Design a pi controller for the displacement of load element

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Reference no: EM132171612

Using MATLAB The project is to design a PI controller for the displacement of a load element.

The simple model of the system is shown above with a mass m in addition to the viscous damping b.

Assume the input is the load u and the output is the displacement x. m= 14kg b=2.9 N-s/m 1-Derive the Transfer Function of the system (plant) before adding the controller.

The input is the load u and the output is the angular displacement x. (e.g. TF(s) = X(s)/U(s)). 2-Use Simulink to draw the block diagram of the system. Plot the time-response of the displacement x due to a unit-step input of the load u. Discuss the stability and the steady-state error.

3-For the same model in (2), add a unit-step disturbance D(s) to the system, and plot the time- response of the displacement x.

The unit-step input of the load u is unchanged. Discuss the stability and the steady-state error.

4-Add P controller to the system model in (3).

In a new Simulink model, redraw the block diagram of the new model with the P controller. a-Plot the root locus of the system with P controller using Matlab.

b-Use low, mid-, and high values for Kp and plot the time-response of the displacement x due to a unit-step reference input with and without unit-step disturbance D(s).

Discuss the stability and the steady-state error in all cases. Briefly describe how your controller will respond to the disturbance D(s).

5-Add PI controller to the system model in (3).

In a new Simulink model, redraw the block diagram of the new model with the PI controller. a-Plot the root locus of the system with PI controller using Matlab. Also plot the root locus of the system when Kp = 0 (i.e. only the I controller is used). b-For Kp = 0, use low, mid-, and high values for Ki and plot the time-response of the displacement x due to a unit-step reference input with and without unit-step disturbance D(s).

Discuss the stability and the steady-state error in all cases. Briefly describe how your controller will respond to the disturbance D(s). 6-Repeat (5-b) using Low, mid-, and high values of Kp. Give a brief conclusion. m= 14kg b=2.9 N-s/m.

Reference no: EM132171612

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