Digital controllers for SISO systems: a review and a new algorithm

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Abstract
Several digital control algorithms for linear single-input single-output systems are examined and the effect of the sampling period on their performance is analysed in terms of rippling, overshoot and settling time. The problem is addressed in the frequency domain (z-transform) and it is shown that each controller works for some classes of systems but that none works for all. The similarities and differences of these controllers are established and an explanation of their deficiencies is given based on the location of the zeros of the discrete system. The insight gained leads to a simple new rule for the design of a controller which combines the advantages of the different algorithms but at the same time is free of their problems. A single tuning parameter is included which directly affects the closed-loop speed of response and bandwidth. The parameter can be used to detune the controller in the event that the real system differs from the model on which the controller design is based. No tuning is necessary when the available model is exact, unless smaller values for the manipulated variable, at the cost of a slower response, are preferred.

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