數位控制系統
( Digital Control Systems )
Electrical Engineering Department
National Taiwan University
109-2 (Feb - Jun, 2021)
----- News & Actions -----
  • Action Items: (1/1/21)
  • 近期學習課程時間表 (6/1/21)
    • 期末專題報告評分： 6/29 (Tue), before 11pm
  • 專題報告評分 (6/21/21)
    • 繳交期末專題報告評分表格檔案，
      - By 6/29 (Tue), before 11pm
      - Submit your evaluation file to NTU Cool
    • 專題報告評分表檔案：
      - 點選下載： 評分表檔案
      - 總共 11 組，針對每一組的五個項目，給予評分
      - 評分依據：
      ..... A: 有不錯的討論
      ..... B: 有討論，但，不夠好
      ..... C: 看不出來有討論？
      - 每一項評分標準與進行方式，
      - 請參考講義區 dcs02_Project (pages 5, 7-8, 9-11) 的說明。
    • 專題報告 (60%) 的評分，如下所示：
      --- Writing style & contents (10%)
      --- Technical content (20%)
      --- Evaluation by other students, teaching assistant, instructor (20%)
      --- Your evaluation quality (10%)
  • Articles and Reports about Control (updated on 9/11/18)
  • OLD news are moved to the bottom of the webpage.
  • Digital Control Systems in 107-2 (2019): (Course Webpage)
  • Signals and Systems in 2017: (Course Webpage)

----- Lecture Notes -----
Week Subject Date Lecture PDF Code HW
XYZ Exam (Cancelled) X/Y - Covers HW 2, 3, 4, 5
- Time: 2pm-4pm 		... Sample (DCS)
Sample (CS)
19 Project Evaluation 6/29
Tue 		- Submit your evaluation file to NTU Cool
.... .... dcs02_Project
.... .... 評分表檔案 		評分表範例檔案

by 6/29
18 6/22 -
...
17 Project Report Files 6/19
Sat 		- Submit one zipped file of all files,
.... .... e.g., video, docx, pptx, pdf, m, etc.
.... .... to NTU Cool
- Guidelines:
.... .... dcs02_Project, .... pages 5, 7-8, 9-11
HW
補交
by 6/19
16 6/8 -
...
15 IO Design
Polynomial Approach 		6/1 -
- 35_InputOutputDesign
- 		fig511_change_w.m
fig511_change_zeta.m
fig512_change_obspole
fig513_change_h.m
14 IO Design
Polynomial Approach 		5/25 -
- 35_InputOutputDesign
-
- CT Feedback Analysis
- Example
- 		fig504_motor_step.m
fig505_motor_step.m
block504.mdl
fig510_nominal.m
block510.mdl
block510.slxc
13 Discretized C(s)
Delay
Compensation
5/18 -
- 34_DelayCompen
- 		Lag_a.mdl
Lag_b.mdl
Lag_c.mdl
LeadLag.mdl
KatzExample.mdl
RattanExample.mdl 		HW-6 Problem
- by 5/29
12 Discretized C(s)
Discrete Design
Emulation Design 		5/11 -
- 32_DiscreteDesign
- 33_EmulationDesign
- 		... ...
11 SS Design
Observer Design
Output Feeback Proposal 		5/4 -
- 31_StateSpaceDesign
- 		arm_bode.m
arm_impulse.m
block419.mdl
arm_controller.m
block420.mdl
arm_observer.m
block421.mdl
ylblalgn.m
sfbdesign.m
obsdesign.m
Kalman3.m
10 SS Design
State Feedback 		4/27 -
- Aircraft Pitch Model
-
- 31_StateSpaceDesign
- 		SSModel.m

place.m
place_control.m
place_CTDT.m

different_h.m
block402.mdl

HW_5_2_b.slx
HW_5_2_b.slxc
HW-5 Problem
- by 5/8

- Solution
09 Stability
Controllability
Observability 		4/20 -
- 21_DesignExample
- 22_Stability
- 23_Controllability....
..........Observability
- 		rlocus
rlocus_nyquist
rlocus_bode_nyquist 		Proposal Project
- by 5/1
08 Project
DesignExample
Stability
4/13 - 02_Project
-
- 21_DesignExample
- 22_Stability
RootLocus_1.m
RootLocus_2.m
Output_K.m
block318.mdl
HiddenOsc_1.m
block319.mdl
HiddenOsc_2.m
block320.mdl

rlocus
rlocus_nyquist
rlocus_bode_nyquist 		HW-4 Problem
- by 4/24
-
- Solution
07 Holiday 4/6 ... ...
06 Sampling
TimingAnalysis 		3/30 -
- dcs10_DTModel
- dcs14_Sampling
- dcs15_TimingAnalysis

