Scheduled adaptive control

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. 

However, the main reason for the lack of wide application of on-line adaptive control is the lack of economic incentive. On-line identification is rarely required because it is usually possible to predict with off-line tests how the controller must be retuned as conditions vary. The dynamics of the process are determined at different operating conditions, and appropriate controller settings are determined for all the different conditions. Then, when the process moves from one operating region to another, the controller settings are automatically changed. This is called openloop-adaptive control or atn scheduling. 

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

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. 

Adaptive control can be thought of as a system that automatically designs a control system. The adaptation can result in automatically scheduling or... 

Had the reactor been a batch reactor instead of a CSTR, the controllers would be combined with an adaptive control system which would have updated the controllers, i.e. the control parameters, as the batch progressed. The batch reactor would also have had a separate logical control system to take the reactor through the batch schedule. 

Suppose that the process is well known and that an adequate mathematical model for it is available. If there is an auxiliary process variable which correlates well with the changes in process dynamics, we can relate ahead of time the best values of the controller parameters to the value of the auxiliary process variable. Consequently, by measuring the value of the auxiliary variable we can schedule or program the adaptation of the controller parameters. Figure 22.1 shows the block diagram of a programmed adaptive control system. We notice that it is composed of two loops. The inner loop is an ordinary feedback control loop. The outer loop includes the parameter adjustment (adaptation)... 

Figure 22.2 (a) Feedback control loop for Example 22.1 (b) corresponding gain scheduling adaptive control. 

Adaptive Control Decision Making Monitoring Process Scheduling... 

Tlie slope of the titration curve can be used to schedule the process gain and hence the controller gain. Alternatively, the curve can be used to convert the controlled variable to percent reagent demand per section 8-4. Either method frees up the adaptive controller to identify the changes rather than the whole shape of the curve. Finally, the curves and dynamic models can be used for dynamic online pH estimators, MFC, and real-time optimization of reagent consumption. 

Use gain scheduling or signal characterization based on the titration curve to free up an adaptive controller to find the changes in the curve. 

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],... 

The great interdependence of public health and agriculture can be no better illustrated than by the problem of insecticide residues in food. Compounds, vehicles, and spraying schedules adapted for insect control must be selected by the agriculturalist in such a way as to ensure an acceptable product at harvest. However, once the product is harvested and offered for human food, it becomes the concern of various public health agencies. The health of the agricultural operator who applied the insecticide is also a matter for medical and public health attention. 

Traditionally the PERT diagram did not involve costs, but in the early 1960s a plan called PERT/Cost was developed that was similar to the cost-control concepts of CPM. Some authors claimed they were now essentially the same. PERT/Cost involves obtaining one cost for each activity. If the expected time were,the same as the normal time, the procedure for cost control would be the same as for a CPM system. The PERT system can also be easily adapted to the method presented for speeding up projects (crashing). The remarks made previously about scheduling and obtaining time estimates apply equally well to PERT and CPM. 

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