Study and Analysis of Various Tuning Methods of PID Controller for AVR System

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1 Inernaional Journal of esearch in Elecrical & Elecronics Engineering olume, Issue, July-Sepember, 203, pp , IASTE Online: , Prin: ABSTACT Sudy and Analysis of arious Tuning Mehods of PID Conroller for A Sysem Apurva Tripahi, am Lauan erma, Md. Sanawer Alam Deparmen of Elecronics Insrumenaion and Conrol Engineering, Azad IET, Uar Pradesh Technical Universiy, Lucknow, India This paper describes a brief sudy of several uning rules for uning of PID conroller. PID conrollers can compensae many pracical processes and are widely acceped in indusrial applicaions. The sysem aken up for he sudy is he Auomaic olage egulaor (A) sysem which is approximaed o 4 h order sysem. In his mehod design of a conroller based on ZN uning mehod is deermined and comparison is made beween he various uning mehods. Malab sofware is used for simulaion. Keywords: A sysem, PID conroller, Tuning rules, ZN Tuning Mehod.. INTODUCTION The PID conroller is a feedback mechanism widely used in a variey of applicaions. The conroller calculaes an error ha is he difference beween a measured process variable and he desired se-poin value needed by he applicaion. PID conrollers will aemp o minimize he process error by coninually adjusing he inpus []. Alhough his is a powerful ool, he conrollers mus be correcly uned if hey are o be effecive. The deerminaion of proporional (Kp), derivaive (Td) and inegral (Ti) consan are known as uning of PID conroller. The mos popular uning echnique is he Ziegler-Nichols mehod. Ziegler and Nichols give he manual uning of PID conroller. This is off line pracical mehod of PID consans deerminaion. In his mehod, he sysem is in open loop configuraion. There are several oher mehods of uning of PID conroller e.g. CH mehod and WJC mehod [2]. In his paper a comparison is carried ou beween all hese mehods. 2. THE A SYSTEM The main purpose of he A sysem [3] is o mainain he erminal volage of a synchronous generaor a a specified level. I mainly consiss of four main pars, namely amplifier, excier, generaor and a volage sensor. In his sudy he mahemaical model is obained by linearizing he model of hese componens by ignoring he sauraion and oher nonlineariies presen, also by considering he major ime consans and ignore ohers. The resuling ransfer funcion of he componens can be wrien as Amplifier Model. The amplifier model is represened by a gain K A and ime consan T A (s) K A = e(s) + TAs, Typical values of K A are in he range of 0 o 400. The amplifier ime consan is very small ranging from 0.02 o0. s. 93

2 Inernaional Journal of esearch in Elecrical & Elecronics Engineering olume-, Issue-, July-Sepember, 204, Excier model. The ransfer funcion of a modern excier may be represened by gain K E and ime consan T E F(s) KE = (s) + E Typical values of K E are in he range of 0 o 400. The ime consan T E is in he range of 0.5 o.0 s. Generaor model. In he linearized model, he ransfer funcion relaing he generaor erminal volage o is field volage can be represened by a gain K G and a ime consan T G (s) K G = F(s) + TGs, These consans are load dependen, K G may vary beween 0.7 o.0, and T G beween.0 and 2.0 from full load o no load. Sensor model. The sensor is modelled by a simple firs-order ransfer funcion, given by s(s) K = (s) + T is very small, ranging from of 0.00 o 0.06 s. A Sysem ref + - s e K p K i K s s d K A A K E E K G G PID Conroller Amplifier Excier Generaor f s K Sensor Figure.2. Block Diagram scheme of A sysem along wih PID conroller The numerical ransfer funcion model for differen componens of he A sysem are presened below: Amplifier: Generaor: The plan model is herefore (s) 0 (s) 0.s, Excier: F(s) (s) 0.4s, e (s) F (s) s, Sensor: s (s) (s) 0.0s In his sudy we have done experimens for wo ypes of conrol problem, namely: Se poin racking conrol: in his problem he oupu of he generaor i.e. generaor volage mus follow he change in he reference volage. In our sudy he uni sep change is applied o he reference volage, firs he reference volage is increased by he uni sep hen i is decreased by he same amoun o achieve he same seady sae as before. Fig 4. shows he simulaion resuls for 94

