenuation for sinusoidal disturbancesof periods 5, 10, 20, 30, and 50 min and amplitude 25◦C.� At the 95 per cent level determine the controller attenuation for sinusoidal distur-bances of periods 10, 20, 30, 40, and 100 min and amplitude 25◦C.� Plot attenuation versus the logarithm of the disturbance period. Compare the curvesusing their dead time to time constant ratios that you calculated in Workshop 3.

Present your findings on diskette in a short report using MS-Word. Also includeon the disk a copy of the HYSYS files which you used to generate your findings.

process reaction curve

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