授業/制御工学特論2011

Advanced Automation†

[lecture #1] 2011.9.1 review of classical control theory†

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[lecture #2] 2011.9.8 CACSD introduction with review of classical control theory†

• introduction of Matlab and Simulink
  • Basic usage of MATLAB and Simulink used for 情報処理演習及び考究II/Consideration and Practice of Information Processing II: Advanced Course of MATLAB

sample0908.m

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[lecture #3] 2011.9.15 given by Prof. Kimura cancelled†

[lecture #4] 2011.9.22 given by Prof. Kimura cancelled†

[lecture #5] 2011.9.29 given by Prof. Kimura cancelled†

supplementary lectures will be given by Prof. Kimura.†

[lecture #3] 2011.10.6 CACSD introduction with review of classical and modern control theory†

1. relationship between TF and SSR (higher order case)
   ex1006_1.m
   mod1006.mdl
2. open-loop stability
   • can be checked by poles of TF and eigenvalues of A-matrix in SSR
     ex1006_2.m
3. closed-loop stability
   • can be checked graphically by Nyquist stability criterion and Bode plot with GM(gain margin) and PM(phase margin)
     ex1006_3.m
   • can be checked numerically by poles of closed-loop TF and eigenvalues of A-matrix in closed-loop SSR
     ex1006_4.m

%-- 10/6/2011 1:25 PM --%
ls
ex1006_1
ex1006_2
ex1006_3
grid on
-0.8*1.5
ex1006_4

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[lecture #4] 2011.10.13 Intro. to robust control theory (H infinity control theory)†

• H infinity norm
  1. robust stabilization
  2. performance optimization

• Example of performance optimization problem : disturbance attenuation problem
  • controller design with trial and error
    ex1013_1.m
  • controller design with H infinity control theory
    ex1013_2.m

s = tf('s');
G = 1/(s+1);
norm(G, inf)
G = 1/(s^2+0.1*s+1);
norm(G, inf)
bode(G)
ex1013_1
ex1013_2

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[lecture #5] 2011.10.7 Introduction to Robust Control (cont.)†

• H infinity norm
  1. robust stabilization
  2. performance optimization

1. a class used to represent plant uncertainty and/or perturbation ... H infinity norm
2. small gain theorem
   • connects the closed-loop H infinity norm and robust stability condition
   • sketch proof ... Nyquist stability criterion
3. practical example of robust stabilization problem
   • unstable plant with perturbation
     ex1020_1.m
   • multiplicative uncertainty model
     ex1020_2.m
   • H infinity controller design
     ex1020_3.m
     mod1020.mdl

%-- 10/20/2011 1:41 PM --%
ex1020_1
ex1020_2
ex1020_3
mod1020
c
c = 0.8

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[lecture #6] 2011.10.27 norm (vector space, normed linear space), singular value, mixed sensitivity problem†

• H infinity norm ... {robust stabilization, performance improvement}
• norm
  norm.pdf
  • size of {number, signal, system}
  • defined on vector space (linear space)
    • ---> normed linear space
    • ... optimization
• H infinity norm : scalar (SISO) ---> matrix (MIMO)
  • absolute value ---> maximum singular value
    norm2.pdf
  • robust stabilization or performance optimization problem ---> mixed sensitivity problem
• reference
  • Feedback control theory / John C. Doyle, Bruce A. Francis and Allen R. Tannenbaum
    
    • 2. Norms for signals and systems
    • 3. Basic concepts
    • 4. Uncertainty and robustness ... p.62 Eq.(4.10) H infinity norm condition in mixed sensitivity problem
  • Robust and optimal control / Kemin Zhou, John C. Doyle and Keith Glover
    
    • 2. Linear algebra (2.7 Vector norms and matrix norms, 2.8 Singular value decomposition)
    • 4. Performance specifications (4.1 Normed spaces, 4.3 Hardy spaces H_2 and H_infinity)
    • 9. Model uncertainty and robustness
    • 16. H infinity control: simple case
    • 17. H infinity control: general case

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[lecture #8] 2011.11.10 state space representation of connected system, state space representation of generalized plant for various control problem, mixed sensitivity problem (by Prof. Kimura)†

see Prof. Kimura's page

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[lecture #9] 2011.12.1 robust control design example: Robust Control System Synthesis for Pneumatic Systems (given by Prof. Kimura)†

