Module 3. Process Control. Version 2 EE IIT, Kharagpur 1

Transcription

1 Moule 3 Process Control Verson 2 EE IIT, Kharagur 1

2 Lesson 13 Controller Tunng Verson 2 EE IIT, Kharagur 2

3 Instructonal Objectves At the en of ths lesson, the stuent shoul be able to Exlan the mortance of tunng of controller for a artcular rocess Name the three exermental technques for controller tunng Exlan the three methos for tunng of P, I an D arameters Exlan the terms: Auto Tunng, Bumless Transfer an Integraton Wn U. 1. Introucton The mortance of P-I-D controller an the features of P, I an D actons were elaborate n the last lesson. It was also mentone that the controller coul be easly ncororate n a rocess, whatever be the tye of a rocess: lnear or nonlnear, havng ea tme or not. It s neeless to say that the controller arameters nfluence heavly the erformance of the close loo system. Agan, the choce of the value of the P, I an D arameters s very much rocess eenent. As a result, thorough knowlege about the lant ynamcs s mortant for selecton of these arameters. In most of the cases, t s ffcult to obtan the exact mathematcal moel of the lant. So, we have to rely on the exermentaton for fnng out the otmum settngs of the controller for a artcular rocess. The rocess of exermentaton for obtanng the otmum values of the controller arameters wth resect to a artcular rocess s known as controller tunng. It s neeless to say, that controller tunng s very much rocess eenent an any mroer selecton of the controller settngs may lea to nstablty, or eteroraton of the erformance of the close loo system. In 1942 two ractcng engneers, J.G. Zegler an N.B. Nchols, after carryng out extensve exerments wth fferent tyes of rocesses roose certan tunng rules, there were realy accete an tll now are use as basc guelnes for tunng of PID controllers. Subsequently, G.H. Cohen an G.A. Coon n 1953 roose further mofcatons of the above technques. Stll then, the methos are commonly known as Zegler-Nchols metho. Substantal amount of research has been carre out on tunng of P-I-D controllers snce last sx ecaes. Several other methos have also been roose. Most of them are moel base,.e. they assume that the mathematcal moel of the system s avalable to the esgner. In fact, f the mathematcal moel of the system s avalable, many of them erform better than conventonal Zegler-Nchols metho. But the strength of the ZN metho s that t oes not requre a mathematcal moel, but controller arameters can smly be chosen by exermentaton. We woul be scussng the three exermental technques those come uner the commonly known Zegler-Nchols metho. Now let us look back to whatever scusse n lessons 11 an 12. The close loo system can be escrbe as shown n Fg. 1. Verson 2 EE IIT, Kharagur 3

4 The error sgnal s fe to the controller an the controller roves outut u(t). Snce the caacty of the controller to elver outut ower s lmte, an actuator s neee n between the controller an the rocess, whch wll actuate the control sgnal. It may be a valve ostoner to oen or close a valve; or a amer ostoner to control the arflow through a amer. The controller consere here s a P-I-D controller whose nut an outut relatonsh s gven by the equaton: t e() t 1 ut () K et () + τ + e( τ) τ t τ 0 Our objectve s to fn out the otmum settngs of the P,I,D arameters, namely K, τ an τ through exermentaton, whch wll rove satsfactory close loo erformance, of the artcular rocess n terms of, say, stablty, overshoot, settng tme etc. Three methos of tunng are elaborate n the followng sectons. 2. Reacton Curve Technque Ths s bascally an oen loo technque of tunng. Here the rocess s assume to be a stable frst orer system wth tme elay. The close loo system s broken as shown n Fg.2; a ste ' nut s ales at m, outut s measure at b. In fact, a bas nut may be necessary so that the lant outut ntally becomes close to the nomnal value. The ste nut s suermose on ths bas value. The nut an the outut resonse are lotte by sutable means as shown n Fg. 3. Verson 2 EE IIT, Kharagur 4

5 M,L an K are measure. Let us efne the followng terms corresonng to Fg. 2: Sloe N, Tme Constant TK/N Lag Rato RL/T Then, the recommene otmum settngs, for P, P-I an P-I-D controller are as follows. Otmum settngs M R P-Control: K (1 + ) NL 3 P-I Control: K P-I-D Control: K M 9 ( NL 10 + R ); 12 M 4 R ( + ); NL 3 4 τ 4 L 11+ 2R τ τ R L R 32 L R 8R 3. Close Loo Technque (Contnuous Cyclng metho) The major objecton to the tunng methoology usng reacton curve technque s that rocess has to be run n oen loo that may not always be ermssble. For tunng the controller when the rocess s n uner close loo oeraton, there are two methoologes. The frst one, contnuous cyclng metho s exlane below. Verson 2 EE IIT, Kharagur 5

