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H2 optimal control of disturbance-delayed systems with application to vehicle suspensions
Authors:Lei Zuo  Samir A Nayfeh
Institution:  a GPRD - Automation Engineering, Abbott Laboratories, Abbott Park, IL, USA b Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
Abstract:Optimal control of systems with time delays among disturbances, such as vehicle suspensions, is a relatively simple but long-standing problem in time-delayed control. We consider the exact H2 optimal control of systems with time-delayed disturbances and develop a computationally efficient approach for controller synthesis. We extend the Lyapunov-based H2 norm computation to systems with time-delayed disturbances and then derive a concise formula to explicitly evaluate the sensitivity of the system H2 norm with respect to controller gains. Thence, a set of necessary conditions for H2 optimal control of such systems using static output feedback are obtained in the form of algebraic equations. Gradient-based methods are adapted to optimize the controller gains. The method is also extended to reduced-order and decentralized control. As an application, a passive suspension system for an eight-DOF four-wheel vehicle is designed via structured H2 optimization. The results are compared with those of a design based on a Pade expansion for the time delays and a design obtained by neglecting the disturbance delays.
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