State Observers Design for Controlling the Vehicle Brake Dynamic Behaviour

The brake squeal noise generated during the duty of brake is a common problem and more is a complicated in the vehicle and has not been solved till now. Generally, contacting of two bodies to each other with unstable oscillation generates the squeal noise. Minimizing this brake squeal noise during the duty of the brake is very important for the comfort of the passengers and stability of the car. A multi-degree-of-freedom mathematical model has been built to study the effect of the different parameters on the brake squeal noise. The state-space equations developed have been solved using the program MATLAB. The program has been used in this study to calculate the complex eigenvalues, which indicate the natural frequencies and the instability of the system. It is evident from the analysis that the squeal noise of the brake is a self-induced vibration and generally divided into two groups, the first group is the low frequency vibration less than 1 kHz and the second group is the high frequency vibration more than 1 kHz till 15 kHz that involved in the paper. The system is considered to be completely state controllable and hence it will be “observable”, then poles of the closed-loop system will be placed at a desired location by means of state feedback through the state feedback gain matrix.

This term of observability is found to be important because, in practice, the difficulty encountered with state feedback control is that some of the state variables are not accessible for direct measurement, with the result that it becomes necessary to estimate the immeasurable state variable in order to construct the control signals.