授業/応用数学2B_2012 の履歴差分(No.2)

• 履歴一覧
• 現在との差分 を表示
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• 履歴 を表示
• 授業/応用数学2B_2012 へ行く。
  • 1 (2012-10-03 (水) 17:46:34)
  • 2 (2012-10-03 (水) 18:29:22)
  • 3 (2012-10-10 (水) 17:01:35)
  • 4 (2012-10-17 (水) 16:34:48)
  • 5 (2012-10-24 (水) 18:29:24)
  • 6 (2012-10-31 (水) 14:00:38)
  • 7 (2012-11-07 (水) 14:58:12)
  • 8 (2012-11-20 (火) 19:09:54)
  • 9 (2012-12-05 (水) 13:22:02)
  • 10 (2012-12-19 (水) 13:11:08)
  • 11 (2013-01-09 (水) 15:41:00)

• 追加された行はこの色です。
• 削除された行はこの色です。

*Advanced Automation [#z9bc7ec1]
*応用数学2B 2012年度 [#n0b8fc2b]

** &color(green){[lecture #1]}; 2012.9.6 review of classical control theory [#p164acd2]
#ref(2012.09.06-1.jpg,left,noimg,whiteboard #1);
#ref(2012.09.06-2.jpg,left,noimg,whiteboard #2);
#ref(2012.09.06-3.jpg,left,noimg,whiteboard #3);
#ref(2012.09.06-4.jpg,left,noimg,whiteboard #4);
** &color(green){[第1回]}; 2012.10.3 [#d7c79036]

** &color(green){[lecture #2]}; 2012.9.20 given by Prof. Kimura [#i0fba71e]
-Q:独習用に、複素解析の良い本を紹介してほしい
-A:たまたま手元にある本ですが、薄い本の割には演習問題も多く含まれていて、その解答も不親切ではない（解き方のヒントも載っている）本として、「改訂　工科の数学４　複素関数（培風館）」があります。僕の持っているのは1994年版（第22刷）で、ミスプリントも少ないようです。どの本というよりもむしろ、複数の本を持って読み比べる事を勧めます。amazonの書評なども参考にしてみては。

** &color(green){[lecture #3]}; 2012.9.27 CACSD introduction with review of classical and modern control theory [#q23883cb]
-Q:シラバスは無いのか？
-A:あります。リンクはないようですが、ダウンロードはできました(10月2日)

+ introduction of Matlab and Simulink
--[[Basic usage of MATLAB and Simulink>/:~kobayasi/easttimor/2009/text/text_fixed.pdf]]
used for 情報処理演習及び考究II/Consideration and Practice of Information Processing II: Advanced Course of MATLAB
//
+ relationship between &color(black,cyan){TF}; and &color(black,lightgreen){SSR}; 
#ref(ex0927_1.m)
//
+ open-loop stability can be checked by &color(black,cyan){poles of TF}; and &color(black,lightgreen){eigenvalues of A-matrix in SSR};  
#ref(ex0927_2.m)
#ref(mod0927_2.mdl)
//
+ closed-loop stability
-- graphical test by &color(black,yellow){Nyquist stability criterion}; and &color(black,yellow){Bode plot}; with &color(black,yellow){GM};(gain margin) and &color(black,yellow){PM};(phase margin)
#ref(ex0927_3.m)
#ref(mod0927_3.mdl)
-- numerical test by &color(black,cyan){poles of closed-loop TF}; and &color(black,lightgreen){eigenvalues of A-matrix in closed-loop SSR}; 
#ref(ex0927_4.m)
-- example: stabilization of unstable system
#ref(ex0927_5.m)
#ref(mod0927_5.mdl)
-Q:質問があるときは、どうすれば良い？
-A:できるだけ当日の授業中に聞いてください。聞きにくければ授業後でも良いです。

