# ECE 438 { Digital Control

Electronics - Devices

Nov 15, 2013 (4 years and 6 months ago)

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Syllabus Motivation Digital Control Loop
ECE 438 { Digital Control
Digital Control Loop
Associate Prof.Dr.Klaus Schmidt
Department of Mechatronics Engineering { Cankaya University
Elective Course in Electronic and Communication Engineering
Credits (2/2/3)
Course Webpage:http://ECE438.cankaya.edu.tr
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Content and Structure
Content
Introduction of the digital control loop
Discrete-time plant modeling
Analysis of discrete-time systems and the digital control loop
Synthesis of digital control loops
Disturbances and digital control loops with multiple sampling times
Quasi-continuous control
Structure
2 lecture hours:Monday 9:40 { 11:30
2 laboratory hours:Tuesday 11:40 - 13:30
Oce hours:Monday 12:30 - 13:30
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
10 Quizzes (10%)
13 Laboratory Exercises (25%)
1 Midterm Exam (25%)
1 Final Exam (40 %)
Literature
Prentice-Hall,Inc.,2001 (ISBN:0-13-958653-9) (Main Textbook)
Astrom,Karl and Murray,Richard:\Feedback Systems:An Introduction for
Scientists and Engineers",Princeton University Press,2008 (ISBN:
0-691-13576-2)
Oppenheim,Alan V.and Willsky,Alan S.:\Signals and Systems",2nd Edition,
Prentice Hall,1998 (ISBN:0-13-651175-9)
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Motivation:Starting Point
Feedback Control System
u
y
r
G
C
Explanation
Plant modeling as dierential equation,continuous-time transfer
function
p
Various controller design methods for continuous-time systems (bode
plot design,root locus design,pole placement design,:::)
p
) Result:continuous time controller
) Question:how to realize the controller
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Motivation:Analog Controller Realization
PID-Controller
u(t) = K
P
 (e(t) +
1
T
I
Z
e(t) +T
D
_e(t))
Analog Circuit Realization
Gap 1
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Motivation:Analog Controller Realization
Gap 2
Fixed control strategy:realizes only one control algorithm
Possibly long design time
Expensive
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Motivation:Digital Controller Realization
Properties
Execution of the control algorithm on a digital computer
Microcontroller,programmable logic controller (PLC),industrial PC
(IPC)
Realization of dierent control algorithms possible
Basic Structure
Gap 3
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Motivation:Digital Controller Realization
Issues
u
y
r
G
C
1
Possibly no continuity of the actuator (for example step motor,
power electronic actuators,:::)
2
Possibly no continuity of the sensors (for example radar antenna,
ultrasonic sensor,incremental encoder,:::)
3
Possibly no continuity of the signal processing when using a digital
computer (for example microcontroller,programmable logic
controller,industrial PC,:::)
) Case 3 is the main topic of this lecture
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:Block Diagram
Schematic
Gap 4
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:Explanation
Continuous Plant:G
System to be controlled
Continuous-time input signal u and output signal y
Digital Controller
Computes the control algorithm at specied times t
0
;t
1
;t
2
;:::
In the k-th time step (t
k1
to t
k
),the control algorithm computes
the current value u(t
k
) of the input signal from current and past
values of the reference signal (r(t
0
);:::;r(t
k
)) and output signal
(y(t
0
),...,y(t
k
)) and from past values of the input signal
(u(t
0
);:::;u(t
k1
))
) only uses values that are determined at discrete time instants t
0
;t
1
;:::
) new input signal is available at the start of each sampling instant t
k
) notation:r
k
:= r(t
k
),u
k
:= u(t
k
) and y
k
:= y(t
k
)
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:A/D Conversion
Analog/Digital (A/D) Converter
Interface at the input of the digital controller
Each sampling time t
k
:captures measurement y
k
and reference r
k
Remark:r
k
is usually also generated by the digital controller
Result:series of numbers y
0
;y
1
;:::and r
0
;r
1
;:::as digital controller
input for the control algorithm execution
Gap 5
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:A/D Conversion
Sample and Hold Circuit
Output follows input voltage if switch is on
Output keeps last input voltage value if switch is o
Gap 6
A/D Conversion
Converts input voltage to digital number
Quantization of input voltage
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:D/A Conversion
Digital/Analog Converter
Interface at the digital controller output
Each time instant t
k
:determination of the control signal u(t) in the
k +1-st sampling interval (t
k
 t < t
k+1
) from the control
algorithm's output u
k
Technical realization:customary D/A converters supply the constant
control signal u(t) = u
k
for the interval t
k
 t < t
k+1
(0-order hold)
Gap 7
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:Flow Diagram
Gap 8
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:Example
System Description
Plant description:y(t) = 0:25
R
u(t)dt
Reference sequence:(r
k
) = (1;0;0;:::)
Control algorithm:u
k
= 2 (r
k
y
k
)
Sampling time:T = 1
D/A-converter:zero-order hold
Computation
Gap 9
Klaus Schmidt Department
ECE 438 { Digital Control
Syllabus Motivation Digital Control Loop
Digital Control Loop:Example
Computation
Gap 10
Klaus Schmidt Department
ECE 438 { Digital Control