Project - Speed Control of a Direct Current (DC) motor

MOTOR Schematics

By applying Kirchhoff’s law of voltage

Vs= Ra*Ia + La*(d(Ia)/dt) +Vb

Vb= Km*(d(θ)/dt); T=Kt*Ia

Here Km & Kt are the back emf and torque constants respectively

Angular velocity ‘w’=. θ

The open loop transfer function for the motor speed ‘w’ & supply voltage ‘Vs’ can be derived as

W(s)/Vs(s) = Kt/[(J*La) *s^2 +(J*Ra+B*La) *s+(B*Ra+Kt*Km)]

The state space model for poles

d/dt [. Θ; t] = [-B/J Kt/J; -Km/La -Ra/La] [. Θ; t] + [0; 1/La] Vs

y = [1 0] [. Θ; t]

The Simulation Model of the DC Motor along with the PID controller to control the speed of the motor

Case:1

The response of the DC motor by the PID controller, Kp, and Kd was taken from the Poles placement method, and Ki was taken as a random value to observe the response

With the taken PID gain values the system is able to achieve the reference signal at the end of the time period. Which is unstable control of the system.

Case:2

In case 1 we can see that more overshoot due to the high Ki value so we decrease the Ki value to

Ki =10, kept Kp and Kd as same.

From the above response found that improved rise time and settling time but overshoot is high.

To reduce the overshoot as well as settling time we will tune Ki, Kp, Kd gain values.

Case:3

By tuning the Kp and Kd values accordingly the feedback response improved that overshoot almost reduced to range of 5% -10%.

By further tuning we can achieve the better results

Case:4

After further tuning, the response achieved

• Settling time < 2s
• Overshoot <5%
• Steady State error <1%

The tuning of Ki, Kp, and Kd values and the effect on the response will be as in the below data.

Closed-loop system	Rise time	Overshoot	Settling time	Steady-state error
Kp	Decrease	Increase	Small change	Decrease
Ki	Decrease	Increase	Increase	Decrease
Kd	Small change	Decrease	Decrease	No-change

Model Configuration