1. Homework-2.1: 1-DOF quarter car model.
Figure shows a 1-DOF quarter car model of a vehicle. Generate open loop and closed loop diagrams and study closed loop control for a ground motion (step input) with Matlab/Simulink.
mb=240 kg, k=16000 N/m, c=980 Ns/m
x(t): Output of body
z(t): Ground motion
u(t): Sky-hook damper (Control input)
DEU-MEE 5017 Advanced Automatic Control

2. k=16000 N/m, c=980 Ns/m (Suspension) mt=36 kg (Tyre mass)
Homework-2.2: 2-DOF quarter car model. (Preumont,p.45)
Figure shows a more detailed quarter car model with 2-DOF. Generate open loop and closed loop diagrams and study closed loop control for a ground motion (step input of 0.05 m) with Matlab/Simulink.
mb=240 kg (Body mass)
k=16000 N/m, c=980 Ns/m (Suspension)
mt=36 kg (Tyre mass)
kt= N/m (Tyre stiffness)
xb(t): Displacement of body
xt(t): Displacement of tyre
z(t): Ground motion
u(t): Sky-hook damper (Control input)

3. yG yA yB 0.05m Homework-2.3: 2-DOF half-vehicle model. L1 L2 G k u1
m=1050 kg, I=670 kg-m2 k=35300 N/m, c=2000Ns/m L1=1.7 m, L2=1.4 m
Disturbance: yA, yB (road inputs)
Control input: u1 (force actuator)
General coordinates: yg and
Control aim: Consider to reduce vehicle oscillations. G yG k u1 c L1 L2
m,I yA yB
0.05m
The mathematical model of a 2-DOF vehicle is given below.
Study the problem by using MATLAB code and MATLAB/Simulink for the step road input of 0.05 m. Desired criteria: ts should be less than 1.5 sec and the first maximum peak should be less than 0.10 degree.
a) Draw the open-loop block diagram. Find the open-loop transfer function and compare the responses.
b) Draw the closed-loop block diagram. Find the closed-loop transfer function and compare the responses.