- Lecture:
... SS-7: Sampling
... SS-7: (Video)
... List of Related Papers

- References:
- SS-7: Sampling
- SS-7: (Video)
- Videos of Sampling Effect
...... Aliasing x1
...... Aliasing x4
...... 55 Minute Alias
...... Propeller Effect
...... Wagon-wheel effect
- Speech: by Yutaka Yamamoto
...... Video
...... Slides
...... Paper
-
- (Response
_01_pole.m)

- (Sampling
_01_CTDT.m)

- (ccsdemo)
HW-3
Problem
- by 4/10
-
- Solution
05 z-T 3/23 -
- dcs10_DTModel
- dcs13_zTransform
- 		- (dsc13_zT.m)

- (Response
_01_pole.m)

- (Sampling
_01_CTDT.m) 		HW-3
Problem
- by 4/10
-
- Solution
04 DT Model-IO
z-T 		3/16 -
- dcs12_DTModel_IO
- dcs13_zTransform

- References:
- SS-2: LTI Systems
- SS-2: (Video)
... pp. 3-11
- SS-10: The z-T
- SS-10: (Video)
... 2-8 30 39 50 52
60-61 71-74
- 		- (dsc13_zT.m)
03 DT Model-SS
DT Model-IO 		3/9 - dcs11_DTModel_SS
- dcs12_DTModel_IO

- References:
- Lecture:
- SS-2: LTI Systems
- SS-2: (Video)
... pp. 3-11 		- ss, c2d
HW-2
Problem
- by 3/20
- Solution
02 DT Model-SS 3/2 - dcs10_DTModel
- dcs11_DTModel_SS
- References:
- IEEE Xplore
- System Models
- System of DEs
... pp. 511 515-518
524 562 578
- System Models in LS
- Solution of 1st-order DE
... pp. 52 54 58 59
- SS Solution in LS 		( )
01 Intro 2/23 - dcs01_Intro ( ) HW-1 Problem
pp. 2-11, 22-24,
25-28, 28-29
Book-A&W 1997
...
Sol
Week Subject Date Lecture PDF Code HW
----- Homeworks -----
  • Homework Template File

  • Homework 6 (updated on 5/18/21)
    • Assigned: 5/18, 2021 , Deadline: 5/29, 2021
    • Topics: Discretized Controller with Delay Compensation
      - Please read the following paper:
      .......... D. Raviv, E.W. Djaja,
      .......... "Techniques for Enhancing the Performance of Discretized Controllers,"
      .......... IEEE Control Systems Magazine, 19(3): 52-57, June 1999.
      .......... (Paper PDF)
      - And edit your Matlab/Simulink codes to finish the following tasks:
      ...(a) Obtain the result in Table 1 with Ts = 0.1, 0.01, 0.05 and other choices.
      ...(b) Obtain the result in Figure 5 with Ts = 0.1, 0.01, 0.05 and other choices.
      ...(c) Obtain the result in Figure 6 with Ts = 0.01, and other choices.
      ...(d) Obtain the result in Figure 7 with Ts = 0.03, and other choices.
      ...(e) Obtain the result in Figure 8 with Ts = 0.15, and other choices.
      ...(f) Write a paragraph on what you learn from this homework.
    • Actions:
      - Please use the homework template to edit your plots/codes and paragraphs
      ....... on summarizing the information you catch from each section.
      - Submit your HW06 report
      ----- to NTU Cool by 11pm, 5/29, 2021 (Sat)

