Comprehensive Report: PID Controller in Motor Speed Control System

This report delves into the application of Proportional-Integral-Derivative (PID) controllers in motor speed control systems. It begins by defining tracking error and the role of the PID controller in minimizing this error, explaining the controller's function in processing error signals and generating control signals. The report then breaks down the components of a PID controller, detailing the effects of proportional, integral, and derivative gains on system performance, including rise time, overshoot, settling time, and steady-state error. It highlights the advantages of PID controllers, particularly their ease of implementation and wide applicability across various industries. Furthermore, the report discusses the design process for PID controllers in motor control, including the use of open-loop response analysis and tuning methods like Ziegler-Nichols. It also contrasts the PID controller with the Smith Predictor, especially in scenarios involving dead time delays, and provides references to relevant literature.

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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

an increase in the control signal and this helps in drawing down the error. This term
however has disadvantages as it makes the system to be slow and oscillatory. The system
takes time for the integrator to unwind when there is a change in the sign of error signal.
In summary integral gain has an effect of increasing both overshoot and settling time of
the system. It also decreases rise time and steady-state error.
c. The idea of using feedback in control systems is the most powerful thing. So far, the most
dominating form of feedback used in modern society is the PID controller. The strength
of a PID mainly lies in its feasibility and ease to implement. It is also essential in dealing
with practical issues such as, avoiding integrator windup and also avoiding actuators
from saturating. PID controller is also used in a wide range of problems such as
instrumentation, motor drives, memories, automotive, flight control and many more. PID
controller comes in various forms, the controller comes as built-in controller in modern
day robotics, as single loop PID controllers, as software in PLC and other control
systems. Though the controller has been proofed important in control system, much of
the theory on it has not been captured in literature, and this has brought many mistakes
being repeated when there was a migration to pneumatics. There have been significant
interests lately and this has seen an emergence of automatic tuning, emergence of model
predictive control requiring tuned PID controllers.
d. For motor speed control, A PID controller is superior to the PI controller since it
decreases the later deteriorates the transient response while the PID is able to decrease
rise time, maximum overshoot and settling time while also eliminating the steady-state
error.
In designing a PID controller for motor control, an open-loop response of the system is
obtained to find the characteristics of the system. A proportional control is then added to
reduce rise time. Then a derivative control is added to reduce overshot. Overshoot should
be limited to a certain value to protect the motor from damage since the PID controller is
in the forward loop and its output is fed to the armature. An integral control is added to
eliminate steady-state error so that the motor can accelerate to its steady-state speed in the
shortest time. For fine-tuning the PID parameters, Ziegler Nichols tuning method or
Matlab tuning can be used.

e. An alternative to the PID controller in a slow process with dead time delay is the Smith
Predictor. An example of such a control application is a heat exchanger system where the
measured process variable is the temperature of the hot fluid that exits the exchanger and
the fluid’s temperature is regulated by a cooling liquid whose flow rate is controlled by
the Smith Predictor. The effect of regulating the cooling fluid does not yield immediate
temperature change in the hot fluid. The Smith Predictor tackles this by comparing the
actual process output with a prediction that takes into account the deadpoint. This is
essential as temperature change is a slow process. When a PID controller is used in this
scenario, since its constantly measuring the output without taking into account deadtime,
it will over-regulate the cooling liquid and cause cooling of the hot fluid below the
setpoint and the same in under-regulating the cooling liquid until setpoint is achieved.
The result is loss of stability of the system.

References
Astrom,J, & Hagglund,T (2001), The future of PID control, Lund University of Technology
Franklin, G.F., Powell, J.D. and Emami-Naeini, A., 2014. Feedback control of dynamic systems.
Prentice Hall Press.
Jung, J.W., Leu, V.Q., Do, T.D., Kim, E.K. and Choi, H.H., 2014. Adaptive PID speed control
design for permanent magnet synchronous motor drives. IEEE Transactions on Power
Electronics, 30(2), pp.900-908.
Lemus, J.P.T., Vélez, G.C. and Rodrıguez, N.J.C., 2018. PID Controller Design for DC Motor.
Tan, K.K., Wang, Q.G. and Hang, C.C., 2012. Advances in PID control. Springer Science &
Business Media.
Vilanova, R. and Visioli, A., 2012. PID control in the third millennium. London: Springer.
University of Michigan, Carnegie Mellon University and University of Detroit Mercy (n.d),
Control tutorials for MATLAB & SIMULINK[Online]. Available from
http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=ControlPID [accessed
June 20, 2019].