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Automotive Control

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Submitted By naman12345
Words 506
Pages 3
ME 50400 and ECE 59500
AUTOMOTIVE CONTROL
Home Work Set 5
Note: You may make any reasonable assumption in case of missing parameter(s).
1. Consider the linearized vehicle model with state variables as vehicle body side slip angle and vehicle yaw rate. This model captures the vehicle dynamics in X-Y and  (yaw) directions. Using the vehicle dynamics equations for a reduced single track vehicle model along with the wheel models, build a
SIMULINK model that will have the output as yaw rate. Plot the step response for a steering angle input.  cF  cR
   m .v

CoG CoG
   c l c l

F F
   R R

JZ


cR lR  cF lF  cF 

 1
2
 m .v 
  mCoG .vCoG
     CoG CoG  W
2
2
 c R l R  c F l F     c F l F 




JZ
J Z .vCoG




  y  0 1 

 
Also determine the stability limits for the open loop transfer function via root locus. The vehicle parameters are as follows: mCoG = 1450 kg; vCoG = 15 m/s; lF = 1.05 m; lR = 1.5 m; JZ = 2545 kg-m2; cF = 25500 N/rad; cR = 62000
N/rad; Iwi = 1.1 kg-m2; reff = 0.3 m;
2. For the vehicle parameters stated in problem 1, design a steering-based (control input being w) yaw stability control system with proportional-integral-derivative (PID) terms to obtain a desired natural frequency of 9 rad/sec and damping ratio of 0.5. Also, assume that the vehicle is 1.5 m wide and center of gravity is located at the center. Determine the closed loop system response for step and ramp inputs.
What are your PI gain values? Note your observations on the stability of the closed loop system.
3. Given the vehicle parameters in problem 1, design a PI (proportional plus integral) anti-lock brake control system for the vehicle to maintain a desired slip ratio of 0.15. Assume that the desired damping ratio of 0.6 and desired natural frequency is 10 Hz for this problem. Assume that the road surface is covered with packed snow with a peak friction coefficient of 0.33 at a slip ratio of 0.15. Also, assume that the static weight distribution of the vehicle weight is 60% front axle and 40% rear axle. You may neglect the dynamic weight transfer due to deceleration and steering. Plot the step response for both front and rear wheel (for both open loop and closed loop systems).
4. Design an engine-torque control based traction control system (PD - proportional plus derivative) to maintain wheel acceleration slip ratio at 0.2. Assume no engine intervention. Also assume that the road surface and static vehicle weight distribution are same as in problem 3. Assume that the desired damping ratio of 0.7 and desired natural frequency is 6 Hz for this problem. Use the vehicle parameters stated in problem 1, as necessary. Plot the step response for both front and rear wheel for both open loop and closed loop systems.

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