Design of Static Output Feedback Controllers for an Active Suspension System

Abstract

This paper presents a method by which to design linear quadratic (LQ) static output feedback (SOF) controllers with a 2-DOF quarter-car model for an active suspension system. Generally, it is challenging to implement linear quadratic regulator (LQR), designed with a full-car model, in actual vehicles because doing so requires 14 state variables to be precisely measured. For this reason, LQR has been designed with a quarter-car model and then applied to a full-car model. Although this requires far fewer state variables, some of them are still difficult to measure. Thus, it is necessary to design a LQ SOF controller which uses available sensor signals that are relatively easily measured in real vehicles. In this paper, a LQ SOF controller is designed with a quarter-car model and applied to a full-car model for ride comfort. To design the controller, an optimization problem is formulated and solved by a heuristic optimization method. A frequency domain analysis and a simulation with a simulation package show that the proposed LQ SOF controllers effectively improve the ride comfort with an active suspension system.INDEX TERMS active suspension control, static output feedback control, 2-DOF quarter-car model, 7-DOF full-car model, linear quadratic regulator

Design of Virtual Reference Feedforward Controller for an Active Suspension System

“…In the previous literature, LQRq was designed for a full-car model under the assumption that a full-car model can be composed of four quarter-car models [33,34]. The controller derived from LQRq for the full-car model was called LQRfq.…”

“…As shown in ( 6) and ( 11), LQRq and LQRfq do not need roll and pitch angles of a sprung mass for feedback control. However, it was shown that LQRq and LQRfq improved the roll and pitch motions of a sprung mass without measuring the roll and pitch angles of a sprung mass [34].…”

“…These signals have been used for semiactive suspension control [44][45][46][47][48]. In the previous work, it is assumed that the suspension stroke and its derivative are available to determine the control inputs [34]. This paper follows the assumption.…”

“…In this paper, the heuristic optimization method, CMA-ES, is applied to determine the optimum gain matrix KSOF [49]. A detailed description of the optimization procedure with CMA-ES can be found in the previous work [34]. Let denote the LQ SOF controller, KSOF, which is obtained by solving (15), as LQSOFq.…”

“…As shown in Fig. 1, a 2-DOF quarter-car model is adopted as a vehicle model because a controller designed with it can be directly applied to the full-car model [33,34]. In this paper, a virtual reference on heave motion of a sprung mass representing a bump is defined with an exponential function or a normal distribution, regardless of a real bump profile.…”