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Digital Control Systems

https://ceiba.ntu.edu.tw/961_dcs_ee

Course information

Professor Kuen-Yu Tsai

Dept. of Electrical Engineering, National Taiwan University

Autumn 2007

What is a Digital Control System?

· A digital computer receives and operates on signals in digital (numerical) form. · A digital control system uses digital signals and a digital computer to control a plant.

Reference input (digital) (digital) (analog) Actuator Plant Output (analog)

Digital computer

Digital-to-analog converter (D/A)

(digital)

Analog-to-Digital converter (A/D)

Sensor (analog)

DCS aut '07 20070920

Prof. Kuen-Yu Tsai/NTUEE

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Main Objectives

· Basic:

Analysis of discrete-time and sampled-data systems Basic digital controller design techniques

· Bonus:

Introduction to advanced topics (tbd) related to digital control systems Application to your own research at NTU Develop good presentation and technical writing skills in English

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Let me know more about you

· Email a student information sheet to CA by Oct. 4 (Thu.)

2% penalty if not received

· Student id/name/department/division/advisor · List of control/system related courses taken/audited, project work etc. · Your research topics from your advisor? Or what would that be related? · [ ]definitely take this course [ ]audit [ ]tbd

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Prerequisites

· Undergraduate-level feedback control theory (eg.

[FPE])

Classical control/Laplace transforms Basic state-space approaches

· Aware of A/D, D/A conversion (ADC/DAC), and computer clocks/interrupts

company websites have lots of info.

· (e.g., analog.com, national.com, ti.com, www.linear.com)

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Basic course info

· · · · · Instructor: Prof. Kuen-Yu Tsai (), (02)33663689, EE2-509 Course Assistant: Philip Chooi-Wan Ng (), (02)33669679, MD-714 Time/Location: 2:20-5:20 Friday, MD-303 Office hour: 10-12am Friday, EE2-509 Textbook (required)

[FPW98] G. F. Franklin, J. D. Powell, and M. Workman, "Digital Control of Dynamic Systems," 3rd ed., 1998 .m [FPE] G. F. Franklin, J. D. Powell, and A. Emami-Naeini, "Feedback Control of Dynamic Systems," 3rd ed., 1994 or newer .m

· (Some) References (nice to have)

[OW96] A. V. Oppenheim and A. S. Willsky, "Signals and Systems", 2nd ed. [OS99] A. V. Oppenheim and R. W. Schfer, "Discrete-time Signal Processing," 2nd ed. [SP96] S. Skogestad and I. Postlethwaite, "Multivariable Feedback Control" 1996

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Grading

(% subject to minor adjustments)

·

·

Attendance (10%)

Homework (10%)

If 75% : 10%; else: 0% Late arrival: 50% attendance if you miss the first hour On-time FTP submission: 5%; HW solution presentation/brief grading: 5%

·

· ·

Midterm (30%)

Based on homework assignment Open-book, open-note, computer OK (no "Team work"!!)

Final Project/Report (50%)

Start discussion with Prof. Tsai ASAP Try to apply [FPW] materials to advance your research project

Bonus Projects (20%)

Bonus Experiment reports Clarification/Presentation of course materials Additional homework presentation

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Access to CSCAD/CACSD tools

· Matlab with Control System Toolbox and Simulink

Preferred due to [FPW] usage Wide industry acceptance; student version available Control Tutorials for Matlab (CMU) Matlab/Simulink Tutorials (Mathworks)

· Scilab (free!)

General system and control

· Mathematica Control System Professional

Symbolic capability

· SLICOT NICONET

Hi-performance, (free!) Fortran and Matlab libraries

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LW/WW/LD 1/38/0921 2/39/0928

Topic(s)

Course Information Introduction to digital control systems

Comment(s)

HW1 out (CTLTI)

3/40/1005

4/41/1012 5/42/1019 6/43/1026 7/44/1102 8/45/1109 9/46/1116

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Review of continuous-time control

Discrete systems analysis (I) Discrete systems analysis (II) Sample-data systems (I) Sample-data systems (II) Design using transform techniques Discrete equivalents

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HW1 due/present HW2 out HW3 out (DTLTI) HW2 due/present HW3 due/present

LW/WW/LD

Topic(s)

MIMO design using state-space methods (I)

MIMO design using state-space methods (II)

Comment(s)

HW4 due; Final project proposal due

10/47/1123

11/48/1130

12/49/1207

13/50/1214 14/51/1221

Quantization Effects, Sample rate selection

Spectrum analysis by FFT Introductory System Identification*

HW4 present

HW5 due HW5 present

15/52/1228

16/1/0104

Review Session*

Final Exam Open book, notes, and laptop. No collaboration

17/2/0111

18/3/0118

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Final project report/presentation 1st version due

Final project report/presentation final version due

Prof. Kuen-Yu Tsai/NTUEE

10% penalty for each day; class present Last lecture

Final-exam week Late date to submit grades: 01/28

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Essentials of good presentation materials and technical documents

· Must: Page number, author, affiliation and time (last modified date) in most pages · Must: List of references · Must: Refer to references

Distinguish what is prior-art, what is your contribution or opinion

· A picture is worth a thousand words!

Use figures, pictures, block diagrams, and tables, etc to summurize Clear labeling and units

· Explain ,,simple things

Equations, abbreviations, etc. Do not make assumptions!

