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Monitoring and Control of Information-Poor Systems: An Approach Based on Fuzzy Relational Models by Arthur L. Dexter

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8

Incorporating Fuzzy Inputs

The two main causes of the uncertainty associated with the inputs to a controller in an information-poor system are imprecision in the definition of the setpoint and measurement noise. Figure 8.1 shows the location of these inputs (the setpoint, the measured plant output and any measured disturbance) in the control system. This chapter will describe techniques for dealing with uncertainties associated with the setpoint and the measured values of the plant output. Ways of taking measured disturbances into account will be considered in the next chapter.

8.1 Fuzzy Setpoints and Fuzzy Measurements

8.1.1 Fuzzy Setpoints

As can be seen in Figure 8.2, an imprecise setpoint can be considered as a fuzzy control objective.

For example, when controlling thermal comfort in a building, it is more meaningful to specify the control objective as “to maintain the air temperature at about 24°C” rather than give a precise temperature setpoint. The setpoint is then a fuzzy set defined by an appropriate membership function. The grade of membership of this fuzzy set can be used as a measure of the degree of satisfaction of the control objective and the α-cut of the fuzzy setpoint set indicates the range of values of the air temperature that satisfy the control objective by at least α.

8.1.2 Fuzzy Measurements

Direct use of a noisy signal can result in unacceptable levels of control activity, particularly when the controller uses the time derivative of the signal as one ...

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