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DEPARTMENT OF MECHANICAL ENGINEERING

FACULTY OF ENGINEERING

INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

MEC3825

CONTROL SYSTEMS

GROUP MEMBERS

OMAIR A A MAHROUQ 0627667

BURHANI MAKAME BURHANI 0735463

DATE OF SUBMISSION: 18/02/2010



Complex model of vehicle suspension system

Equations of motion: 1 = -b1 ( 1- 2) – K1(X1-X2) + U

M2 2 =b1( 1- 2) + K1(X2 – X1) + b2( - 2) + K2(W –X2) – U

Block Diagram:



Simple model of vehicle suspension system

Equations of motion:m + b + ky = b + ku

Transfer Function:

The input U is the height of the road.

The output Y is the height of the vehicle.

m + b + ky = b + ku

Assuming y(0) = 0, (0) = 0, and u(0¡) = 0

(ms2 + bs + k)Y = (bs + k)U

Y/U = (bs + k)/( ms2 + bs + k)

Block Diagram:



System Analysis

We will take a sample system that has the following values:

m= 1500kg, b=250Nsm, and k =50000N/m

Open loop system:

Thus our transfer function becomes

()

The block diagram for this system is:

The system response is:

Steadystate value= 1



Rise time = 0.2

Max overshoot % = 100%

Steady state error= 0

Closed loop system:

Our transfer function becomes

()



Steadystate value= 0.5

Rise time = 0.2


Steady state error= 0.5



Closed loop system with Proportional controller

Set Kp = 10


() ( )

( ) ( )






Rise time = 0.01

Max overshoot % = 89%Steady state error= 0.1

Closed loop system with Proportional and integral controller:

Set Ki = 4


()

)






Rise time = 0.01



Closed loop system with Proportional Integral Derivative controller:

Set Kd = 0.1


()

)





Steadystate value= 1

Rise time = 0.01



Conclusion

We can see the effects of the controllers clearly:

When adding the proportional controller, the rise time decreased significantly

from 0.2s to 0.01s.



When adding the integral controller, the steady state error decreased from 0.1 to

0, and thus was compeltely eliminated

When adding the Derivative controller, the Max overshoot decreased from 70%

to 50%

Thus we can see how adding controllers to the system, enhances its performance.

However, each controller while improving one system charachterisitc, will affect another,

thus a compromise must be found to suit the application.

control systems mini projectnewww - mec3825

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