Design, analysis and application of a new disturbance rejection PID for uncertain systems

In this paper, a new disturbance rejection proportional–integral–derivative (DR-PID) scheme is proposed for a class of minimum phase plants with low relative order. The essential active disturbance rejection (ADR) mechanism that is otherwise hidden in PID control structure has been illuminated and clarified in this paper for the first time.The proposed DR-PID scheme is derived on the basis of a modified disturbance observer to embed the active disturbance rejection mechanism seamlessly in the classical PID structure. Such a DR-PID scheme is implemented in a typical two-degree-of-freedom control structure that contains a standard PID controller and a pre-filter. The internal stability condition is established by investigating the closed-loop poles according to Rouche’s theorem. The ensuing internal stability condition provides effective guidelines for DR-PID design that has infinite gain margin with minimum plant information. Five numerical comparisons are performed to illustrate the effectiveness of the new DR-PID scheme. The physical realizability of the proposed DR-PID scheme is also demonstrated by experiments on a magnetic levitation system. •The active disturbance rejection mechanism of PID controller is clarified for the first time.•A new and simple disturbance rejection PID control scheme is proposed.•New internal stability conditions for PID control are established.•The proposed PID control systems have infinite gain margin.