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An adaptive control system is one whose parameters are automatically adjusted to compensate for corresponding variations in the properties of
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t he process. The system is, in a word, adapted to the needs of the process. Naturally there must be some criterion on which to base an adaptive program. To specify a value for the controlled variable (i.e., the set point) is not enough-adaption is not required to meet this specification. Some objective function of the controlled variable must be specified in addition. It is this function that determines the particular form of adaption required. The objective function for a given process may be the damping of the cont rolled variable. In essence, there are then two loops, one operating on the controlled variable, the other on its damping. Because damping identifies the dynamic loop gain, this system is designated a dynamic adaptive system. It is also possible to stipulate an objective function of the steady-state gain of the process. A control system designed to this specification is then steady-state adaptive. There is, in practice, so little resemblance between these two systems that their classification under a single title-adaptive-has led to much confusion. A second distinction is to be made, this not on the objective function, but rather on the mechanism through which adaption is introduced. I f enough is known about a process that parameter adjustments can be related to the variables which cause its properties to change, adaption may be programmed. However, if it is necessary to base parameter manipulation upon the measured value of the objective function, adaption is effected by means of a feedback loop. This is known as a selfadaptive system.
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The prime function of dynamic adaptive systems is to give a control loop a consistent degree of stability. Dynamic loop gain is then the objective function of the controlled variable being regulated; its value is to be specified. The property of the process most susceptible to change is gain. In some cases the steady-state gain changes, which is usually termed a nonlinearity. Other processes exhibit a variable period, which reflects upon their dynamic gain. But by whichever mechanism loop stability is affected, it can always bc restored by suitable adjustment of controller gain. (This assumes that the desired degree of damping could be achieved in the first place, which rules out limit cycling.) Many cases of variable process gain have already been cited. In general, an attempt is made to compensate for these conditions by the introduction of selected nonlinear functions into the control system. For example, the characteristic of a control valve is customarily chosen
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FIG 6.20. Two multipliers are necessary for Row adaptation of all three modes.
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with this purpose in mind. But compensation in this way can fall short for several reasons. 1. The source of the gain variation lies outside the loop, and hence is not identified by controller input or output. 2. The required compensation is a combined function of several variables. 3. The gain of the process varies with time. Perhaps the most readily assimilated example of a process which could benefit by adaptive control is that of a single capacity plus variable dead time. Dead time would vary inversely with flow, in the manner shown in the heat-exchanger example given in Chap. 2. Response of the loop without adaption was presented in Fig. 2.14. In this example, an equalpercentage valve was used to provide gain compensation for changes in flow. This method worked, but it in turn made loop gain dependent on the magnitude of the controlled variable. The trade-off was inevitable because the variable which affected the process gain, i.e., flow, is outside the loop. Exact compensation may be obtained by programming the settings of the controller as functions of flow. Because the period of the loop varies directly with dead time, derivative and reset time ought to vary inversely with flow. And since process dynamic gain varies inversely with flow, the proportional band should too. Knowing this, it is possible to write a flow-adapted control algorithm: (6.13) The adaptive term j is the fractional flow through the process, and I , R, and D are the optimum settings at full-scale flow. Placing all the j terms inside the parenthesis indicates how the adaption might be performed: (6.14) ;
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