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Research Papers

# Predictive Control of Suspension Systems Through Combining Dynamic Matrix and Constrained Variable Structure Controllers

[+] Author and Article Information

Department of Systems Design Engineering,
University of Waterloo,
200 University Avenue West,
e-mail: amozaffari@uwaterloo.ca

Alireza Doosthoseini

Department of Mechanical Engineering,
K. N. Toosi University of Technology,
No. 17 Pardis Street, Vanak Square,
Tehran 19991-43344, Iran
e-mail: doosthoseini@kntu.ac.ir

Department of Systems Design Engineering,
University of Waterloo,
200 University Avenue West,

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 23, 2016; final manuscript received July 2, 2016; published online August 19, 2016. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 138(12), 121007 (Aug 19, 2016) (19 pages) Paper No: DS-16-1053; doi: 10.1115/1.4034157 History: Received January 23, 2016; Revised July 02, 2016

## Abstract

In this paper, a controller called dynamic matrix constrained variable structure controller (DM-CVSC) is proposed. The controller takes advantages of both dynamic matrix (DM) and constrained variable structure controllers. As a result, DM-CVSC is a robust trajectory tracking controller dealing with the constraints on control inputs and also makes decision based on the future behavior of the vehicle. The controller is applied to a linearized model of half-car suspension systems which are subject to different types of road disturbances and measurement noises. In this paper, it is shown that there is a simple formulation for calculating the range of sliding gains for single-input single-output (SISO) linear control systems. As for the multi-input multi-output (MIMO) linear control systems, the calculation of upper sliding gain profile for controller leads to a search problem. To show the efficiency of the proposed controller, it is applied to four different cases involving specific road disturbances and measurement noises. The performance of the proposed controller is compared to various control techniques.

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## Figures

Fig. 1

Schematic illustration of 4DOF half-car model

Fig. 2

Displacements of front and rear body mass for the nonpredictive controllers for the four case studies

Fig. 3

Displacements of front and rear body mass for the rival predictive controllers for case 1

Fig. 4

Displacements of front and rear body mass for the rival predictive controllers for case 2

Fig. 5

Displacements of front and rear body mass for the rival predictive controllers for case 3

Fig. 6

Displacements of front and rear body mass for the rival predictive controllers for case 4

Fig. 7

Control effort of front and rear actuators calculated by DM-CVSC, CVSC, and SMC

Fig. 8

Capability of controllers constraint handling for DM-CVSC, CVSC, and SMC

Fig. 9

Control effort of front and rear actuators calculated by DMC and DM-CVSC

Fig. 10

Detailed variation of control commands in the critical range for DMC and DM-CVSC

## Errata

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