3 Inernaional Journal of esearch in Elecrical & Elecronics Engineering olume-, Issue-, July-Sepember, 204, differen uning echniques. Table 4. shows he comparison of ime-domain performance measures viz. rise ime, seling ime, overshoo. egulaory Conrol: This ype of conrol problem is also called disurbance rejecion conrol. Since he load demand may vary so in ha case he conroller mus be uned o mainain he volage applied o excier in such a way ha he oupu volage of he generaor is mainained consan wihin he limis allowed. In he case of load changes, we have considered he uni sep change in he load and he Fig 4.2 shows he simulaion resuls for his problem using differen uning echniques. Table- 4.2 shows he comparison of he various performance indices. 3. PID CONTOLLE TUNING ULES In his sudy we have considered 5 differen echniques [4] for uning he PID Conroller for A sysem hese echniques include four classical echniques based on he frequency response characerisics of he A sysem hese are namely: Ziegler-Nichols uning mehod. Chein-hrones eswick(ch) 0% overshoo mehod. Chein-hrones eswick(ch) 20% overshoo mehod. The Wang-Juang-Chan(WJC) uning mehod. 3. ZIEGLE NICHOLS TUNING METHOD In 942 Ziegler and Nichols boh employees of Taylor Insrumens described simple mahemaical procedures, he firs and second mehod respecively, for uning PID conrollers [5]. These procedures are now acceped as sandard in conrol sysem pracice. Boh echniques make prior assumpions on he sysem model, bu do no require ha hese models be specifically known. Ziegler Nichols formulae for specifying he conrollers are based on plan sep response [6]. 3. ZN eacion curve mehod The reacion curve mehod is applied o plans wih sep responses o form he graph shown in fig 3. his ype of response is ypical of a firs order sysem wih ransporaion delay. The response is characerized by wo parameers, L he delay ime and T he ime consan. These are found by drawing a angen o he sep response a is poin of inflecions and noing is inersecions wih he ime axis and he seady sae value. Figure 3. The response curve for Ziegler Nichols reacion curve mehod Ziegler and Nichols derived he following conrol parameers based on he model 95

4 Inernaional Journal of esearch in Elecrical & Elecronics Engineering olume-, Issue-, July-Sepember, 204, ZN Frequency esponse Mehod Table 3. Ziegler nichols reacion curve mehod Conroller K c T i T d P T/L 0 PI 0.9T/L L/0.3 0 PID.2T/L 2L 0.5L Ziegler-Nichols uning rule was he firs such effor o provide a pracical approach o une a PID conroller [7]. According o he rule, a PID conroller is uned by firsly seing i o he P-only mode bu Adjusing he gain o make he conrol sysem in coninuous oscillaion. The corresponding gain is referred o as he ulimae gain (Ku) and he oscillaion period is ermed as he ulimae period (Pu). Then, he PID conroller parameers are deermined from Ku and Pu according o he given Ziegler- Nichols uning able. Table:3.2 Conroller Parameers for Ziegler-Nichols frequency Mehod Conroller K p T i T d P 0.5 Ku 0 PI 0.45 Ku Pu/.2 0 PID 0.6Ku Pu/2 Pu/8 3.3 Chien Hrones eswick PID Tuning Algorihm The Chien Hrones eswick (CH) mehod [8] emphasizes he se-poin regulaion or disurbance rejecion. In addiion one qualiaive specificaion on he response speed and overshoo can be accommodaed. Compared wih he radiional Ziegler Nichols uning formula, he CH mehod uses he ime consan T of he plan explicily [9]. The CH PID conroller uning formulas are summarized in Table 3.3 for se-poin regulaion. The more heavily damped closed-loop response, which ensures, for he ideal plan model, he quickes response wihou overshoo is labelled wih 0% overshoo, and he quickes response wih 20% overshoo is labelled wih 20% overshoo. Similarly, Table 3.4 is used o design conrollers for disurbance rejecion purposes. Table 3.3 CH Tuning Formulae For Se-Poin egulaion. Table 3.4 CH Tuning Formulae For Disurbance ejecion. 96

