Robust PID $\times$ (n-1) Stage PD Controller

This paper presents a design technique based on the root locus method fur a class of $n^{th}$ order plants using PID (Proportional-Integral-Derivative) x (n-1) stage PD controller. It is intended to satisfy both transient and steady state response specifications. This controller can be used instead of a conventional PID controller for the higher order plants to obtain better performances. The controlled system is approximated as a stable and robust second order controlled system. Only adjusting the controller gain, the desired performances of the controlled system are satisfied. For the stable plant including the plant with small dead time, the controlled system is made robustly stable. In case of the unstable plant, when the controller gain is adjusted higher than the critical value, the unstable plant can also be made stable. Robustness properties given by this controller proposed in this paper have also been demonstrated by numerical examples.