Synthesis of robust PID Control systems using stability feeler and partial model matching

In this paper, we propose a new method for the synthesis of robust proportional, integral, and derivative (PID) control systems. The proposed method is based on the idea of partial model matching. The stability feeler, a tool for robust stability analysis, is used to stabilize closed-loop systems with uncertainties. An advantage of the proposed method is that it guarantees robust stability of control systems. To clarify the effectiveness of the proposed method, two types of simulations are given. One is the case where the nominal plant is not stable. The other is the case where the plant is not robustly stable although the nominal plant is stable. The simulation results when the nominal plant is not stable show that the controller derived by the proposed method robustly stabilizes the closed-loop system, whereas that derived by conventional partial model matching method cannot stabilize it. Moreover, when the plant is not robustly stable, it can be seen that the controller by the proposed method can robustly stabilize the system. Therefore, it is shown that the proposed method enables one to derive PID controllers robustly stabilizing closed-loop systems.