Design of multivariable H∞ PID controller using frequency response

In this paper, an optimization method of the multivariable PID controller for H_∞ control is proposed. This method uses only the frequency response of the plant and it does not need the state space representation. The linear matrix inequality restrictions can be imposed on the PID gain matrices. Starting from a stabilizing gain, this method gives a sequence of PID gains for which the H_∞ norm performance index is monotonically nonincreasing. A method of finding a starting point is also given for stable plants. The usefulness is demonstrated by numerical examples.