5 Ampliude Ampliude Inernaional Journal of esearch in Elecrical & Elecronics Engineering olume-, Issue-, July-Sepember, 204, The Wang Juang Chan Tuning Formula Based on he opimum ITAE crierion, he uning algorihm proposed bywang, Juang, and Chan [0] is a simple and efficien mehod for selecing he PID parameers. If he k,l, T parameers of he plan model are known, he conroller parameers are given by T T 0.5L L K p k(t L) () 0.5LT T T 0.5L T i d T 0.5L 4. SIMULATION ESULTS Simulaion are performed using MATLAB simulink for ZN mehod,ch mehod and WJC mehod o validae he performance. For A sysem: Z-N PID.4 Z-N eacon Curve CH 0% PID.2 CH 20%PID WJC PID Sepoin racking for A sysem (2) Time (sec) Figure 4.- For Se poin racking Table 4. Se-poin conrol Name of he Mehod K p T i (sec) T d (sec) T r (sec) (sec) O.S.(%) Z-N Frequency response Z-N eacion Curve CH 0% CH 20% WJC T r : ise ime; : Seling ime; O.S.: Overshoo Disurbance ejecion Z-N frequency response PID Z-N eacion Curve PID CH0% PID CH20% PID WJC PID Time (sec) Figure-4.2 For regulaory performance 97

6 Inernaional Journal of esearch in Elecrical & Elecronics Engineering olume-, Issue-, July-Sepember, 204, 5. CONCLUSION Table 4.2 egulaory Performance Name of he Mehod (sec) Z-N frequency response mehod Z-N reacion curve mehod CH 0% PID CH 20% PID WJC mehod 6.46 When WJC and CH 0% OS mehods are applied hen zero overshoo is observed. When ZN frequency response mehod is applied i provides minimum seling ime and nearly minimum rise ime oo. In case of rise ime eacion curve mehod is faser in his case. Overall ZN frequency response mehod can be used where some overshoo canno have more affec he sysem performance. WJC mehod is aking maximum ime o be seled ou of hese five mehods esed here. The CH mehod gives zero overshoo for rajecory conrol and he seling ime is nearly equal o he seling ime of WJC mehod, bu he rise ime in boh hese mehods is more han wice han ha in ZN and eacion curve mehods. From he responses aken in disurbance rejecion mode he ZN frequency response mehod provides beer resuls ou of hese five mehods used here for case sudy. WJC mehod gives poor performance measures and he peak in CH mehod is somewha equal o ZN mehods bu he seling ime is more han ha in ZN mehod. The CH and WJC mehods are good for racking conrol and for disurbance rejecion case Ziegler-Nichols mehod provide beer performance measures. WJC mehod works saisfacorily and provides average resul in disurbance rejecion. I can be chosen for boh ypes of conrol problems. EFENCES [] ajkumar Bansal, Divya ai, ijay Bhuria, Design of z-n uned pid conroller for higher order sysem. [2]..avi,T.Thyagarajan, Applicaion of adapive conrol echnique o ineracing Non Linear Sysems, IEEE 20 pp [3] Zwe-Lee Gaing, A Paricle Swarm Opimizaion Approach for Opimum Design of PID Conroller in A Sysem, IEEE ransacions on energy conversion, vol. 9, no. 2, june [4] Aidan O'Dwyer, PI and PID conroller uning rules: an overview and personal perspecive Dublin Insiue of Technology. [5] D. Marshiana and Dr.P.Thirusakhimurugan Design of Ziegler Nichols Tuning conroller for a Non-linear Sysem. [6] Kasuhiko Ogaa, Modern conrol engineering Prenice Hall; 5 ediion, Sepember 4, [7] J.G.Ziegler and N.B.Nichols, ocheser.n.y, Opimum Seings for Auomaic Conrollers, Trans.ASME,64,942,pp [8] Dingyü Xue,. YangQuan Chen, Derek P. Aheron, Linear Feedback Conrol Analysis and Design wih MATLAB. July 3, [9] Yanhong Zhang, Zhongqiao Zheng, Jiansheng Zhang,"esearch on he parameers selfuning fuzzy PID conroller," 2009 Second Inernaional Symposium on Knowledge Acquisiion and Modeling, /09. [0] Ousaloup, P. Melchoir, P. Lanusse, C. Cois, and F. Dancla. he crone oolbox for malab. In Proc of he h IEEE Inernaional Symposium on Compuer Aided Conrol Sysem Design - CACSD, Anchorage, USA,