CONTROL OF AN AUTOMOTIVE SUSPENSION SYSTEMCONTENTSINTRODUCTIONOBJECTIVESSYSTEM VARIABLESTECHNICAL SPECIFICATIONSDESIGN STATE SPACE REPRESENTATION4.1 DIFFERENTIAL EQUATIONSTABILITY ANALYSIS BASED ON EITHERVALUESFO NCTIONS YAPUNOVIMULATIONS USING MATLAB6. 1 MATLAB CODE FOR STEP ANSWERCONCLUSION REFERENCES1. INTRODUCTION: 1.1 OBJECTIVE: The main theme of the project is to take a control system from any source and make it stable by making appropriate modifications. After making the system stable, we need to perform the stability analysis either by eigenvalues ​​or by Lyapunov function and simulate the obtained transfer function to check the stability. We will use Mat Lab for computer simulation, for a step-by-step answer. Control system: A control system is a device that manages, commands, directs or regulates the behavior of other devices or systems. A feedback control system plays a vital role while designing a control system. It has the ability to take into account the system output and helps the system adjust to meet the design criteria. An automatic control system has played a major role in the advancement 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 and manufacturing industries and in the design of cars and trucks in the automobile industry. 1.2 SYSTEM VARIABLES: An automobile suspension system is a system that is responsible for the safety and smooth driving of the vehicle by avoiding disturbances caused by small dips and holes in the road. The suspension carries all the weight of the vehicle on the tires, so it must have active and semi elements...... middle of paper .......1 MATLAB CODE FOR ANSWER TO STEP: 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. stepped response of the suspension systemFig. root locus7.CONCLUSIONS: The vehicle suspension control system was found to be stable when we use both eigenvalues ​​and Lyapunov stability. The frequency response of the matlab was generated using the step response. As the eigenvalues ​​turned out to be negative, they were placed on the left side as much as possible, which is illustrated by the root locus graph. The main control element is in the form of a shock absorber and actuator for the suspension system. A system was modeled in state space and equations were derived and transfer functions were derived. The system turns out to be asymptotically stable.