By Leigh, James R
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Extra info for Applied control theory
5 Synthesis of a controller in the z domain In selecting the desired transfer function, if, it must be borne in mind that: (a) If if is set equal to unity, division by zero occurs and the controller does not exist. (b) If the process contains a transport delay, then H must contain a delay at least equal to this. Otherwise the controller will contain positive powers of z and be unrealisable since this implies prediction.
Knowledge of these and similar relations, which can be worked out for each case, allow estimates to be made of the approximate transfer function of a process in a very short time from the results of simple tests that most process managers will tolerate. 1, the most direct route to finding controller coefficients is to use an iterative numerical technique. First a criterion, / , is defined that is to be minimised by choice of controller coefficients. Possible choices are: (a) A = jJ 00 (b) J2 = J e(t)2 dt; (c) h = rt\e(t)\dt; Jo where it is understood that at time 0 a step is applied to the system, either to the input or as a load disturbance.
The algorithms are often modified to prevent step changes in desired value from being differentiated. 4) yn being the process output. A further modification is to incorporate a facility to prevent "wind-up' of the integral term. The simplest method is to disable the integration when the actuator becomes saturated. 3) implicitly contains this facility. Similarly some mechanism is needed to prevent the integral term building up to a large spurious value after a set-point change. The simplest strategy is to immobilise the integral term completely whenever the input to the controller exceeds some pre-set value.
Applied control theory by Leigh, James R