  • Homework 5 (updated on 4/27/21)
    • Assigned: 4/27, 2021 , Deadline: 5/8, 2021
    • Topics: Design in State-Space Model
      - Problem 5-1:
      ....... Consider the system
      ....... Determine a linear state-feedback controller
      .......such that the closed-loop poles are in 0.1 and 0.25.
      - Problem 5-2:
      ....... Consider the continuous-time system:
      ....... Sampling the system with h = 0.2 gives:
      ....... Determine a linear state-feedback controller such that the closed-loop characteristic polynomial is:
      ....... Simulate the closed-loop system when x(0) = [ 1 0 ]^T and
      ....... plot all the signals (states, input, output) of the systems.
      ....... Note that in your simulation the plant should be the CT model.
      - Problem 5-3:
      ....... Given the system:
      ....... Determine the linear state-feedback controller:
      ....... such that the states are brought to the origin in two sampling intervals.
      ....... Is it possible to determine a linear state-feedback controller
      ....... that can take the system from the origin to x(k) = [ 2 8 ]^T.
      ....... Determine an observer that estimates the states
      ....... such that the observer has the desired characteristic polynomial.
    • Actions:
      - Please use the homework template to write several paragraphs
      ....... on summarizing the information you catch from each section.
      - Submit your HW05 report
      ----- to NTU Cool by 11pm, 5/8, 2021 (Sat)

  • Homework 4 (updated on 4/13/21)
    • Assigned: 4/13, 2021 , Deadline: 4/24, 2021
    • Topics: Stability, Controllability, Observability
      - Problem 4-1:
      ....... Consider the system
      ....... Determine the values of K for which the closed-loop system is stable
      - Problem 4-2:
      ....... Is the following system (a) stable, (b) observable, (c) reachable?
      - Problem 4-3:
      ....... Consider the system
      ....... Determine a control sequence
      ....... such that the system is taken from the initial state, x(0), to the origin
      ....... Which is the minimum number steps
      - Problem 4-4:
      ....... Given the system
      ....... For which values of K in the proportional controller
      ....... is the closed-loop system stable?
    • Actions:
      - Please use the homework template to write several paragraphs
      ....... on summarizing the information you catch from each section.
      - Submit your HW04 report
      ----- to NTU Cool by 11pm, 4/24, 2021 (Sat)

  • Homework 3 (updated on 3/23/21)
    • Assigned: 3/23, 2021 , Deadline: 4/10, 2021
    • Topics: z-Transform and Sampling
      - Problem 3-1:
      ....... Consider the system described by the difference equation
      ....... Determine the pulse-transfer function and the poles and zeros
      ....... Determine the output sequence of the difference equation
      ....... Find the relationship between poles/zeros and the kernel functions
      - Problem 3-2:
      ....... Consider the system
      ....... Simulate the system and
      ....... determine the overshoot for different values of a and b
      - Problem 3-3:
      ....... Sketch the magnitude of the spectrum
      ....... when the signal has been sampled with:
      ....... (a) h = 2 pi /10 (s); (b) h = 2 pi /20 (s); (c) h = 2 pi /50 (s).
      - Problem 3-4:
      ....... Watch the following plenary speech:
      ....... Signal Processing via Sampled-Data Control
      ....... - A Challenge to Go Beyond Shannon
      ....... By Prof. Yutaka Yamamoto (Kyoto University, Japan)
      ....... Video Link
      ....... http://www.ieeecss-oll.org/lecture/signal-processing-sampled-data-control-challenge-go-beyond-shannon
      ....... http://archive.dimacs.rutgers.edu/Workshops/ControlTheory/Slides/Yamamoto.pdf
      ....... https://ieeexplore.ieee.org/document/6072311
    • Actions:
      - Please use the homework template to write several paragraphs
      ....... on summarizing the information you catch from each section.
      - Submit your HW03 report
      ----- to NTU Cool by 11pm, 4/10, 2021 (Sat)

