Set-point weighted PID controller tuning for time-delayed unstable processes

The set-point weighted proportional, integral, and derivative (PID) controller has been shown to be equivalent to an error feedback PID controller with a PD controller in the inner loop; and, many nonerror feedback designs have been unified under the frame of tuning the set-point weighted PID controller. A simple method is then proposed to reform an existing PID control system into a set-point weighted PID control system for unstable processes. To reform an existing error feedback PID control system into the set-point weighted PID control system, the proposed method needs neither the information of the process nor the information of the design methods of the original error feedback PID control system. The only information needed to reform the existing PID control system is the values of the tuning parameters of the original error PID control system. Theoretical analysis shows that if the original error feedback PID control system is stable, the stability of the proposed set-point weighted PID control system is guaranteed automatically. Simulation results show that the performance of the proposed set-point weighted PID control system can be effectively enhanced in comparison with that of the original error feedback PID control system; further, this performance of the proposed set-point weighted PID control system is comparable to that of many other nonerror feedback systems reported in the literature.