Active disturbance rejection for time-varying state-delay systems based on equivalent-input-disturbance approach

Exogenous disturbances largely affect the control performance of systems with time delays. This study considers a control problem of rejecting a disturbance in a PI control system for a time-varying state-delay plant. The equivalent-input-disturbance (EID) approach is integrated in a PI control system. An EID estimator estimates the overall effects of a time-varying delay and a disturbance. An EID estimate is combined into a PI control law to improve control performance. A less-conservative stability condition of the control system is derived using a Lyapunov-Krasovskii functional together with the Jensen's integral inequality and the reciprocally convex combination lemma. Parameters of the controllers in the system are calculated using the condition. Engine idle speed control is used to verify the effectiveness of this approach. Compared with the generalized extended-state observer and the sliding-mode control methods, our method reduced the tracking error to about one third and one sixth, respectively. This demonstrates the validity and superiority of our method.