By H BAXTER WILLIAMS
A whole and incisive survey of the tools used and outlines in their working principles.
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Extra resources for Applied Instrumentation in the Process Industries, Second Edition: Volume 1: A Survey, Second Edition
12. A directionality problem 18 1 Undesired Eﬀects of Input Saturation If, however, the signals u1 (t) and u2 (t) saturate at u01 = 4 and u02 = 17, the decoupling behaviour no longer results when a reference signal r1 (t) = 1(t) is applied. 12b shows the corresponding transients, which clearly indicate that a considerable cross-coupling is caused by input saturation. The examples in Chapter 1 have demonstrated that there are various possible reasons for the detrimental eﬀects of input saturation.
12b shows the corresponding transients, which clearly indicate that a considerable cross-coupling is caused by input saturation. The examples in Chapter 1 have demonstrated that there are various possible reasons for the detrimental eﬀects of input saturation. Undesired overshoots are not only caused by controller windup but also by plant windup. It turns out that plant windup not only produces an undesired oscillatory behaviour (or even an unstable behaviour of the closed loop), but it may also cause directionality problems in MIMO systems.
Given a set of tracking errors, the decoupling controller generates speciﬁc output signals ui (t), which counteract the existing cross-couplings in the system. The individual output signals deﬁne the length, the direction, and the dynamic evolution of the output vector u(t). In the linear case, the vector us (t) = u(t) then constitutes the decoupling control input to the system. If one or more input signals saturate, the direction of us (t) no longer coincides with that of the decoupling output vector u(t) of the controller, which may result in severe cross-couplings.