Control of Automotive Systems
These three projects were carried out under Dr. Srikanthan from the Department of Engineering Design, IIT Madras. These were part of the graduate level course Controls of Automotive Systems.
1. Active Suspension Control Using a Quarter Car and Half Car (Roll) Model
First the equations of motion for the quarter car and half car (roll) models were derived and each converted into a state space representation.
The road excitation is the input for the quarter car model while the road is assumed to be flat for the half car model, the input disturbance is the lateral acceleration of the vehicle. The quarter car model has one actuator while the half car model has two, one for each wheel.
Quarter Car Model
Half Car (Roll) Model
Quarter Car Model Analysis
Effect of variation of tire stiffness
A sensitivity study on the various parameters - suspension spring stiffness, tire stiffness, suspension damping was carried out. The changes in tire deflection and sprung mass acceleration were studied on Bode plots and the trends were explained.
Then, an LQR controller was designed whose closed loop performance is compared below versus the open loop response of the same system on a Bode plot.
LQR Controller Closed Loop vs Open Loop
Half Car (Roll) Model Analysis
An LQR controller was developed for the roll model as well and compared against the open loop system. The angular displacement of the sprung mass is
Impulse Response, LQR vs Open Loop
Rectangular Wave, LQR vs Open Loop
2. Heading Angle Control for an Autonomous Ground Vehicle System
First the governing equations of the Bicycle Vehicle Model were derived and then converted into a state space representation with the steering angle as an input.
Then a P and PI controller were individually tuned to meet certain design specifications at low speed. With the tuning fixed, the performance of the controllers were evaluated at 2 higher speeds.
It was observed that at higher speed the vehicle becomes more agile and often has overshoot. At low speeds the system's response is much slower.
Source: Jazar, R.N, Vehicle Dynamics: Theory & Application, Springer.
PI controller's performance at different speeds
Steering actuator effort at different speeds
3. Design of a Controller for an Electro-Pneumatic Brake System
Given data for the step response of an electro-pneumatic brake system, the transfer function of the system was approximated as a first order system with a delay.
Then a P and PI controller were each tuned to meet certain design specifications - a restriction on the steady state error and that of the actuator effort (physical limitation).
Actual System Response, Model Response
All figures are mine.