PID controller design with time response specifications
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This paper considers the problem of determining a set of stabilizing proportional-integral-derivative (PID) controller gains, for a given linear time invariant plant, that meets or exceeds closed loop step response specifications. The method utilizes two recent results: For a given system, (1) finding a set of stabilizing PID gains for a given system and (2) the relationship between time response (overshoot and speed) and the coefficients of the characteristic polynomial. The method allows us to extract a subset of PID gains that meets stability as well as time domain performance requirements. The computations involved are the intersections of two dimensional sets described by linear and quadratic inequalities in the controller design space. It is illustrated by examples.