Lead-Compensator-Control-of-motor-using-Matlab-Simulink

Using Matlab, design a Lead Compensator control system for motor.
Target Performance Specification: 1. Phase Margin ≥ 30, 2. Steady State Error ≤ 1%

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Ciruit and Motor Free Body Diagrams

This is the circuit and motor free body diagram. Using this, we will calculate the transfer function of the plant.

After Calculation, the transfer function of the plant is equal to the equation above.

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Plant Step Response

Steady State Error exists. Also, ziegler nichols method cannot be applied to this plant.

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Bode Plot

Using Matlab, we get the following Bode Plot;

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Nyquist Plot

Using Matlab, we get the following Nyquist Plot;


For all Ks, the system is stable.

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Designing Lead Compensator

For K=5000, the Crossover Frequency is 1.04e+03 where the Phase is -136°. Therefore the PM is 44°. For Overshoot to be below 10%, PM should be equal or higher than 60°. With an extra margin of 10°, the lead compensator should compensate 26° Phase. The following is the lead compensator transfer function;

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System Result

With the feedback control system, the result are the following;

Simulink results are the following;
 

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Disturbance Rejection

System Model with Disturbance:

Sine Disturbance:

Step Disturbance:

Ramp Disturbance:

Parabola Disturbance:

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User Defined Reference Tracking

The following is the signal defined which will be a reference.

The following is the system model.

Result(Left) and Error(Right):

The error is very minimal.