A simple method of tuning series cascade controllers for unstable systems

A simple method is proposed to design P/PI controllers for a series cascade control system for unstable first order plus time-delay (FOPTD) systems. In this paper, the controller design for unstable FOPTD systems cascaded in series with stable/unstable FOPTD systems is considered. The proposed method is based on equating the coefficients of corresponding powers of s and s ² in the numerator to α ₁ and α ₂ times those of the denominator of the closed-loop transfer function for a servo problem. The open loop system consists of an unstable FOPTD system cascaded in series with a stable/unstable FOPTD system. Only two tuning parameters (α ₁ and α ₂) are required for the design of controllers. The closed-loop performances are evaluated for both the servo and regulatory problems and the performances are found to be better than that of the well established synthesis method. The robustness for uncertainty in the model parameters is studied and compared with that of the controllers designed by the synthesis method.