  • Homework 2 (updated on 3/2/21)
    • Assigned: 3/9, 2021 , Deadline: 3/20, 2021
    • Topics: Discrete-Time Models
      - Problem 2-1:
      ....... Derive the formulas of the DT State-Space System with Inner Time Delay
      ....... Reference:
      ........... Bjorn Wittenmark, "Sampling of a system with a time delay,"
      ........... IEEE Transactions on Automatic Control,
      ........... Vol. 30, No. 5, pp. 507-510, May 1985.
      ........... https://ieeexplore.ieee.org/document/1103985
      - Problem 2-2:
      ....... Derive the discrete-time system
      ....... corresponding to the following continuous-time system
      ....... when a zero-order-hold circuit is used
      - Problem 2-3:
      ....... Use the z-transform
      ....... to determine the pulse-transfer function of the difference equation
      - Problem 2-4:
      ....... Sample the continuous-time system
      ....... Using the sampling interval h = 0.3.
      ....... Determine the pulse-transfer operator
    • Actions:
      - Please use the homework template to write several paragraphs
      ....... on summarizing the information you catch from each section.
      - Submit your HW02 report
      ----- to NTU Cool by 11pm, 3/20, 2021 (Sat)

  • Homework 1 (updated on 2/23/21)
    • Assigned: 2/23, 2021 , Deadline: 3/6, 2021
    • Topics: Read Articles on Digital Control
      - Section 1.2: Computer Technology for Control
      ....... on Pages 2-11 of Book - Astrom & Wittenmark 1997
      - Section 1.4: Inherently Sampled Systems
      ....... on Pages 22-24 of Book - Astrom & Wittenmark 1997
      - Section 1.5: Fundamental Theories
      ....... on Pages 25-28 of Book - Astrom & Wittenmark 1997
      - Section 1.6: Notes and References
      ....... on Pages 28-29 of Book - Astrom & Wittenmark 1997
    • Actions:
      - Please use the homework template to write several paragraphs
      ....... on summarizing the information you catch from each section.
      - Submit your HW01 report
      ----- to NTU Cool by 11pm, 3/6, 2021 (Sat)
    • Book - Computer-Controlled Systems: Theory and Design, (3rd Ed., 1997)
      - by Karl Johan Astrom and Bjorn Wittenmark
      ----- Prentice Hall
      - Book at amazon
      - Book at books.google
      - Book at NTU Library

----- Course Information -----
  • What:
    • Topics: Digital Control Systems
    • Course No: EE5073
    • Credit: 3
  • Who:
    • Students:
      • Graduate Students or Senior Students
    • Instructor:
      • Name: Feng-Li Lian (連豊力)
      • Office: Room EE-MD717,
      • Phone: 02-3366-3606
      • Email: fengli@ntu.edu.tw
  • When:
    • Lectures: 1:30pm-4:20pm, Tuesdays (Feb 2021 - Jun 2021)
    • Office Hours: appointment by e-mail
  • Where:
  • Why:
    • For EE graduate students
      interested in Digital Control Systems: Analysis and Design
    • Project-oriented discussion and lectures
  • How:
    • Preview: ~3 hours/per week
    • Lecture: ~3 hours/per week
      • Demonstration, derivation and practice, etc.
    • Review: ~3 hours/per week
    • Homework: ~3 hours/per week
    • Q & A & lecture participation:
      • group discussion
      • lecture questionnaire
      • e-mail
      • website etc.

  • Reference Books:

  • Course Outline:

    • Digital Control Systems
      • A. From Analog to Digital World
      • B. Design Consideration
      • C. Z-transform
      • D. Controller Design
    • Computer Control Systems (Single Centralized Control)
      • A. Real-Time Operation Systems
      • B. Analog to Digital
      • C. Digital to Analog
    • Networked Control Systems (Multiple Distributed Control)
      • A. Control Networks Protocols
      • B. Networked Controllers & Managers
      • C. Networked Sensors
      • D. Networked Actuators

  • Grading:
    • Homework and Programming   30%
    • Midterm Exam   30%
    • Final project and report   40%
=======================================================================
======================== ----- Old News in 109-2 ------ ========================
=======================================================================
  • 作業補充修正： 6/19 (Sat), before 11pm
  • 期末專題報告簡報檔案與影片： 6/19 (Sat), before 11pm