 %-- 9/27/2012 1:07 PM --%
 a = 1
 pwd
 G1 = 1/(s+1)
 ex0927_1
 G1 = 1/(s+1)
 A
 ex0927_2
 G2_tf
 G2_tf.den
 G2_tf.den{:}
 G2_tf.num{:}
 eig(G2_tf)
 G2_ss.a
 eig(G2_ss.a)
 G2_ss
 G2_ss.a
 G2_ss.b
 ex0927_3
 nyquist(1.5*G3_tf)
 nyquist(-1.5*G3_tf)
 bode(-1.5*G3_tf)
 bode(1.5*G3_tf)
 K
 K = 1
 ex0927_4
 ex0927_5
 A
 eig(A)
 K = 0
 K=1
 ex0927_5 
-Q:コーシーの積分定理〜真性特異点を補講してほしい
-A:質問を小さく具体的にしてもらえると答えやすいです。定理などは、まずはそれを認めて、ツールとして使えるようになってください。使う状況としては、制御工学の例で言えば、ナイキストの安定定理の証明を追ってみる。ツールとして使えるようになってから、その定理の証明に取り組むのが、やる気が維持できて良いと思います。

#ref(2012.09.27-1.jpg,left,noimg,whiteboard #1);
#ref(2012.09.27-2.jpg,left,noimg,whiteboard #2);
-Q:教科書の s > 0 は、すべて Re s > 0 という意味か？
-A:そうです。

&color(black,red){!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! the followings are under construction !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!};
-Q:少し早かった
-A:余分な事を早口で喋ったところが、そういう印象を与えたのではないかと思います。
もう少しゆっくり喋るようにします。

** &color(green){[第2回]}; 2012.10.10 [#ibb4f4c3]

** &color(green){[lecture #4]}; 2011.10.13 Intro. to robust control theory (H infinity control theory) [#wf03a700]
- H infinity norm
++ robust stabilization
++ &color(black,yellow){performance optimization};
** &color(green){[第3回]}; 2012.10.17 [#y557b8dc]

- Example of performance optimization problem : disturbance attenuation problem
-- controller design with trial and error
#ref(ex1013_1.m)
-- controller design with H infinity control theory
#ref(ex1013_2.m)
** &color(green){[第4回]}; 2012.10.24 [#z0d38824]

 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
** &color(green){[第5回]}; 2012.10.31 [#ze53d1a0]

#ref(2011.10.13-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.13-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.13-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.13-4.jpg,left,noimg,whiteboard #4);
** &color(green){[第6回]}; 2012.11.7 [#a25375d4]

** &color(green){[lecture #5]}; 2011.10.7 Introduction to Robust Control (cont.) [#w07bf0cb]
- H infinity norm
++ &color(black,yellow){robust stabilization};
++ performance optimization
** &color(green){[第7回]}; 2012.11.14 中間テスト [#p4878489]

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

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

#ref(2011.10.20-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.20-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.20-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.20-4.jpg,left,noimg,whiteboard #4);

** &color(green){[lecture #6]}; 2011.10.27 norm (vector space, normed linear space), singular value, mixed sensitivity problem [#e3da44ba]
- H infinity &color(red){norm}; ... {robust stabilization, performance improvement}
- norm
#ref(norm.pdf);
-- size of {number, signal, system}
-- defined on &color(red){vector space (linear space)};
--- ---> normed linear space
--- ... optimization 
- H infinity norm : scalar (SISO) ---> matrix (MIMO)
-- absolute value ---> maximum &color(red){singular value};
#ref(norm2.pdf);
-- &color(black,yellow){robust stabilization or performance optimization problem ---> mixed sensitivity problem};
- reference
-- Feedback control theory / John C. Doyle, Bruce A. Francis and Allen R. Tannenbaum
#ref(feedback_control_theory.jpg);
--- 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
#ref(robust_and_optimal_control.jpg); 
--- 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

#ref(2011.10.27-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.27-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.27-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.27-4.jpg,left,noimg,whiteboard #4);
#ref(2011.10.27-5.jpg,left,noimg,whiteboard #5);

