授業/制御工学特論2018
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開始行:
[[授業]]
*Advanced Automation [#x7f11daf]
[[latest lecture>#r9c48324]]
** &color(green){[lecture #1]}; 2018.9.6 outline of the l...
- outline of this lecture
-- syllabus([https://vos-lc-web01.nagaokaut.ac.jp/])
-- evaluation
--- mini report #1 ... 10%
--- mini exam #1 ... 10%
--- mini report #2 ... 10%
--- mini exam #2 ... 10%
--- final report ... 60%
-- [[schedule2018]] (tentative)
-- map &ref(授業/制御工学特論2017/map_v1.1.pdf); for revi...
- review : stabilization of SISO unstable plant by classi...
-- transfer functions / differential equations
-- poles / eigenvalues
-- impulse response / initial value response
-- ...
%-- 2018/09/06 12:48 --%
s = tf('s')
P = 1/(s-1)
pole(P)
impulse(P)
k = 2
Tyr = feedback(P*k, 1)
help feedback
Tyr = feedback(P*k, 1)
step(Tyr)
k
k = 10
Tyr = feedback(P*k, 1)
step(Tyr)
#ref(2018.09.06-1.jpg,left,noimg,whiteboard #1);
#ref(2018.09.06-2.jpg,left,noimg,whiteboard #2);
#ref(2018.09.06-3.jpg,left,noimg,whiteboard #3);
#ref(2018.09.06-4.jpg,left,noimg,whiteboard #4);
-Q: Q3とQ4で話した内容で&br;
古典制御:初期値が0である代わりにインパルスを入れる&br;
現代制御:初期値がある代わりにインパルスを入れない&br;
であっていますか?正確に聞きそびれたので教えてください
-A: 合っています。H∞制御の導入のところでまた詳しく説明す...
** &color(green){[lecture -]}; 2018.9.13 canceled [#o708b...
** &color(green){[lecture #2]}; 2018.9.20 review of class...
+ introduction of Matlab and Simulink
&ref(授業/制御工学特論2015/text_fixed.pdf); Basic usage o...
-- interactive system (no compilation, no variable difini...
-- m file
//-- example: stabilization of inverted pendulum (sorry i...
//--- [[derivation of equation of motion>http://c.nagaoka...
//--- [[stabilization of 1-link pendulum>http://c.nagaoka...
//--- [[stabilization of 2-link pendulum>http://c.nagaoka...
//
+ system representation: Transfer Function(TF) / State-Sp...
//
-- example: mass-spring-damper system
-- difinition of SSR
-- from SSR to TF
-- from TF to SSR: controllable canonical form
+ open-loop characteristic
-- open-loop stability: poles and eigenvalues
-- Bode plot and frequency response &ref(ex0920_1.m); &re...
--- cut off frequency; DC gain; -40dB/dec; variation of c
--- relation between P(jw) and steady-state response
+ closed-loop stability
-- Nyquist stability criterion (for L(s):stable)
-- Nyquist plot &ref(ex0920_2.m); &ref(mod0920_2.mdl);
--- Gain Margin(GM); Phase Margin(PM)
%-- 2018/09/20 13:05 --%
demo
t = [1, 2, 3]
who
a = t'
who
a(5) = 1
a(5,4) = 100
pwd
ex0920_1
who
P
P.den
P.den{:}
P
eig(P)
pole(P)
Pss = ss(P)
Pss
Pss.a
eig(Pss.a)
ex0920_2
#ref(2018.09.20-1.jpg,left,noimg,whiteboard #1);
#ref(2018.09.20-2.jpg,left,noimg,whiteboard #2);
#ref(2018.09.20-3.jpg,left,noimg,whiteboard #3);
#ref(2018.09.20-4.jpg,left,noimg,whiteboard #4);
#ref(2018.09.20-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #3]}; 2018.9.27 review of class...
+ LQR problem
-- controllability
-- cost function J >= 0
-- (semi)-positive definiteness
+ solution of LQR problem
-- ARE and quadratic equation
-- closed loop stability ... Lyapunov criterion
-- Jmin
&ref(授業/制御工学特論2015/lqr.pdf); ≒ &ref(授業/制御工学...
