Control of an Automobile Suspension System

CONTROL OF AN AUTOMOBILE SUSPENSION SYSTEM

CONTENTS

INTRODUCTION

OBJECTIVE

SYSTEM VARIABLES

TECHNICAL SPECIFICATIONS

DESIGN

STATE SPACE REPRESENTATION

4.1 DIFFERENTIAL EQUATION

STABILITY ANALYSIS

BASED ON EIGEN VALUES

LYAPUNOV FUNCTION

SIMULATIONS USING MATLAB

6.1 MATLAB CODE FOR STEP RESPONSE

CONCLUSION

REFERNCES

1. INTRODUCTION:

1.1 OBJECTIVE: The Main Theme of the project is to take a control system from any source and make it stable by doing appropriate changes. After making the system stable, we have to do the stability analysis either by Eigen values or by lyapunov function and simulate the obtained transfer function to check for stability. We are going to use Mat lab for the computer Simulation, for step response.

Control System: A Control system is a device thatmanages, commands, directs or regulates the behavior of other devices or systems.

A Feed Back Control system plays a vital role while designing a Control system. It has the ability to take the system output and helps the system to adjust itself to meet the design criteria. An automatic control system has played a major role in the advance of engineering technology. In addition to its major importance in vehicle suspension systems Automatic control is also useful in the numerical control of machine tools andin the manufacturing industries and in the design of cars and trucks in the automobile industries.

1.2 SYSTEM VARIABLES: An automobile suspension system is one which is responsible for a safety and smooth driving of the vehicle by avoiding disturbances, caused by small pits and holes on the road. The suspension carries the whole weight of the vehicle on the tires, so it should have some active and semi ...

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....1MATLAB CODE FOR STEP RESPONSE:

a= [10 1]

b = [200 16.64 2]

s=tf(x,y)

[A,B,C,D]=tf2ss(x,y)

eig(A)

step(a,b)

rlocus(a,b)

stepinfo(s)

Fig. step response for the suspension system

Fig. root locus

7.CONCLUSIONS:

The control system on vehicle suspension was found to be stable when we use both the Eigen values and the Lyapunov stability.

The frequency response for the matlab was generated using the step response

As the Eigen values were found to be negative , they were placed on the left side as much as possible and this is shown by root locus graph.

The main controlling element is found as an damper and an actuator for the suspension system.

A system has been modeled in state space and equations have been derived and the transfer functions have been derived.

The system is found to be asymptotically stable.