Question

control system

Design a system that will run on a PID process

Answer 1

Let us Design a DC motor speed control system which is operated by a PID controller for optimum tracking of the setpoint (speed). In this segment, the mathematical model and the transfer function of a DC-Motor will be described and the control phenomenon will be simulated in MATLAB/SIMULINK environment for the demonstration of the input-output responses.

Mathematical Modelling of DC-Motor:

The system dynamics can be represented by these differential Equations:

Where,

J is the moment of inertia 
b is the viscous friction of the motor 
Ke is the EMF constant
Kt is the torque constant of the motor
R is the resistance
L is the inductance 

The equations above can be written in the Laplace domain as:

So, the transfer function can be determined as:

Let us choose arbitrary parameter values for the motor to be demonstrated:

So the transfer function becomes:

Now, simulating the DC-Motor with the help of a PID control in SIMULINK under a step input with amplitude 2000:

Model:

Output:

From the output Response graph, you can see that our desired speed 2000 RPM is tracked successfully with very small oscillation and settling time with the help of a PID controller.

The PID parameters are:

Kp = 2, Ki = 10, Kd = 1.