Design of Static Output Feedback and Structured Controllers for Active Suspension with Quarter-Car Model

Abstract

This paper presents a method to design active suspension controllers for a 7-Degree-of-Freedom (DOF) full-car (FC) model from controllers designed with a 2-DOF quarter-car (QC) one. A linear quadratic regulator (LQR) with 7-DOF FC model has been widely used for active suspension control. However, it is too hard to implement the LQR in real vehicles because it requires so many state variables to be precisely measured and has so many elements to be implemented in the gain matrix of the LQR. To cope with the problem, a 2-DOF QC model describing vertical motions of sprung and unsprung masses is adopted for controller design. LQR designed with the QC model has a simpler structure and much smaller number of gain elements than that designed with the FC one. In this paper, several controllers for the FC model are derived from LQR designed with the QC model. These controllers can give equivalent or better performance than that designed with the FC model in terms of ride comfort. In order to use available sensor signals instead of using full-state feedback for active suspension control, LQ static output feedback (SOF) and linear quadratic Gaussian (LQG) controllers are designed with the QC model. From these controllers, observer-based controllers for the FC model are also derived. To verify the performance of the controllers for the FC model derived from LQR and LQ SOF ones designed with the QC model, frequency domain analysis is undertaken. From the analysis, it is confirmed that the controllers for the FC model derived from LQ and LQ SOF ones designed with the QC model can give equivalent performance to those designed with the FC one in terms of ride comfort.

Design of Static Output Feedback Controllers for an Active Suspension System

“…Among several controller design methodologies proposed for active suspension control, the linear quadratic regulator (LQR) has been adopted because it can provide a systematic way to design a full-state feedback controller for active suspension by tuning the weights of performance measures such as the ride comfort and road adhesion [1,4,27]. The LQR has been designed with state-space equations derived from the 2-DOF quarter-car, 4-DOF halfcar and 7-DOF full-car models.…”

“…On the other hand, the 7-DOF full-car model is most relevant to actual vehicles because it describes the vertical, roll and pitch motions of a single sprung mass and the vertical motions of four unsprung masses [23]. However, a controller designed with the quarter-car model has not been applied to the full-car case except in one study [27]. An active suspension controller has also been designed with the full-car model in case the designed controller is to be applied to actual vehicles [20,21,27].…”

“…However, a controller designed with the quarter-car model has not been applied to the full-car case except in one study [27]. An active suspension controller has also been designed with the full-car model in case the designed controller is to be applied to actual vehicles [20,21,27].…”

“…Generally, a Kalman filter has been adopted as a state observer for a full-state feedback controller or LQR. To date for active suspension control, the combination of Kalman filter and a LQR, i.e., the linear quadratic Gaussian (LQG), has been studied extensively [27][28][29][30].…”

“…Because there are no guaranteed methods by which to find a stabilizing or optimal controller for LQ SOF control, a heuristic optimization method is applied to find an optimal gain matrix in this case. Then, the LQ SOF controller designed with the quarter-car model is directly applied to the full-car model consider the fact that each corner of the full-car model can be regarded as the quarter model [27]. It can be expected that this controller has little effects on the roll and pitch angles of the sprung mass because it cannot use the roll and pitch angles or the rates for feedback due to the quarter-car model.…”