+ example
&ref(ex0927_1.m); &ref(mod0927_1.mdl);
%-- 2018/09/27 13:01 --%
ex0927_1
A
B
Uc
det(Uc)
eig(Q)
P
A'*P
A'*P + P*A + Q - P*B/R*B'*P
A'*P + P*A + Q - P*B*inv(R)*B'*P
Jmin
J
plot(t, J)
#ref(2018.09.27-1.jpg,left,noimg,whiteboard #1);
#ref(2018.09.27-2.jpg,left,noimg,whiteboard #2);
#ref(2018.09.27-3.jpg,left,noimg,whiteboard #3);
#ref(2018.09.27-4.jpg,left,noimg,whiteboard #4);
-Q: 計算する時間もっとほしいです
-A: もう少し見回って進捗を見るようにします。すみません。
** &color(green){[lecture #4]}; 2018.10.4 relation betwee...
- GOAL: to learn difference in concepts between LQR probl...
//- review of LQR problem and the simple example
+ a simple example relating LQR and H infinity control pr...
-- For given plant G
\[
G = \left[\begin{array}{c|c:c} a & 1 & b \\ \hline \sqrt{...
= \left\{ \begin{array}{l} \dot x = ax + bu + w\\ z = \le...
\]
with zero initial state value x(0) = 0,
find a state-feedback controller
\[ u = -f x \]
such that
\begin{eqnarray}
(i) &&\quad \mbox{closed loop is stable} \\
(ii) &&\quad \mbox{minimize}
\left\{\begin{array}{l} \| z \|_2 \mbox{ for } w(t) = \de...
\| T_{zw} \|_\infty \mbox{($H_\infty$ control problem)}\e...
\end{eqnarray}
-- comparison of norms in (ii) (for a = -1, b = 1, q = 1,...
\[
\begin{array}{|c||c|c|}\hline
& \mbox{LQR}: f=-1+\sqrt{2} & \quad \quad H_\infty: f=1\q...
J=\|z\|_2^2 & & \\ \hline
\|T_{zw}\|_\infty & & \\ \hline
\end{array}
\]
+ an alternative description to LQR problem
++ J = (L2 norm of z)^2
++ impulse resp. with zero initial value = initial value ...
+ definition of H infinity norm (SISO)
s = tf('s');
G1 = 1/(s+1);
bode(G1);
norm(G1, 'inf')
G2 = 1/(s^2 + 0.1*s + 1);
bode(G2);
norm(G2, 'inf')
+ definition of H infinity norm (SIMO)
+ solve the problem by hand
+ solve the problem by tool(hinfsyn)
&ref(ex1004.m);
%-- 2018/10/04 12:58 --%
s = tf('s');
G1 = 1/(s+1);
bode(G1);
norm(G1, 'inf')
G2 = 1/(s^2 + 0.1*s + 1);
bode(G2);
norm(G2, 'inf')
format long e
norm(G2, 'inf')
grid on
ex1004
#ref(2018.10.04-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.04-2.jpg,left,noimg,whiteboard #2);
#ref(2018.10.04-3.jpg,left,noimg,whiteboard #3);
#ref(2018.10.04-4.jpg,left,noimg,whiteboard #4);
#ref(2018.10.04-5.jpg,left,noimg,whiteboard #5);
#ref(2018.10.04-6.jpg,left,noimg,whiteboard #6);
-Q: z を L して Z(s) = Tzw W(s) の Tzw の導出? について...
-A: その直前の話
\[X(s) = \frac{1}{s - (a - bf)}W(s) = \frac{1}{s + 1 + f}...
\]
が大丈夫とすると、
\[z = \left[ \begin{array}{c} \sqrt{q} \\ -\sqrt{r} f \en...
\left[ \begin{array}{c} 1 \\ -f \end{array}\right]x
\]
より、
\[
Z(s) = \left[ \begin{array}{c} 1 \\ -f \end{array}\right]...