** &color(green){[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) [#b334e7c8]

see [[Prof. Kimura's page>http://mcweb.nagaokaut.ac.jp/~rescue-eng]]

#ref(aa-111110-1.jpg,left,noimg,whiteboard #1);
#ref(aa-111110-2.jpg,left,noimg,whiteboard #2);
#ref(aa-111110-3.jpg,left,noimg,whiteboard #3);
#ref(aa-111110-4.jpg,left,noimg,whiteboard #4);

** &color(green){[lecture #9]}; 2011.12.1 robust control design example: Robust Control System Synthesis for Pneumatic Systems (given by Prof. Kimura) [#z313cf27]

** &color(green){[lecture #10]}; 2011.12.8 Speed control of two inertia system with servo motor (1/3) [#v76c2b3e]
- Experimental setup
#ref(apparatus.ppt);
#ref(setup.pdf)
-- Objective for control system design
++ speed tracking
++ robust against inertia-load variation
- Modelling 
-- frequency response experiment results:
#ref(frdata_small_offset0.dat)
#ref(frdata_small_offset5.dat)
#ref(frdata_small_offset10.dat)
#ref(frdata_large_offset0.dat)
#ref(frdata_large_offset5.dat)
#ref(frdata_large_offset10.dat)
-- example of m-file
#ref(freqresp.m)
#ref(nominal.m)
#ref(weight.m);
 >> freqresp
 >> nominal
 >> weight
- Controller design (mixed sensitivity problem)
-- example of m-file
#ref(cont.m)
 >> cont
-- design example
#ref(cont.dat)
#ref(cont_order.dat)
#ref(cont.mat)
#ref(result_small.dat)
#ref(result_large.dat)
//-- example of m-file to compare designed controllers
//#ref(compare.m)

- report
+design your controller(s) so that the system performance is improved compared with the given example above
+Draw the following figures and explain the difference between two control systems &color(red){(your controller and the example above)};:
++bode diagram of controllers
++gain characteristic of closed-loop systems
++time response of control experiment
+Why is the performance of your system improved(or unfortunately decreased)?
--&size(30){&color(red){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 &size(30){&color(red){not later than 23th(Fri) Dec};};

- program sources for frequency response experiment
#ref(freqresp.h)
#ref(freqresp_module.c)
#ref(freqresp_app.c)
-- format of frdata.dat file
--- 1st column: frequency (Hz)
--- 2nd column: gain
--- 3rd column: phase (deg)
- program sources for control experiment
#ref(hinf.h)
#ref(hinf_module.c)
#ref(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.  

#ref(2011.12.08-1.jpg,left,noimg,whiteboard #1);

 %-- 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')



** &color(green){[lecture #11]}; 2011.12.15 Speed control of two inertia system with servo motor (2/3) [#y647f1bc]

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

#ref(2011.12.15-1.jpg,left,noimg,whiteboard #1);
#ref(2011.12.15-2.jpg,left,noimg,whiteboard #2);

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

** &color(green){[lecture #12]}; 2011.12.22 Speed control of two inertia system with servo motor (3/3) [#v5379e4b]

-preparation of your own controller(s)

[[participant list2011]]

** &color(red){supplementary lectures will be given by Prof. Kimura.}; [#p03d48d9]

-example for changing ws = 2 pi 0.1 -> 2 pi 0.01
#ref(cont_ws.m, cont.m);

-example to compare time responces
#ref(compare_result.m);

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


**related links [#zd9154ee]
//-東ティモール工学部復興支援/support of rehabilitation for faculty of eng. National University of Timor-Leste
//--[[How to control objects>/:~kobayasi/easttimor/2009/index.html]] to design, to simulate and to experiment control system by using MATLAB/Simulink with an application of Inverted Pendulum
--[[Prof. Kimura's page>http://sessyu.nagaokaut.ac.jp/~kimuralab/index.php?%C0%A9%B8%E6%B9%A9%B3%D8%C6%C3%CF%C0]]