09/30/12 − Page 1 EE 4314 Lab 3 Handout Speed Control of the DC Motor System Using a PID Controller Fall 2012 IMPORTANT: This handout is common for all workbenches. 1. Lab Information a) Date, Time, Location, and Report Due Please check your lab schedule on Blackboard for your lab date, time, and workbench. The lab will be held at NH250. Your lab report is due on Wednesday at 11:59 pm two weeks after your lab session. b) Preliminary Work You are required to complete the Preliminary Work given in the next section of this handout and to read the rest of the handout before you come to the lab for the experiment. At the beginning of the lab, the TA will check your preliminary work. Get a printout of your answers and results and show it to the TA when you go to your lab session. c) Lab Report After the lab, you will work on the problems at the end of the handout on your own and are required to submit a report on that. Please check the information about the assignment in the lab report section at the end. d) Some Notes and Rules - Do not forget to sign the attendance sheet. - Login to the account created for your group and use the folders provided to save your work. - Do not change the experiment hardware setup unless instructed by the TA or by the lab procedure in the handout. - Cooperate with your group mates to increase your efficiency in performing the experiment. - Bring a USB memory device to get a copy of the experiment data at the end of the lab. - Keep clear from the moving parts of the experiment setup when it is running.
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09/30/12 − Page 1
EE 4314 Lab 3 Handout Speed Control of the DC Motor System Using a PID Controller
Fall 2012
IMPORTANT: This handout is common for all workbenches.
1. Lab Information
a) Date, Time, Location, and Report Due
Please check your lab schedule on Blackboard for your lab date, time, and workbench. The lab
will be held at NH250. Your lab report is due on Wednesday at 11:59 pm two weeks after your
lab session.
b) Preliminary Work
You are required to complete the Preliminary Work given in the next section of this handout
and to read the rest of the handout before you come to the lab for the experiment. At the
beginning of the lab, the TA will check your preliminary work. Get a printout of your
answers and results and show it to the TA when you go to your lab session.
c) Lab Report
After the lab, you will work on the problems at the end of the handout on your own and are
required to submit a report on that. Please check the information about the assignment in the lab
report section at the end.
d) Some Notes and Rules
- Do not forget to sign the attendance sheet.
- Login to the account created for your group and use the folders provided to save your work.
- Do not change the experiment hardware setup unless instructed by the TA or by the lab
procedure in the handout.
- Cooperate with your group mates to increase your efficiency in performing the experiment.
- Bring a USB memory device to get a copy of the experiment data at the end of the lab.
- Keep clear from the moving parts of the experiment setup when it is running.
09/30/12 − Page 2
2. Preliminary Work
This part of the handout provides the preliminary information that you need to understand the
experiment, conduct it, and interpret the results. Follow the steps below to complete the preliminary
work. Provide your answers and results on a paper and present it to the TA when you go to your lab
session.
This lab focuses on the tuning of a PID (Proportional-Integral-Derivative) controller to regulate
the rotational speed of the DC motor system. PID control is the predominant method in industry for
control of various plants and processes that may include motors, engines, valves, and other actuation
schemes.
The block diagram of a basic feedback control system is shown in Figure 1 where y(t) denotes the
process output, r(t) denotes the reference/setpoint which is the desired output, e(t) = r(t) − y(t) denotes
the control error and u(t) is the control signal computed by the controller based on the control error.
Figure 1 Basic feedback control structure
The controller in Figure 1 uses the error signal to determine the required control signal that drives
the process. The input-output relationship of a basic PID controller in time-domain is given as:
tedt
dKdeKteKtu D
t
IP
0
(1)
The control signal, u(t), is a linear combination of proportional (P), integral (I), and derivative (D)
terms of the error signal, e(t). These three terms are accompanied by constant gains KP, KI, and KD.
Designing a PID controller is essentially the process of determining the values of these constants,
which is also known as tuning the controller.
a) Study Example 2.5 – Transfer function of the DC motor in the textbook (Dorf & Bishop, 12th
ed., p. 70). The DC motor system that you will be working on in the lab is a permanent magnet
DC motor hence the control is through the armature voltage/current. You are interested in the
transfer function of the motor that relates the rotational speed of the rotor to the input voltage.
Given the transfer function in eq. 2.70 in the textbook that relates the input voltage and rotor
angular position:
(2)
where K and τ are motor constants, θ is the angular position of the rotor, and Vin is the input
voltage to the armature circuitry, show that the transfer function relating the rotational speed of
the rotor to the input voltage is given by
(3)
y(t) r(t) + e(t) u(t) Controller
(e.g. PID)
Plant/Process
(e.g. Motor)
_
Σ
09/30/12 − Page 3
where ω is the angular speed of the rotor. First, show how θ and ω are related in time and
frequency domains. Then, replace θ(s) in (2) by the expression in terms of ω(s) and find H(s).
b) Given the transfer function in (3), find the response of that system for a unit step input assuming
zero initial conditions. That is,
(4)
First, represent the input in frequency domain and replace it in (3) to find ω(s). Then, find the
inverse Laplace transform of ω(s) by using partial fraction expansion method and referring to
Table 2.3 Important Laplace Transform Pairs in page 59 of the textbook. The result should give
you a time domain expression for ω(t). Sketch ω(t) for t ≥ 0 by assuming several values for t
including t = 0, τ, and ∞.
c) Create a Simulink model as shown in Figure 2 for the motor system and run it to observe the
step response on the scope. Modify the transfer function block according to the following motor
constants: K = 0.9, τ = 0.26 s. Do not forget to set the ‘step time’ of the step source to 0. Plot the
result using simout variable and compare it with your sketch of ω(t).
Figure 2 A Simulink model for the DC motor system
d) Find the transfer function C(s) of the PID controller represented by equation (1).
?sE
sUsC (5)
e) You will be using the open-loop Ziegler-Nichols PID Tuning method described in your
textbook (p. 490) for assigning initial values to the PID gains. Fill out the values in where R is
the initial slope of the step response of the system and Td is the transport delay. In the step
response the DC motor system, there is typically no transport delay. That is, the motor starts
moving immediately after the input is applied. In this case, you can take Td as 0.1×τ, where τ is
the time constant of the system (τ = 0.26 s). For finding R, use your simulation result in part (c).
09/30/12 − Page 4
Table 1 Open-Loop Ziegler-Nichols PID Controller Gain Tuning