Understanding PID Controller for Motor Speed Control

Student
Professor
Control and instrumentation
Date

a. The difference between the desired and the actual output in the controls system is referred
to as tracking error. In the motor speed control system, tracking error is due to external
disturbances, such as change in the torque the load connected to the motor, which in turn
change parameters of the system. Eventually a difference between the potentiometer
input set placed to monitor the change and the actual motor speed is noted. The difference
is what is called error signal. The controller is thus responsible for controlling the speed
of the motor. The process is described briefly below. The tracking error is fed to the
controller, in our paper we shall consider PID controller. PID controller will then
performs error signal’s integral and derivative in respect of time. Output of the controller
(control signal) which is equal to derivative gain (Kd) times time derivative of tracking
error plus proportional gain times tracking error plus integral gain (Ki) times time
integral of tracking (equation 1), is fed to the plant.
U(t)=Kp*e(t)+Kd*d/dt(e)+Ki*integral of e(t)............1
The new output from the plant based on the control signal from the controller is then
feedback and compared with input reference signal, to find new tracking error, and the
same process continues.
b. Transfer function of a proportional integral derivative (PID) is given by the equation
below. Which is obtained by doing a Laplace transform of equation 1
Gc(s)=Kp+Ki/s+Kd*s.......................................2
Where Kd is the derivative gain, Ki the integral gain and Kp the proportional gain.
Proportional gain (Kp) increases control signal proportionally for the same error level.
Effects of proportional gain can be summarized by these two effects. First, it causes a
decrease in the steady-state error and rise time of the system. Then secondly, it causes an
increase in the overshoot and significantly small changes in settling time. Adding
derivative gain to the controller makes it predict the error. With derivative term upward
sloping of error signal causes a significant increase of control signal, even when the size
of error is way too low. This prediction for error signal causes damping effect to the
system. While derivative gain (Kd) does not affect steady-state error, it causes a decrease
in both overshoot and settling time. And finally, derivative gain causes a small variation
in rising time. Integral gain (Ki) keeps building if steady state error persist, this leads to