*Advanced Automation [#n6ab2895] **2010.9.9 CACSD introduction [#pf7ea7ea] - 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 #ref(2010.9.9-1.jpg,left,noimg,whiteboard #1); #ref(2010.9.9-2.jpg,left,noimg,whiteboard #2); **2010.9.16 CACSD introduction [#pf7ea7ea] -review of clasical control theory ++ transfer function ++ Bode diagram ++ characteristics of 2nd-order system ++ Nyquist stability criterion ++ gain margin and phase margin -review of modern control theory ++ state-space representation #ref(ex1.m) #ref(mod1.mdl) #ref(ex2.m) #ref(ex3.m) #ref(ex4.m) #ref(2010.9.16-1.jpg,left,noimg,whiteboard #1); #ref(2010.9.16-2.jpg,left,noimg,whiteboard #2); **2010.9.30 Intro. to Robust Control [#m35d72cd] - H infinity norm ++ robust stabilization ++ performance improvement #ref(ex21.m) #ref(ex22.m) s = tf('s') G = 1/(s+1) norm(G, 'inf') P = 1/(s^2 + 0.2*s + 1) K = 1 nyquist(P*K) help impulse impulse(P) T = 1/(1 + P*K) impulse(T) sqrt(2)/(2*pi) 1/ans step(T) ex21 ex22 #ref(2010.9.30-1.jpg,left,noimg,whiteboard #1); #ref(2010.9.30-2.jpg,left,noimg,whiteboard #2); #ref(2010.9.30-3.jpg,left,noimg,whiteboard #3); ** 2010.10.7 Introduction to Robust Control (cont.) [#gfc16a3d] - H infinity norm ++ robust stabilization <-- ++ performance improvement #ref(ex23.m) #ref(ex24.m) #ref(ex25.m) #ref(mod2.mdl) #ref(2010.10.7-1.jpg,left,noimg,whiteboard #1); #ref(2010.10.7-2.jpg,left,noimg,whiteboard #2); #ref(2010.10.7-3.jpg,left,noimg,whiteboard #3); #ref(2010.10.7-4.jpg,left,noimg,whiteboard #4); ** 2010.10.14 norm, vector space, normed linear space [#ma3b796e] - H infinity &color(red){norm}; ... {robust stabilization, performance improvement} - norm -- size of {number, signal, system} -- defined on &color(red){vector space (linear space)}; --- ---> normed linear space --- ... optimization #ref(norm.pdf) #ref(2010.10.14-1.jpg,left,noimg,whiteboard #1); #ref(2010.10.14-2.jpg,left,noimg,whiteboard #2); #ref(2010.10.14-3.jpg,left,noimg,whiteboard #3); #ref(2010.10.14-4.jpg,left,noimg,whiteboard #4); ** 2010.10.21 eigenvalue, eigenvector, singular value decomposition [#yfa0a4e4] - H infinity norm : scalar (SISO) ---> matrix (MIMO) -- absolute value ---> maximum &color(red){singular value}; -- background: mixed sensitivity problem {robust stabilization and performance improvement are simultaneously considered} #ref(norm2.pdf) 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(2010.10.21-1.jpg,left,noimg,whiteboard #1); #ref(2010.10.21-2.jpg,left,noimg,whiteboard #2); #ref(2010.10.21-3.jpg,left,noimg,whiteboard #3); #ref(2010.10.21-4.jpg,left,noimg,whiteboard #4); #ref(2010.10.21-5.jpg,left,noimg,whiteboard #5); ** 2010.10.28 state space representation of connected system, state space representation of generalized plant for various control problem, mixed sensitivity problem [#be4365ec] #ref(2010.10.28-1.jpg,left,noimg,whiteboard #1); #ref(2010.10.28-2.jpg,left,noimg,whiteboard #2); #ref(ex26.m) ** 2010.11.4 robust control design example: Robust Control System Synthesis for Pneumatic Systems [#z86a8e2b] see [[RubustControlOfPneumatic-e.pdf>http://sessyu.nagaokaut.ac.jp/~kimuralab/index.php?plugin=attach&refer=%C0%A9%B8%E6%B9%A9%B3%D8%C6%C3%CF%C0&openfile=RubustControlOfPneumatic-e.pdf]] in Prof. Kimura's homepage for detail #ref(2010.11.4-1.jpg,left,noimg,whiteboard #1); #ref(2010.11.4-2.jpg,left,noimg,whiteboard #2); ** 2010.11.11 robust control design example (cont.) [#h2f8cc41] + Design H infinity controller with Eqs.(41)-(47) and generalized plant depicted in Fig.3 in the pdf file. ++ Confirm the following m-file for design: #ref(pneum.m); #ref(pneum_ans.m); ++ Derive the generalized plant by hand and correct the m-file. ++ Run the m-file to find controller. + Simulation #ref(simu_pneum.mdl); #ref(simu_pneum_noise.mdl); simu_pneum plot(t, y, 'r', t, r, 'b'); simu_pneum_noise plot(t, y, 'r', t, n, 'b') &color(red){========== Caution!!! The followings are under construction ==========}; ** Speed control of two inertia system with servo motor (1/3) [#ucb6f027] - Problem setup - Modelling (frequency response experiment) ** Speed control of two inertia system with servo motor (2/3) [#ce40f227] - Controller design -report ... **related links [#c31aa7a5] //-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]]