40 Automatic tuning of PID controllers using a combined time- and frequency-domain method by M. Thomson,* PhD, CEng, MIEE, P G. Cassidy,† BSc, MSC, AIEE and D. J. Sandoz,† BEng, PhD, CEng, MIEE * Dept of Electrical and Electronic Engineering, Manchester Polytechnic; †Vuman Industrial Control Systems, Vuman Ltd. The paper describes an automatic tuning method for the design of PID controllers. Its starting point is the require- ment for accurate modelling of process deadtime which is calculated from a discrete model description of the process. Controller design is achieved by a combination of pole- zero cancellation and frequency-response methods which ensures that the system exhibits favourable gain and phase characteristics and good relative stability even for processes with large deadtime. Results are presented for the control of a steam/water heat exchanger and illustrates the useful- ness of this technique. Keywords: Deadtime modelling, automatic PID tuning. List of symbols used a;, bi Process difference-equation coefficients a Ratio of integral and derivative times G~ c Controller transfer function GP p Process transfer function k Time index K Process gain Kp Controller gain Ku u Ultimate gain n Integer deadtime ~ c Controller phase contribution Øm Phase margin s Laplace operator T Process deadtime A T Fractional process deadtime Ts Sample time T,, TZ Process time constants Td Derivative time T, Integral time T,, Ultimate period u, U Process input co Frequency Wd d Normalised frequency co,, Undamped natural frequency oo Gain crossover frequency y, Y Process output I Damping ratio z z-transform operator Introduction Central to the analytical design of three-term (Pill) process controllers is the requirement for reliable process modelling. On-line system identification techniques which use random signal testing are often more appropri- ate than traditional frequency-response or process- reaction-curve testing methods for process plant modelling. These methods naturally give rise to a process model expressed in discrete form whereas there exists a full literature on Pm tuning techniques which requires the specification of process dynamics in continuous form. Process deadtime has a marked effect on tuning relation- ships, and accurate specification of this from the discrete model is not straightforward. This paper describes a method whereby deadtime can be assessed accurately, thus allowing design criteria to be met. A novel technique of PED design is also presented which combines the methods of pole-zero cancellation and frequency- response gain and phase-margin specifications to select appropriate tuning parameters. This approach has proved promising both in simulation and on tests on an experimental heat exchanger rig, and results of these experiments are presented in the paper. Derivation of the process model Many processes can be adequately represented by the second-order lag plus deadtime model given by Gp(s ) - Kc~~ exp( - sT ) - Y( s) ...( 1 ) G~(s s s +2~cvns+co&dquo; 2 U(s) s &dquo; ’~ ~ ~ In system identification methods such as recursive least squares, the PRBS interval ( Ts) must be significant in rela- tion to process time constants for effective modelling and are typically chosen to be between one-third and one-half of the dominant process time constant. Hence, to model process deadtime ( T ) adequately, the structure of the dis- crete model must be such as to allow evaluation of dead- time other than in terms of integer multiples of sample time. To this end a discrete model is required of them: Yk + -aiYx+~zYk-W;’bWx-n n + b2 Uk - n - +b3uk-n-2 ...(2) Deadtime comprises an integer number of sample periods n together with a fractional time delay AT with 0 % AT% 1: which is to be determined from the coeffi- cients of Eqn ( 2 ). For situations in which deadtime is an at UNIV ARIZONA LIBRARY on January 7, 2015 tim.sagepub.com Downloaded from