· Usually the audience knows much LESS than you do

DCS aut '07 20070920

Prof. Kuen-Yu Tsai/NTUEE

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Essentials of a HW presentation

· Brief overview of a technique (PID, RL, LL, or SS,... etc)

What can it do?

· Background theories related to the solution of a particular HW problem · Solution of the HW

How the theories above are applied to solve this problem Nice and clear Matlab code/plots

· Grading

Instructor (70%)

· Base on the content and the quality of the presentation materials

Student vote

· 1: below expectation; 2: just OK; 3: above expectation; 4: Super! · CA to organize and count

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Prof. Kuen-Yu Tsai/NTUEE

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HW1 Problem1

(PID techniques)

· Consider the system shown in Figure 1 which represents control of the angle of a pendulum which has no damping

a) b)

c)

d)

What condition must D ( s ) satisfy so that the system can track a ramp reference input with constant steady-state error? For a transfer function D ( s ) that stabilizes the system and satisfies the condition in part (a) ,find the class of disturbances w ( t ) that the system can reject with zero steady-state error. Show that although a PI controller satisfies the condition derived in part (a), it will not yield a stable closed-loop system. Will a PID controller work; that is, satisfy part (a) and stabilize the system? If so, what constraints must K p , K I and K D satisfy ? Discuss qualitatively and briefly the effects of small variations on the controller parameters K p ,, K I and K D on the systems step response rise time and overshoot.

DCS aut '07 20070920

Prof. Kuen-Yu Tsai/NTUEE

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(cont.)

W

R

D(S)

1 s2

K

Y

Figure 1

DCS aut '07 20070920

Prof. Kuen-Yu Tsai/NTUEE

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HW1 Problem2

(root locus techniques)

· Consider a pendulum with control torque Tc and disturbance torque Td whose differential equation is 4 T T

c d

Assume there is a potentiometer at the pin that measures the output angle , that is, y .

a) Design a lead compensation using a root locus that provides for an Mp < 10% and a rise time, tr < 1sec. b) Add an integral term to your controller so that there is no steady-state error in the presence of a constant disturbance, Td, and modify the compensation so that the specifications are still met.

DCS aut '07 20070920

Prof. Kuen-Yu Tsai/NTUEE

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HW1 Problem3

(lead/lag compensation techniques)

· Consider a pendulum with control torque Tc and disturbance torque Td whose differential equation is 4 T c T d Assume there is a potentiometer at the pin that measures the output angle , that is, y .

a) Design a lead compensation using frequency response that provides for a PM > 500 and a bandwidth, B W > 1rad/sec. b) Add an integral term to your controller so that there is no steady-state error in the presence of a constant disturbance, Td, and modify the compensation so that the specifications are still met.

DCS aut '07 20070920

Prof. Kuen-Yu Tsai/NTUEE

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HW1 Problem4

( State space method)

· Consider a pendulum with control torque Tc and disturbance torque Td whose differential equation is

4 T c T d Assume there is a potentiometer at the pin that measures the output angle , that is, y = .

a) Taking the state vector to be

write the system equations in state form. Give values for the matrices F, G, H. b) Show, using state-variable methods, that the characteristic equation of the model is s 2 4 0 .

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c)

Write the estimator equations for

^ ^

d)

e) f)

Pick estimator gains [L1, L2]T to place both roots of the estimatorerror characteristic equation at s = 10. Using state feedback of the estimated state variables and , derive a control law to place the closed-loop control poles at s = 2 2j Draw a block diagram of the system, that is, estimator, plant, and control law. Demonstrate the performance of the system by plotting the step response to a reference command on (i) , and (ii) Td .

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Prof. Kuen-Yu Tsai/NTUEE

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Backup

Contact Information

· Advisor : Kuen-Yu Tsai email : [email protected] Phone Number : 02-33663689 Office : EE2-509 Office Hour : Fri. 10:00~12:00 am · CA : Philip Chooi-Wan Ng email : [email protected] Phone Number : 02-33669679 Office : MD-714

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Prof. Kuen-Yu Tsai/NTUEE

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Abbreviation/terminology

· · · · · · · · · · · · · · ADC Analog to Digital Converter ASAP As Soon As Possible CA Course Assistant Cont. Continue CMU Carnegie Mellon University CACSD Computer Aided Control System Design CSCAD Control System Computer Aided Design DAC Digital to Analog Converter DCS Digital Control Systems DSP Digital Signal Processing or Digital Signal Processor HW HomeWork TBD To Be Determined LW Lecture Week per NTU calendar WW Work Week per Microsoft Outlook calendar

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References

1. [FPW98] G. F. Franklin, J. D. Powell, and M. L. Workman, "Digital Control of Dynamic Systems," 3rd ed., 1998 .m 2. [FPE] G. F. Franklin, J. D. Powell, and A. EmamiNaeini, "Feedback Control of Dynamic Systems," 5th ed., 2006 .m 3. [OW96] A. V. Oppenheim and A. S. Willsky, "Signals and Systems", 2nd ed. 4. [OS99] A. V. Oppenheim and R. W. Schfer, "Discrete-time Signal Processing," 2nd ed. 5. [SP96] S. Skogestad and I. Postlethwaite, "Multivariable Feedback Control" 1996

DCS aut '07 20070920 Prof. Kuen-Yu Tsai/NTUEE 22

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