Based on data and design criteria provided provided had to develop a PI controller for Cruise Control of a vehicle in Simulink

1. Problem Statement 1:

2. Simulink Model
Case 2:
I implemented this equation in the simulink model
 I propose a PI controller for this problem statement. I had also checked and tried
with a PID controller but the PI was giving me enough leverage on the full scale of
the problem statement.
 The gain selected can be seen below:

3. Problem Statement 2:

4. Simulink Model
Case 2(D):
I implemented this equation in the Simulink model:
I kept the same PI controller with the same gain as in case of problem statement 1
and system response in terms of design criteria is satisfied.

5. Case 3(E):
fr has a variation of 5%
I implementedthis to check in the Simulink model by putting a gain of 0.95 and
1.05 to test each case.
Case 4(E):
Note : Gain2=Gain4=Gain7=(Cd*A*Dens)/(2*m)

6. Case 5(F):
Gain=g*k+ (Cd*A*Dens)/ (2*m)
In all the 4 cases a PI controller witha proportional gain of 800 and an integral gainof
35 meets all the design requirements.
Summary of all cases:
Rise time
Max
Overshoot
Steady State
Error
Settling
time
Peak Time
Steady State Value
of Traction Force,U
sec % - sec sec Nm
Case
1
3.8 2.8 0 20 8.5 500
Case
2
3.54 6.5 0 37 8.5 165.46
Case
3
3.54 6.6 0 37 8.5 161.15
Case
4
3.54 6.5 0 37 8.5 176.15
Case
5
3.54 6.5 0 36.5 8.5 178.15
Note:I have takena saturationblock after the PI controller for engine torque demand
taking into account a FDR of 5 and hence saturation at 2500Nm for safety of the
transmission since most passenger cars won’t have a Final Drive Ratio above 5

7. Comparison of the velocity trend for the different cases:
 Overshoot increases when we take the actual parameters (friction and
aerodynamic drag) into account. Alsoat kick off these is a slight lag due to the
increased resistive forces.
Comparison of the traction force for the different cases:
 Tractionforce requiredtocontinue inthe steady state is more realistic whenwe
consider the actual parameters(aerodynamic drag and actual friction)
 As expectedwhenfrictionis lower we needlower steady state tractionfor and
vice versa