Scheduled programmed adaptive control

This is employed where a process is well-known and an adequate mathematical model is available. If there is an auxiliary process variable which correlates well with any changes occurring in process dynamics, then the best values of the controller parameters can be related ahead of time to the value of the auxiliary variable. Consequently, by measuring the value of the auxiliary variable, the adaptation of the controller parameters can be scheduled (or programmed). 

The relevant block diagram is composed of two loops (Fig. 7.97)—a normal feedback loop and a loop which contains the parameter adjustment mechanism (comparable to feed-forward compensation—Section 7.14.1). 

Gain Scheduling Adaptive Control is a special application of this procedure. For example we may have a control valve whose characteristic (input signal/valve stem position relationship) is non-linear. In this case, the valve stem position would be measured in order to obtain the gain of the valve (the appropriate relationship must be known) and the valve gain is used then to adjust the gain of the controller. If the auxiliary variable relationships are more complicated then it may be necessary to employ a Programmed Adaptive Control procedure. 

Difficulties that can be experienced with this form of control are 47)  

This is employed when the process is not well-known. The Model Reference Adaptive Controller contains a reference model to which the command signal or set point change is applied as well as to the process itself (Fig. 7.98) 4 ). The output of the reference model is postulated as the desired controlled process output and this is compared with the actual process output. The difference (or error) e , between the two outputs is used to adjust the controller parameters so as to minimise the relevant integral criterion. For example, if the ISE criterion is employed then the quantity 

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Fig. 7.97. Block diagram of scheduled (programmed) adaptive control system...

An adaptive control system can automatically modify its behaviour according to the changes in the system dynamics and disturbances. They are applied especially to systems with non-linear and unsteady characteristics. There are a number of actual adaptive control systems. Programmed or scheduled adaptive control uses an auxiliary measured variable to identify different process phases for which the control parameters can be either programmed or scheduled. The "best" values of these parameters for each process state must be known a priori. Sometimes adaptive controllers are used to optimise two or more process outputs, by measuring the outputs and fitting the data with empirical functions. 

Yet another approach to this situation would be to adjust the controller parameters, the controller gain for example, with the variation in load of set point to compensate for the variation in process gain. This approach is termed gain scheduling [5,6] or programmed adaptation [7,8] and can be considered to be form of adaptive control [5],... 

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