Active control of quarter-car and bridge vibrations using the sliding mode control

Abstract

Purpose: The aim of this study is to model the active suspension system using conventional PID and sliding mode control, which is a robust control method, in order to increase the road holding and passenger comfort (Figure A). Theory and Methods: The equations of motion of the 3-degree-of-freedom quarter-car and bridge model examined in this study were obtained by the Lagrangian method. A total of 7 second-order differential equations were obtained, including 3 equations of motion of the car and 4 equations of motion of the bridge beam. These equations are reduced to 14 first-order differential equations with the help of state space forms. Then, the Runge-Kutta method was used to solve these equations. The dynamic responses of the quarter car while passing over the bridge were analyzed with the commercial analysis program MATLAB. Results: As a result of the study, it was understood that the displacement and acceleration values of the passenger seat take their maximum values at the critical speeds of the car-bridge and car-road system. In addition, it is understood that the dynamic responses acting on the car change at some speed value of the car according to the profile of the road. Conclusion: In this study, the vertical displacement and acceleration of the passenger seat were controlled using conventional PID and sliding mode control. In addition, the dynamic interaction between the any flexible foundation and the multi-degree-of-freedom car model can be examined in more detail by using the controllers and solution method used in this study.