[lecture #10] 2011.12.8 Speed control of two inertia system with servo motor (1/3)†

• Experimental setup
  apparatus.ppt
  setup.pdf
  • Objective for control system design
  1. speed tracking
  2. robust against inertia-load variation
• Modelling
  • frequency response experiment results:
    frdata_small_offset0.dat
    frdata_small_offset5.dat
    frdata_small_offset10.dat
    frdata_large_offset0.dat
    frdata_large_offset5.dat
    frdata_large_offset10.dat
  • example of m-file
    freqresp.m
    nominal.m
    weight.m

    >> freqresp
    >> nominal
    >> weight

• Controller design (mixed sensitivity problem)
  • example of m-file
    cont.m

    >> cont

  • design example
    cont.dat
    cont_order.dat
    cont.mat
    result_small.dat
    result_large.dat

• report

1. design your controller(s) so that the system performance is improved compared with the given example above
2. Draw the following figures and explain the difference between two control systems (your controller and the example above):
   1. bode diagram of controllers
   2. gain characteristic of closed-loop systems
   3. time response of control experiment
3. Why is the performance of your system improved(or unfortunately decreased)?
   • due date: 28th(Wed) Dec 17:00
   • submit your report(pdf or doc) by e-mail to kobayasi@nagaokaut.ac.jp
   • You can use Japanese
   • maximum controller order is 20
   • submit your cont.dat, cont_order.dat, and cont.mat to kobayasi@nagaokaut.ac.jp not later than 23th(Fri) Dec

• program sources for frequency response experiment
  freqresp.h
  freqresp_module.c
  freqresp_app.c
  • format of frdata.dat file
    • 1st column: frequency (Hz)
    • 2nd column: gain
    • 3rd column: phase (deg)
• program sources for control experiment
  hinf.h
  hinf_module.c
  hinf_app.c
  • format of result.dat file
    • 1st column: time (s)
    • 2nd column: motor speed (rad/s)
    • 3rd column: motor torque (Nm)
    • 4th column: reference speed (rad/s)
• configuration of control experiment
  • reference signal is generated as described in hinf_module.c:

    if((t > 3)&&(t < 7)){
      r = 10.0;
    }else{
      r = 5;
    }

  • two inertia-load discs (small and large) are used

• Difficulties of our plant: As motor speed is approximately calculated by using difference for one sampling period in hinf_module.c like

  thetaM_rad = (double)read_theta(0) / (double)Pn212 * 2 * M_PI;
  speedM_rad = (thetaM_rad - thetaM_rad_before) / msg->sampling_period;
  thetaM_rad_before = thetaM_rad

  sampling period should not become too small. On the other hand, sampling period should be chosen as small as possible so that desiged continuous-time controller could be closely implemented by its descretized version. Therefore, we have a dilemma to control our plant. The sampling period 0.25 msec was chosen by traial and error so that noise in measured speed is not too large. The gain in high frequency range of continuous-time controller should be small enough for discretization.

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%-- 12/8/2011 1:22 PM --%
freqresp
nominal
weight
load result_small.dat
result_small
plot(result_small(:,1),result_small(:,2))
plot(result_small(:,1),result_small(:,2), 'b', result_small(:,1),result_small (:,4),'r')

[lecture #11] 2011.12.15 Speed control of two inertia system with servo motor (2/3)†

• explanation of design example (cont. from the previous lecture)
• preparation of your own controller(s)

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%-- 12/15/2011 1:06 PM --%
cont
help hinfsyn
K
Ktf = tf(K)
bode(K, 'r', Ktf, 'b')
legend('ss', 'tf')
help fitsys

[lecture #12] 2011.12.22 Speed control of two inertia system with servo motor (3/3)†

• preparation of your own controller(s)

participant list2011

supplementary lectures will be given by Prof. Kimura.†

• example for changing ws = 2 pi 0.1 -> 2 pi 0.01

  #ref(): The style ref(filename,pagename) is ambiguous and become obsolete. Please try ref(pagename/filename)

• example to compare time responces
  compare_result.m

%-- 12/22/2011 1:20 PM --%
nominal
ctrlpref
nominal
weight
cont
ks
cont
compare_result

related links†

• Prof. Kimura's page

Contents

0．トップ

1. 掲示板

2．メンバー

3. 研究テーマ

4. 研究生活

5．イベント

6．授業

7．学生実験

8．研究室内のページ

9．情報公開

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