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FIXED STRUCTURE PID CONTROLLER DESIGN FOR STANDARD H∞ CONTROL PROBLEM

Abstract A frequency domain design method of fixed structure multivariable PID controllers that satisfy the performance index of the standard H ∞ control problem with the LMI (linear matrix inequality) constraints of the PID gains is proposed. Frequency dependent bilinear matrix inequalities on the PID gain are derived and they are approximated by LMI's for each frequency. By solving an LMI problem iteratively starting from a stabilizing PID gain, the proposed method gives a convergent sequence of PID gains so that the sequence of H ∞ norm may be non-increasing.