\]
すなわち、
\[
T_{zw}(s) = \left[ \begin{array}{c} 1 \\ -f \end{array}\r...
= \left[ \begin{array}{c} \frac{1}{s + 1 + f} \\ \frac{-f...
\]
です。
** &color(green){[lecture #5]}; 2018.10.11 relation betwe...
+ complete the table in simple example
+ confirm the cost function J for both controllers by sim...
-- block diagram in the simulink model
-- how to approximate impulse disturbance
-- impulse disturbance resp. with zero initial condition ...
+ confirm the closed-loop H infinity norm for both contro...
-- H infinity norm = L2 induced norm
-- review: steady-state response; the worst-case disturba...
-- what is the worst-case disturbance in the simple examp...
+ general state-feedback case: &ref(授業/制御工学特論2015...
-- includes the simple example as a special case
-- LQR &ref(授業/制御工学特論2015/lqr.pdf); is included a...
%-- 2018/10/11 12:58 --%
sqrt(2-sqrt(2))
mod1011
f
ex1004
a
b
q
r
A
f
f = -1+sqrt(2)
x0
x0 = 0
h
h = 0.1
zz
h = 0.001
zz
f = 1
zz
x0 = 1
zz
f
h
h = 1
x0
x0 = 0
zz
zz(end)
zz(end)/ww(end)
sqrt(zz(end)/ww(end))
h
h = 100
sqrt(zz(end)/ww(end))
f = sqrt(2)-1
h
sqrt(zz(end)/ww(end))
#ref(2018.10.11-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.11-2.jpg,left,noimg,whiteboard #2);
-Q: LQR は外乱を考慮しない制御理論という認識でよいか
-A: 元の問題に外乱の項が無い、という意味ではそうです。が...
一方、明示的に外乱(ノイズ)の項を加えたLQG問題もあります。
** &color(green){[lecture #6]}; 2018.10.18 Mixed sensitiv...
+ outline: &ref(授業/制御工学特論2017/map_v1.1_mixedsens1...
-- sensitivity function S and complementary sensitivity f...
+ H infinity control problem (general case)
-- with generalized plant G
-- including the state-feedback case)
+ reference tracking problem
-- corresponding generalized plant G ?
-- how to translate the condition (ii) into one with H in...
-- introduction of weighting function for sensitivity fun...
+ design example &ref(ex1018_1.m); &ref(ex1018_2.m);
+ the small gain theorem
-- proof: Nyquist stability criterion
//+ from performance optimization to robust stabilization
%-- 2018/10/18 12:58 --%
ex1018_1
P
pole(P)
eig(P)
ex1018_2
G
who
K_hinf
eig(K.a)
eig(K_hinf.a)
ex1018_2
K_hinf
figure(5)
bode(K_hinf)
-Q: \[
{}^\forall \ \omega
\] とか \[ {}^\forall \ \Delta \] とかの ∀って何でしたっ...
-A: 「すべての」です。
-Q: ex1018_2.m の 13行目の説明がはやくて分からなかった。
-A: hinfsyn ... H∞制御問題を解きます。第一引数に一般化プ...
#ref(2018.10.18-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.18-2.jpg,left,noimg,whiteboard #2);
#ref(2018.10.18-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #7]}; 2018.10.25 Mixed sensitiv...
+ review: the small gain theorem ... robust stability = H...
+ outline: from point to set &ref(授業/制御工学特論2017/m...
+ normalized uncertainty Delta
+ uncertainty model
+ how to determine P0 and WT
-- example: frequency response of plant with perturbation...
-- frequency response based procedure for P0 and WT &ref(...
+ robust stabilization problem and equivalent problem
-- design example and simulation &ref(ex1025_3.m); &ref(m...
%-- 2018/10/25 13:25 --%
ex1025_1
ex1025_2
ex1025_3
mod1025
c
c = 0.8
c = 1.3
c = 2
#ref(2018.10.25-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.25-2.jpg,left,noimg,whiteboard #2);
#ref(2018.10.25-3.jpg,left,noimg,whiteboard #3);
#ref(2018.10.25-4.jpg,left,noimg,whiteboard #4); ... sorr...
