Sequential synthesis of PID controllers based on LQR method

The linear quadratic regulator (LQR) method is generalized to allow synthesis of PID controllers in MIMO processes. The proposed method is sequentially applied to produce proportional, integral and derivative actions. Three major usages are conceived for the proposed methodology: (i) de novo design of PID controllers, (ii) addition of derivative action to existing PI controllers and (iii) diagonalization of PID gain matrices. The two last procedures can be applied to controllers designed with different methodologies. The developed method was applied to the de novo design of a centralized PID controller for a three input-three output distillation column as well as the addition of derivative action to existing both centralized and multiloop PI controllers for a nonlinear CSTR. Proposed LQR method allowed the synthesis of centralized and multiloop PID controllers with better characteristics for set-point tracking, disturbance rejection, limited use of control signal and insensitivity to plant model uncertainty than those reported by other authors.

Keywords: Lyapunov function, quadratic index, quadratic optimal control, robust control, state-space model.