# Control of an Automobile Suspension System Essay

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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…show more content…
Mass1 is the mass of the body, Mass2 is the Suspension mass of the wheel, C1 is the suspension damping constant and C2 is the damping constant of wheel and tire assembly, k1is the spring constant in the suspension system and k2 is the spring constant of the tire, Xr represents the road input force, X1 force acting on Mass1, X2 the force acting on Mass2 and f represents the control element. Body mass M1= 1350kg Suspension mass, M2 = 165 kg Spring suspension constant, K1 = 52000N/m Spring constant of wheel and tire, K2 = 380000N/m Damping suspension constant, C1 = 280 Ms/m Damping wheel and tire constant, C2 = 12010 Ms/m 3. DESIGN:The dynamic equations of a suspension system for the body mass is M1 X1 = -C1(X1-X2)-K1(X1-X2)+f And the dynamic equation for spring mass is given by M2 X2 = -C1(X1-X2) + K1(X1-X2) +C2(W-X2)+K2(W-X2) – f The above equations are at times when the initial conditions are considered , like a small pit on the road. These equations can be transformed into transfer function by using the laplace transform of above equations. By using the input conditions the output of the transfer function is as follows G(s) = 1+10S/(200S2+16.64S+2) 4.STATE SPACE REPRESENTATION: The state space equations are found out by using MatLab as follows [■((x_1 (t)) ̇@(x_2 (t)) ̇ )] = [■(-0.0817&-0.0103@1.000&0)]*[■(x_1 (t)@x_2 (t))]+[■(1@0)] * u (t) y(t) =