A Study of H infinity and H2 synthesis for Active Vibration Control

Minimization of car vibrations has been a topic of research over the years and many control strategies have been developed. Therefore, there needs to be a method for active vibration control in cars. This paper presents two methods for designing the controller for a quarter car model which would help in minimizing car vibrations and increasing passenger comfort subjected to road disturbances. The methodologies used are H-infinity and H-2 optimal control. The main aim of this article is to design a controller to control the response of a quarter car model to various road inputs. This is a non-linear model with 2 degrees of freedom. It is linearized and modelled as a disturbance rejection (regulatory) problem wherein the effect of disturbances are minimised. Different weighing functions have been considered to take the impact of road disturbances into account. The results are compared with the Proportional Integral Derivative (PID) controller designed using the same system parameters and performance specifications. The behaviour of the open loop and closed loop system is observed by examining the impulse and frequency responses in MATLAB. A detailed discussion is done with the choice of weighing functions. It is found that the disturbance rejection techniques suggested in this paper help in improving the system response