授業/制御工学特論2011 の履歴(No.13)

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• 授業/制御工学特論2011 へ行く。
  • 1 (2011-09-07 (水) 14:00:39)
  • 2 (2011-09-07 (水) 14:06:07)
  • 3 (2011-09-08 (木) 09:44:22)
  • 4 (2011-09-08 (木) 14:15:23)
  • 5 (2011-09-22 (木) 07:51:48)
  • 6 (2011-10-06 (木) 11:21:07)
  • 7 (2011-10-13 (木) 08:58:33)
  • 8 (2011-10-13 (木) 10:52:07)
  • 9 (2011-10-13 (木) 14:32:30)
  • 10 (2011-10-19 (水) 17:40:29)
  • 11 (2011-10-20 (木) 11:34:32)
  • 12 (2011-10-20 (木) 14:33:47)
  • 13 (2011-10-26 (水) 18:07:45)
  • 14 (2011-10-27 (木) 10:33:03)
  • 15 (2011-11-10 (木) 11:01:33)
  • 16 (2011-11-17 (木) 01:06:09)
  • 17 (2011-12-08 (木) 12:25:38)
  • 18 (2011-12-08 (木) 14:20:35)
  • 19 (2011-12-15 (木) 11:22:27)
  • 20 (2011-12-15 (木) 14:22:10)
  • 21 (2011-12-16 (金) 13:31:27)

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Advanced Automation†

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

[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

[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

[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

[lecture #5] 2010.10.7 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

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! the followings are under construction !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[lecture #6] 2010.10.14 norm, vector space, normed linear space†

• H infinity norm ... {robust stabilization, performance improvement}
• norm
  • size of {number, signal, system}
  • defined on vector space (linear space)
    • ---> normed linear space
    • ... optimization

#ref(): File not found: "2010.10.14-1.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.14-2.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.14-3.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.14-4.jpg" at page "授業/制御工学特論2011"

[lecture #7] 2010.10.21 eigenvalue, eigenvector, singular value decomposition†

• H infinity norm : scalar (SISO) ---> matrix (MIMO)
  • absolute value ---> maximum singular value
  • background: mixed sensitivity problem {robust stabilization and performance improvement are simultaneously considered}

A = [2, 1; 0, 1]
[X, L] = eig(A)
X*L/X - A
[U, S, V] = svd(A)
U*U'
V*V'
U*S*V'
U*S*V' - A
sqrt(eig(A'*A))
S

#ref(): File not found: "2010.10.21-1.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.21-2.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.21-3.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.21-4.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.21-5.jpg" at page "授業/制御工学特論2011"

[lecture #8] 2010.10.28 state space representation of connected system, state space representation of generalized plant for various control problem, mixed sensitivity problem†

#ref(): File not found: "2010.10.28-1.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.10.28-2.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "ex26.m" at page "授業/制御工学特論2011"

[lecture #9] 2010.11.4 robust control design example: Robust Control System Synthesis for Pneumatic Systems (given by Prof. Kimura)†

see RubustControlOfPneumatic-e.pdf in Prof. Kimura's homepage for detail

#ref(): File not found: "2010.11.4-1.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.11.4-2.jpg" at page "授業/制御工学特論2011"

[lecture #10] 2010.11.11 robust control design example (cont.)†

1. Design H infinity controller with Eqs.(41)-(47) and generalized plant depicted in Fig.3 in the pdf file.
   1. Confirm the following m-file for design:

      #ref(): File not found: "pneum.m" at page "授業/制御工学特論2011"

      #ref(): File not found: "pneum_ans.m" at page "授業/制御工学特論2011"

   2. Derive the generalized plant by hand and correct the m-file.
   3. Run the m-file to find controller.
2. Simulation

   #ref(): File not found: "simu_pneum.mdl" at page "授業/制御工学特論2011"

   #ref(): File not found: "simu_pneum_noise.mdl" at page "授業/制御工学特論2011"

simu_pneum
plot(t, y, 'r', t, r, 'b');

simu_pneum_noise
plot(t, y, 'r', t, n, 'b')

#ref(): File not found: "2010.11.11-1.jpg" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.11.11-2.jpg" at page "授業/制御工学特論2011"

[lecture #11] 2010.11.18 robust control design example (cont.) (given by Prof. Kimura)†

