**Fuzzy Based Scalar Control of Induction Motor**

### Explanation of Simulink Model

The Simulink model developed for fuzzy logic-based control of scalar control of an induction motor consists of the following elements:

DC source

Voltage source inverter

Induction motor

Here, we are using fuzzy logic-based speed control as well as PID speed control.

The key steps are as follows:

**Speed Measurement:**

The speed of the induction motor is measured in radians per second.

It is then converted to revolutions per minute (RPM) by multiplying it by 602Ï€\frac{60}{2\pi}2Ï€60â€‹.

**Feedback and Error Calculation:**

The measured speed is fed back and combined with the reference speed to calculate the error and rate of change of error.

These values are inputs for the fuzzy logic controller.

**Fuzzy Logic Controller Output:**

The output of the fuzzy logic controller is the slip speed (Ï‰sl\omega_{sl}Ï‰slâ€‹).

The slip speed is added to the actual speed of the induction motor to provide the speed that needs to be maintained.

**Frequency and Amplitude Calculation:**

The calculated speed is converted into frequency using the formula f=PÃ—Ï‰120f = \frac{P \times \omega}{120}f=120PÃ—Ï‰â€‹.

This frequency is converted into amplitude and used to generate a three-phase sinusoidal waveform as a reference.

**Pulse Generation:**

The reference voltage frequency signal is compared with a triangular wave to generate pulses for the voltage source inverter, controlling the induction motor.

### Simulation Results with PID Control

First, we simulate the model using a PID controller with the following reference speed changes:

Initially set to 1500 RPM.

Changed to 1000 RPM after 5 seconds.

The response of the induction motor with PID control is as follows:

There is an overshoot and undershoot in the speed response.

It takes around 3 seconds to reach the initial reference speed of 1500 RPM.

After the speed change to 1000 RPM, it takes around 1.5 seconds to settle to the new reference speed.

### Simulation Results with Fuzzy Logic Control

Next, we simulate the same model using a fuzzy logic-based controller.

The response of the induction motor with fuzzy logic control is:

The speed response is very smooth without overshoot or undershoot.

It reaches the reference speed of 1500 RPM in about 1.25 seconds.

After the reference speed changes to 1000 RPM, it quickly settles to the new speed in about 0.3 seconds.

### Comparison of PID and Fuzzy Logic Control

When comparing the PID and fuzzy logic controllers:

The PID controller exhibits overshoot and undershoot, taking longer to reach the reference speed.

The fuzzy logic controller provides a smooth response, reaching the reference speed quickly without overshoot or undershoot.

### Conclusion

The fuzzy logic-based scalar control has a better response compared to the PID controller. It quickly tracks the reference speed command and provides a smoother operation.

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