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Design of Robust Quadratic-Optimal Controllers for Linear Multivariable Output Feedback PID Uncertain Control Systems

By complementarily fusing the robust regional eigenvalue-assignability condition, the orthogonal-functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is proposed in this paper to design the robust optimal eigenvalue-assignable output feedback PID (proportional-integral-derivative) controller such that (i) the eigenvalues of a linear multivariable uncertain closed-loop system can be retained inside the same specified region as the nominal closed-loop system does, and (ii) a quadratic finite-hoziron integral performance index for the linear nominal multivariable control system can be minimized. A design example of the robust optimal eigenvalue-assignable output feedback PID controller for an uncertain stirred tank system is given to demonstrate the applicability of the proposed integrative approach.