6 Referrng Fg.1, the loo s close wth the controller outut connecte to the actuator nut. Here, the controller s frst set to P-moe, makng τ 0 an τ. The roortonal gan K s ncrease graually to K K, max tll the system just starts oscllatng wth constant amltue contnuously. The outut waveform s lotte as shown n Fg.4. The tme ero of contnuous oscllaton s note. The recommene otmum settngs are: P Control: P-I Control: P-I-D Control: K T u Ponts to Poner K 0.5K max 0.45K max τ, Tu 1.2 Tu Tu K 0.6 K, τ, max τ 2 8 a) Why s the roortonal gan K for PI control s less than the value for P-only control? b) Why K for PID control s more than that PI? 4. Close Loo Technque (Dame oscllaton metho) In many cases, lants are not allowe to unergo through sustane oscllatons, as s the case for tunng usng contnuous cyclng metho. Dame oscllaton metho s referre for these cases. Here, ntally the close loo system s oerate ntally wth low gan roortonal control moe wthτ 0 an τ. The gan s ncrease slowly tll a ecay rato ( 2 / 1 ) of 1/4 th s obtane n the ste resonse n the outut, as shown n Fg. 5. Uner ths conton, the ero of ame oscllaton, T s also note. Let K be the roortonal gan settng for obtanng 1/4 th ecay rato. The otmum settngs for a P-I-D controller are: T T K K; τ ; τ Verson 2 EE IIT, Kharagur 6

7 5. General comments about controller tunng The fferent methoologes of controller tunng, known as Zegler-Nchols metho have been llustrate n the earler sectons. It s to be remembere that the recommene settngs are emrcal n nature, an obtane from extensve exermentaton wth number of fferent rocesses; there s no theoretcal bass behn these selectons. As a result, a better combnaton of the P, I, D values may always be foun, that wll gve less oscllaton an better settlng tme. But wth no a-ror knowlege of the system, t s always avsable to erform the exermentaton an select the controller settngs, obtane from Zegler-Nchols metho. But there s always scoe for mrovng the erformance of the controller by fne-tunng. So, Zegler- Nchols metho roves ntal settngs that wll gve satsfactory, result, but t s always avsable to fne-tune the controller further for the artcular rocess an better erformance s execte to be acheve. Nowaays gtal comuters are relacng the conventonal analog controllers. P-I-D control actons are generate through gtal comutatons. Dgtal oututs of the controllers are converte to analog sgnals before they are fe to the actuators. In many cases, commercal software are avalable for Auto tunng the rocess. Here the controller generates several commans those are fe to the lant. After observng the outut resonses, the controller arameters are selecte, smlar to the cases scusse above. 6. Integraton wnu an Bumless transfer Two major ssues of concern wth the close loo oeraton wth P-I-D controllers are the Integraton Wnu an the requrement of rovng Bumless Transfer. These two ssues are brefly elaborate below. The methoologes for rovng Ant-ntegraton Wnu an Bumless Transfer woul be scusse n the next lesson. Integraton Wnu A sgnfcant roblem wth ntegral acton s that when the error sgnal s large for a sgnfcant ero of tme. Ths can occur every tme when there s large change n set ont. If there s a suen large change n set ont, the error wll be large an the ntegrator outut n a P-I-D control wll bul u wth tme. As a result, the controller outut may excee the saturaton lmt of the actuator. Ths wnu, unless revente may cause contnuous oscllaton of the rocess that s not esrable. Verson 2 EE IIT, Kharagur 7

8 Bumless Transfer When a controller s swtche from manual moe to auto-moe, t s esre that the nut of the rocess shoul not change suenly. But snce there s always a ossblty that the ecson of the manual moe of control an the auto moe of control be fferent, there may be a suen change n the outut of the controller, gvng rse to a suen jerk n the rocess oeraton. Secal recautons are taken for bumless transfer from manual to auto-moe. References 1. B. Ltak: Process Control: Instrument Engneers Hanbook 2. D.R. Coughanowr: Process systems analyss an control (2/e), McgrawHll, NY, D. Eckman: Process Control, Wley, NY, Revew Questons 1. What oes controller tunng mean? 2. Name the three technques for controller tunng, those are commonly known as Zegler- Nchols metho. 3. Exlan the reacton curve technque for tunng of controller. What are ts lmtatons? 4. What o you mean by Auto Tunng? Exlan brefly. 5. What s meant by Bumless Transfer? 6. Why rovson for Ant- ntegraton Wnu s necessary for rocess wth P-I-D control? Answers to Ponts to Poner a) Aton of ntegral control acton to P-only control tens to make the close loo system more oscllatory; n orer to overcome ths roblem, the suggeste value of K wth ZN tunng s reuce. b) Aton of ervatve acton agan ams own the oscllaton; as a result larger value of K n a PID controller s ermssble. Verson 2 EE IIT, Kharagur 8