Experiment 4: Position Control Systems
Introduction
The objective of this lab is to convert the DC motor to an electromechanical positioning
actuator by properly designing and implementing a proportional and a proportional-plus-
derivative (P-D) controller. Simulation and design values for the controller gains
computed in the pre-lab will be compared to values obtained by empirical testing.
Pre-lab
The pre-lab uses previous lab results as well as an understanding of the proposed closed
loop system. Refer to the Implementation Diagrams in: Figure 2, Figure 3 and Figure 4
for guidance. Ensure to take into account all the gains!
1. Using integration in the Laplace domain, derive the transfer function for motor
position from the velocity transfer function obtained in lab 2 and lab 3.
2. Place the position transfer function in a unity feedback loop with proportional
gain controller. See Fig 2 (use it as a guide only). Calculate the closed loop
transfer function of this system and choose Kp (using Equation 1and Equation 2)
to satisfy the following designs with their constraints. If not possible, explain
why:
Design 1:
i. Peak overshoot < 10 % (Use Eq.1 below or text Fig.4.16)
ii. Settling time < 180 msec
Design 2:
i. Peak overshoot < 10 % (Use Eq.1 below or text Fig.4.16)
ii. Settling time < 600 msec
Equation 1: Peak overshoot
2
1
eM
p
Equation 2: Settling time
n
s
t
6.4
3. Change the controller in the previous question to a P-D as shown in Figure 3.
Calculate the closed loop transfer function and choose values of Kd and Kp so as
to satisfy the same design constraints as in question 2, Design 1.
4. Adjust the system to feedback the voltage from the tachometer as well as from the
output potentiometer as in Figure 4. Then choose Kp and Kp1 to satisfy the same
design and the constraints from question 2, Design 1.
