A Convex Optimization Approach in Drive Train Anti-Jerk Control with Measurements of Uncertain Delay

Abstract

Abstract This article presents a convex optimization approach in the synthesis of H 2 delay independent observer-based controller for the control of linear systems with uncertain delay in measurements. The motivation for this technique is highlighted by the sensitivity of stability of the conventional linear quadratic regulator (LQR) against such delay in the example of drive train anti-jerk control in vehicles with electric single-wheel drives. The stability constraint for this approach guaranteeing the asymptotic stability of the closed loop system is derived from Lyapunov-Krasovskii functional and then specified in terms of LMIs. The related H 2 performance is achieved by minimizing a chosen quadratic cost functional which is convex in matrix variables associated with LMIs. An observer-based controller which guarantees asymptotic stability and H 2 performance is developed and its effectiveness is demonstrated in the active damping control of drive train oscillation.