A simple method of tuning parallel cascade controllers for unstable FOPTD systems

A simple method is proposed to design parallel cascade controllers for open loop unstable processes. A proportional (P)controller is considered for the secondary loop and a proportional integral (PI) controller is considered for the primary loop (P/PI control configuration). Coefficients of the corresponding powers of s (Laplace variable), in the numerator is matched with the coefficients of the corresponding powers of s in the denominator of a closed loop transfer function for a servo problem. Three simulation case studies are considered in this paper. The first case involves a stable secondary loop process and an unstable primary process, the second case involves both unstable primary and secondary processes and the third one, a simulation application to a nonlinear bioreactor model equations. For comparison purposes, P/PI controller design is also carried out by improved simultaneous relay autotuning method, synthesis method and minimizing ISE criterion method. It is found that the proposed method gives a better performance. Robust stability analysis using the complimentary sensitivity function is carried out. The present method is found to be more robust.