  • OLD
  • 取消考試與調整學期成績評比方式 (5/22/21)
    • 因應近期疫情的發展，
      - 校方規定所有課程（包含考試） 全面採用程遠距或線上方式辦理。
    • 因此，原本進行的考試評量方式，預計取消。
    • 學期成績的評量方式與比重，預計調整如下：
      - 作業：40%
      - 專題報告：60%
    • 作業 (40%) 的評分，
      - 已經重新評比並且登錄在 NTU-Cool 中的每一份作業評論之中，
      - 分為四個等級：
      --- A：達到目標
      --- B：還需一些精進
      --- C：還需要很大改進
      --- X：未交
      - 所有的作業，可以有一次機會，進行補充修正之後補交，
      - 補交的作業，請在原本的作業上，
      ..... 以紅色粗體等不同的字體新增補充或補強的部分。
      - 把所有的補交的作業壓縮成一個檔案，
      ..... 上傳到 NTU-Cool：作業區- HW 補交。
      - 繳交期限：6/19 (11pm)。
    • 專題報告 (60%) 的評分，如下所示：
      --- Writing style & contents (10%)
      --- Technical content (20%)
      --- Evaluation by other students, teaching assistant, instructor (20%)
      --- Your evaluation quality (10%)
      - 每一項評分標準與進行方式，
      - 請參考講義區 dcs02_Project (pages 5, 7-8, 9-11) 的說明。
    • 如果您有不清楚的地方，或者希望採用其他的成績評定方式，
      ..... 敬請提出您的建議方案。
  • Delay and Sampling (6/1/21)
  • Delay and Sampling (5/25/21)
  • 5/18 考試事宜 (5/14/21)
    • 原本排定在 5/18 進行的考試，延後舉行。
    • 考試時間與方式，等待疫情狀況較穩定之後，再決定。
    • 5/18，以線上直播的方式進行課程，直播連結為： at MS-Teams
      ...... 請在上課時間，進入 MS-Teams 的討論室。
  • Week 14 (5/25/21), Week 15 (6/1/21)
    • Lectures:
      • IO Design
      • ... Polynomial Approach
    • Homework:
      - none
    • References:
      - none
  • Week 13 (5/18/21)
    • Lectures:
      • Discretized C(s)
      • ... Delay Compensation
    • Homework:
      - HW-6: Discretized Controller
      - Deadline: 5/29, 2021
      -
    • References:
      -
      - Discretize a Compensator at Mathworks, --- website ---
      - Continuous-Discrete Conversion — Examples at Mathworks, --- website ---
      - Continuous-Discrete Conversion — Functions at Mathworks, --- website ---
      -
      - Discrete-time PID Controller Implementation at scilab, --- website ---
      -
      - Brian .D.O. Anderson 1992 & 1993,
      --- (Paper PDF)
      .......... "Controller Design: Moving from Theory for Practice,"
      .......... IEEE Control Systems Magazine, 13(4): 16-25, Aug. 1993.
      --- (Seminar Video)
      .......... The 1992 Bode Prize Lecture
      .......... at The 31st IEEE Conference on Decision and Control,
      .......... Tucson, AZ, December 1992.
      - D. Raviv, E.W. Djaja,
      .......... "Techniques for Enhancing the Performance of Discretized Controllers,"
      .......... IEEE Control Systems Magazine, 19(3): 52-57, June 1999.
      .......... (Paper PDF)
  • Week 12 (5/11/21)
    • Lectures:
      • Discretized C(s)
      • ... Discrete Design
      • ... Emulation Design
      • Proposal
    • Homework:
      -
      - Midterm Exam on 5/18, 2pm-4pm
      - （延後再討論 on 5/14）
      -
    • References:
      -
      - Discretize a Compensator at Mathworks, --- website ---
      - Continuous-Discrete Conversion — Examples at Mathworks, --- website ---
      - Continuous-Discrete Conversion — Functions at Mathworks, --- website ---
      -
      - Discrete-time PID Controller Implementation at scilab, --- website ---
      -
  • Week 11 (5/4/21)
    • Lectures:
      • State Space Design
      • ... Observer Design
      • ... Output Feeback
      • Proposal
    • Homework:
      - HW-5: State Space Design
      - Deadline: 5/8, 2021
  • Articles and Reports about Control (updated on 9/11/18)
    • =======================================================================
    ======================== ----- Old News in 107-2 ------ ========================
    =======================================================================