Announcements

1
Announcements!

• Vibrations presentations are Wednesday (November
  19st )
• Bring your presentation on USB drive
• Bring a copy of your slides printed two to a
  page
• E-mail a copy of your presentation to me at
  me4053rogers_at_me.gatech.edu
• Room assignments are posted on the web
• Vibrations abstracts are due Friday (November
  21st ) at 4 pm
• Deposit in green bin outside of the lab
• E-mail a copy of your reportto me at
  me4053rogers_at_me.gatech.edu
• You have been assigned one of the following
• Presentation on Lab 1 (2 Dof)
• Extended Abstract on Lab 1(2 Dof)
• Presentation on Lab 2 (free-free beam)
• Extended Abstract on Lab 2 (free-free beam)
• Assignments are indicated on todays attendence
  sheet and have also posted on the web
• There is a HW assignment due at Controls Lab II
• See website for details

2
Acoustics Grades
3
Controls Lab Week II

• Objectives
• Test the performance P, PD, and PID position
  controllers designed as homework.
• Adjust the PID gain to improve system
  performance.
• Post-laboratory work
• Compare the empirical performance of the various
  controllers to the simulated performance measured
  in the homework.

4

La
Ra
ia
eo(t)
eb
b
q
JL
Kirchoff Voltage Law (KVL)
Back-electromotive force (emf)
Torque-current constant
T
Moment balance on load
5
2nd-order DC Motor Model
where
6
Proportional Control (P-control)
Q
R
E
M
Kp
error
actuator
with P-control, m(t) Kp e(t)
open-loop transfer function
closed-loop transfer function
7
Closed-loop poles roots of denominator of
cl-transfer function
Compare characteristic equation with standard form
See that
and
wn
but z
as Kp
8
Unit Step Response, dependence on proportional
gain
Tm 1 sec
Commanded Response
q
Time
9
Time-domain performance specifications
unit step response
Mp max overshoot
q
? 2 of qss
t
ts , settling time
tr , rise time
10
Max overshoot
Mp depends only on z
Mp
z
11
Performance Specifications
5 max percent overshoot, Mp 0.05
Mp
z
12
2nd performance specification 2 settling time ts
ts 4t
Related to system time constant
What is the time constant of a second-order
underdamped system?
for impulsive input, r (t) d(t), R1
-1
Time constant corresponds to
13
and
Can specify Mp but not ts (z or ?n but not but
not ?n ? )
14
Proportional plus Derivative Control (PD-control)
Q
R
E
M
error
actuator
with PD-control,
.
high e is corrected with Kd
e
t
high e is corrected with Kp
PD anticipates large future error
15
Proportional plus Derivative Control (PD-control)
Q
R
E
M
error
actuator
Open-loop transfer function
Closed-loop transfer function
16
Proportional plus Derivative Control (PD-control)
Q
R
E
M
error
actuator
17
Proportional plus Derivative Control (PD-control)
Q
R
E
M
error
actuator
Can specify both Mp and ts (z and ?n)
18
Implementation issues of PD-control
Pure derivative is not a good idea because of
noise. Instead of
use
Approximates a pure derivative at low frequencies
(below 25 rad/s) then levels off so that
high-frequency noise is not amplified
Note that closed-loop system has a zero in the
numerator- this zero can sometimes destroy
predicted response. In particular, it can give
rise to much larger overshoot than implied by z
of cl poles
19
Proportional plus Derivative plus Integral
Control (PID-control)
Q
R
E
M
error
actuator
with PID-control,
Low but nonzero steady-state error
e
t
As time grows, integral of error increases,
causing m(t) to grow
20
Open-loop transfer function
Closed-loop transfer function
Compare with the following third-order form
Choose s, then equate coefficients of powers of s
in the denominators of each expression for Gcl
to get 3 equations for Kp, Kd, and Ki
21
How do we choose s?
Imag
Desired cl pole locations
-zwn
Real
-s
s nzwn
Choose n to be around 5 so that system appears to
have 2nd-order characteristics
22
PID Gains
n your choice
23
Experimental Setup
Encoder
encoder input
D/A
Quanser data acquisition card
motor
Quanser data acquisition card interface
amplifier
24
Simulink Block Diagram to Initiate Position
Control of Motor
 
Figure 2
25
Linear Simulink Model
26
Nonlinear Simulink Model
X
27
Dead Zone
Saturation
28
MATLAB Dead Zone
Experimental Dead Zone
out
out
Lower Limit
Lower Limit
in
in
Upper Limit
Upper Limit
29
Homework Post Processing

• Design P, PI, and PID controllers based on motor
  parameters determined in week one
• Determine response of motor with each controller
  using linear and nonlinear Simulink models
• Design a PID controller with nonlinear model
  which has optimized performance characteristics
• Post processing Compare experimental responses
  with linear and nonlinear Simulink models