UNIT IV CONTROLLER TUNING:

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1 UNIT IV CONTROLLER TUNING: Evaluation Criteria IAE, ISE, ITAE An ¼ Decay Ratio - Tuning:- Process Reaction Curve Metho, Continuous Cycling Metho An Dampe Oscillation Metho Determination Of Optimum Settings For Mathematically Describe Processes Using Time Response An Frequency Response Approaches Auto Tuning. EVALUATION CRITERIA ( IAE, ISE & ITAE) : The shape of the complete close-loop response, from t=0 until steay state has reache, coul be use for the formulation of a ynamic performance criteria. 1. Integral of the square error (ISE), where 2 ISE ( t) t 0 2. Integral of the absolute vale of the error(iae), where IAE ( t) t 0 3. Integral of the time-weighte absolue error(itae), where IAE t ( t) t 0 Note ( t) ysp( t) y( t) is the eviation (error) of the response from the esire set point. 1

2 To esign the best controller select the type of the controller an ajust the values of controller parameters in such a way that to minimize ISE, IAE or ITAE of the system response. ISE, IAE or ITAE epens on the characteristics of the system we want to control. If we want to strongly suppress large errors, ISE is better than IAE because the errors are square an thus contribute more to the value of the integral. If we want to strongly suppress small errors, IAE is better than ISE because when we square small numbers (smaller than one) they become even smaller. If we want to strongly suppress errors, that persists for long times, IATE criterion will tune the controller s better because the presence of large t amplifies the effect of even small errors in the value of the integral. 2

3 ¼ Decay Ratio: The ratio between first two successive peaks shoul be ¼, which is one of the important ynamic performance criteria. PROCESS REACTION CURVE METHOD OF TUNING A CONTROLLER: Process reaction curve metho is the most popular emprical tuning metho. Consier the control system shown in the follwing figure, which has been opene by isconnecting the controller from the final control element. Introuce a step change [C(s)=1/s] to the final control element. Recor the value of output with respect to time. 3

4 The curve y m (t) is calle the process reaction curve. Between y m an c we have the y ( s) c( s) m follwing transfer function G G ( s) G ( s) G ( s) PRC f p The above equation shows that process reaction is affecte by the process,final control element an measuring element. In Process reaction curve metho the sigmoial shape curve is appromate by first-orer system with ea time. m G PRC ym( s) c( s) t s Ke s 1 The three parameters: static gain K, ea time t, an time constant are estimate from the approximate response. output( at steay state) K input( at steay state) B A B, where S is the slopeof the sigmoial responseat the point of S t time elapseuntill the systemrespone 1.For proportional controller 4 inflection

5 K c 1 t 1 K t 3 2.For proportional-integral controller K c 1 t 0.9 K t 12 I, t 30 3t 9 20t / / 3.For proportional-integral-erivative controller K c 1 K t 4 3 t 4 I, t 32 6t 13 8t / D t /, t / Remarks 1. If the approximation is poor Cohen-Coon settings shoul be viewe only as first gusses neeing certain online correction. 2. Opene loops have a sigmoial response because,almost all physical processes in chemical plants are simple first orer or multicapacity processes whose respose has general overampe shape.the oscillatory unerampe behaviour is prouce mainly by the presence of feeback controllers. 3. (a)the gain of the PI controller is lower than that of the P controller.this is ue to the fact that the integral control moe makes the system more sensitive (May even lea to insatbility) an thus the gain value nees to be more conservative. (b)the stabilizing effect of the erivative control moe allows the use of higher gains in the PID controller (higher than the gain for P of PI controllers) 5

6 ZIEGLER NICHOL S OR CONTINUOUS CYCLING METHOD OF TUNING A CONTROLLER Step 1: After the process has reache steay state (at least approximately), eliminate the integral an erivative control action by setting τ D to aero an τ I to the largest possible value. Step 2: Set the proportional controller gain (K c ) to a small value (e.g.,0.5) an place the controller in automatic moe. Step 3: Introuce a small, momentary set-point change so that the controlle variable moves away from the set point. Graually increase K c in small increments until continuous cycling occurs. The term continuous cycling refers to a sustaine oscillation with constant amplitue. The numerical value of K c that prouces continuous cycling (for proportional- only control) is calle ultimate gain (K cu ). The perio of the corresponing oscillation is referre to as the ultimate perio Pu). Step 4: Calculate the PID controller tuning settings using the Zeigler-Nichols (Z-N) relations. 6

7 Step 5: Evaluate the Z-N controller settings by introucing a small set-point change an observing the close-loop response. Fine tune the settings, if necessary. In practice, controller saturation prevents the response from becoming unboune an prouces continuous cycling. Thus it is very important that controller saturation be avoie uring experimental test. Disavantages. 1. Time-consuming if the process ynamics are slow. The long experimental tests may result in reuce prouction or poor prouct quality. 2. The process is pushe to the stability limits. If external isturbances or process change occur uring the test, unstable operation or a hazarous situation coul result. 3. Z-N tuning is not applicable to integrating or open loop-unstable processes because their control loops typically are unstable at both high an low values of K c, while being stable for intermeiate values. 7

8 DAMPED OSCILLATION METHOD In many cases, plants are not allowe to unergo through sustaine oscillations, as is the case for tuning using continuous cycling metho. Dampe oscillation metho is preferre for these cases. Here, initially the close loop system is operate initially with low gain proportional control moe with τ D =0 an τ I =. The gain is increase slowly till a ecay ratio (p 2 /p 1 ) of 1/4 th is obtaine in the step response in the output, as shown in Fig. Uner this conition, the perio of ampe oscillation, T is also note. Let K be the proportional gain setting for obtaining 1/4 th ecay ratio. The optimum settings for a P-I-D controller are: 8

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13 RELAY AUTOTUNING: Astrom an Hagglun(1984) have evelope an attractive alternative to the continuous cycling metho known as Relay Auto-tuning metho, it is a simple experimental test which is use to etermine ultimate gain (K u ) an Ultimate perio (P u ). For this test, the feeback controller is temporarily replace by an on-off controller (or relay).after the control loop is close, the controlle variable exhibits a sustaine oscillation the characteristics of on-off control. The operation of the relay auto-tuner inclues a ea ban as shown in fig. The ea ban is use to avoi frequent switching cause by measurement noise. The ultimate gain (K u ) an Ultimate perio (P u ) can be obtain from the figure. The Ultimate perio (P u ) is equal to the perio of oscillation for the process output. Astrom an Hagglun(1984) erive an approximate expression for the ultimate gain, 4 K cu a 13

14 where is the relay amplitue (set by the user) an a is the measure amplitue of the process oscillation.pid controller settings can then be calculate from the Z-N settings in table below Moifications an extensions are available for nonlinear, open-loop unstable, an multiple-input, multiple-output processes. Avantages 1. Only a single experimental test is require instea of a trial-an-error proceure. 2. The amplitue of the process output a can be restricte by ajusting relay amplitue. 3. The process is not force to stability limit. 4. The experimental test is easily automate using commercial proucts. Disavantages For slow processes, it may not be acceptable to subject the process to the two or four cycles of oscillation require to complete the test. 14