Exercise

1. step response
2. noise response (noise type: step, sinusoidal wave 1Hz, 50Hz, 500Hz)
3. initial response (x(0) = [1;0;0]）

#ref(): File not found: "2010.11.18-1.jpg" at page "授業/制御工学特論2011"

[lecture #12] 2010.11.25 Speed control of two inertia system with servo motor (1/3)†

• simulation (cont. from Nov.18)
• Problem setup

  #ref(): File not found: "apparatus.pptx" at page "授業/制御工学特論2011"

• Modelling (frequency response experiment)

#ref(): File not found: "2010.11.25-1.jpg" at page "授業/制御工学特論2011"

[lecture #13] 2010.12.2 Speed control of two inertia system with servo motor (2/3)†

• reduced-order controller design (will be given by Prof. Kimura using with the robust control design example)

  #ref(): File not found: "2010.12.2-1.jpg" at page "授業/制御工学特論2011"

  #ref(): File not found: "2010.12.2-2.jpg" at page "授業/制御工学特論2011"

• Problem setup
  • Objective for control system design
  1. speed tracking
  2. robust against inertia-load variation
     setup.pdf
• Modelling
  • frequency response experiment results:

    #ref(): File not found: "frdata_offset0_small.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "frdata_offset0_large.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "frdata_offset5_small.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "frdata_offset5_large.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "frdata_offset10_small.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "frdata_offset10_large.dat" at page "授業/制御工学特論2011"

  • 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 1 (wt1 = 2*pi*50 is set in weight.m)

    #ref(): File not found: "cont1.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "cont_order1.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "cont1.mat" at page "授業/制御工学特論2011"

    #ref(): File not found: "result_small1.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "result_large1.dat" at page "授業/制御工学特論2011"

  • design example 2 (wt1 = 2*pi*20 is set in weight.m)

    #ref(): File not found: "cont2.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "cont_order2.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "cont2.mat" at page "授業/制御工学特論2011"

    #ref(): File not found: "result_small2.dat" at page "授業/制御工学特論2011"

    #ref(): File not found: "result_large2.dat" at page "授業/制御工学特論2011"

  • example of m-file to compare designed controllers

    #ref(): File not found: "compare.m" at page "授業/制御工学特論2011"

• report

1. design your controller 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:
   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(Tue) 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 and cont_order.dat to kobayasi@nagaokaut.ac.jp not later than 24th 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(1) / (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.

[lecture #14] 2010.12.9 Speed control of two inertia system with servo motor (3/3)†

Due to a dimension change of the driven shaft, frequency response experiment has been re-conducted. Please use the following fixed files instead of the ones introduced on the previous lecture.

• frequency response experiment results:

  #ref(): File not found: "frdata_offset5_small_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "frdata_offset5_large_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "frdata_offset10_small_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "frdata_offset10_large_fixed.dat" at page "授業/制御工学特論2011"

• example of m-file

  #ref(): File not found: "freqresp_fixed.m" at page "授業/制御工学特論2011"

  #ref(): File not found: "nominal_fixed.m" at page "授業/制御工学特論2011"

  #ref(): File not found: "weight_fixed.m" at page "授業/制御工学特論2011"

  #ref(): File not found: "cont_fixed.m" at page "授業/制御工学特論2011"

• design example 1 (wt1 = 2*pi*20 is set in weight.m)

  #ref(): File not found: "cont1_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "cont_order1_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "cont1_fixed.mat" at page "授業/制御工学特論2011"

  #ref(): File not found: "result_small1_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "result_large1_fixed.dat" at page "授業/制御工学特論2011"

• design example 2 (wt1 = 2*pi*5 is set in weight.m)

  #ref(): File not found: "cont2_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "cont_order2_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "cont2_fixed.mat" at page "授業/制御工学特論2011"

  #ref(): File not found: "result_small2_fixed.dat" at page "授業/制御工学特論2011"

  #ref(): File not found: "result_large2_fixed.dat" at page "授業/制御工学特論2011"

#ref(): File not found: "2010.12.9-1.jpg" at page "授業/制御工学特論2011"

[lecture #15] 2010.12.16 Speed control of two inertia system with servo motor (cont.)†

• preparation of your own controller(s)

participant list2010

related links†

• Prof. Kimura's page