-Q: additive uncertainty model は multiplicative 〜 を含...
-A: 確かに今日説明したように、W(s) = P0(s)WT(s) とおけば...
-Q:
-Q: ex1025_1.m で
\[ \tilde P(s) = \frac{1}{(s-1)(cs+1)}
\]
の (cs+1) の部分が不安定にならない理由がよく分かりません...
-A: その部分に対応する極は cs + 1 = 0 より、s = -1/c です...
** &color(green){[lecture #8]}; 2018.11.1 Mixed sensitivi...
- review: &ref(授業/制御工学特論2017/map_v1.1_mixedsens2....
- outline:
++ how to design controllers considering both conditions ...
++ gap between nominal performance and robust performance
+ mixed sensitivity problem ---> (1) and (2) : proof
+ generalized plant for mixed senstivity problem
+ design example &ref(ex1101_1.m); minimize gamma by hand
+ gamma iteration by bisection method &ref(ex1101_2.m);
+ nominal performance and robust performance &ref(ex1101_...
+ introduction of robust performance problem
%-- 2018/11/01 12:59 --%
ex1101_1
gam
ex1101_1
K
ex1101_2
ex1101_3
#ref(2018.11.01-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.01-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.01-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #9]}; 2018.11.8 robust performa...
-- [[schedule2018]] mini report #1 and exam #1
+ review
-- mixed sensitivity problem : N.P. but not R.P.
-- robust performance problem (R.P.)
c.f. the last whiteboard
+ an equivalent robust stability (R.S.) problem to R.P.
-- with structured uncertainty Delta hat
+ definition of H infinity norm for general case (MIMO)
-- definition of singular values and the maximum singular...
M = [1i, 1i; 0, 1]
M'
eig(M'*M)
svd(M)
-- mini report #1 &ref(report1.pdf); ... You will have a ...
+ proof of ||Delta hat||_inf <= 1
+ design example: &ref(ex1108_1.m);
-- robust performance is achieved but large gap
-- non structured uncertainty is considered ... the desig...
%-- 2018/11/08 13:03 --%
ex1101_1
ex1101_2
ex1101_3
1i
j
M = [1i, 1i; 0, 1]
M'
eig(M'*M)
svd(M)
(3+sqrt(5))/2
sqrt((3+sqrt(5))/2)
ex1108_1
#ref(2018.11.08-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.08-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.08-3.jpg,left,noimg,whiteboard #3);
#ref(2018.11.08-4.jpg,left,noimg,whiteboard #4);
-Q: 共役複素数の~(バー)と最大を表す~(バー)は行列がR(...
-A: そういうことではなく、単に、複素共役にも最大にも同じ...
-Q: λ(M*M)が実数の証明レポートにしません?
-A: 「mini」レポートにならなさそうなので、今年度はレポー...
** &color(green){[lecture #10]}; 2018.11.15 Robust perfor...
+ return of mini report #1
+ review
-- robust performance but too conservative
ex1108_1
-- robust stability problem for Delta hat and its equival...
-- structured unertainty Delta hat and unstructured uncer...
+ SVD: singular value decomposition
-- definition
-- meaning of the largest singular value
-- 2-norm of vectors (Euclidean norm)
-- SVD for 2-by-2 real matrix &ref(ex1115_1.m);
%-- 2018/11/15 13:01 --%
M = [1, 2; 3, 4]
[U, S, V] = svd(M)
M = [1, 1i/sqrt(2); 1, -1i/sqrt(2)]
[U, S, V] = svd(M)
U'*U
format long e
U'*U
V'*V
M = [1, 2; 3, 4]
[U, S, V] = svd(M)
fomat short
format short
[U, S, V] = svd(M)
ex1115_1
S
sys = tf(1, [1, 1])
sys2 = tf(1, [1, 1])
sys2 = tf(1, [1, 2])
sys = tf(1, [1, 1])
sys
sys2
M = [0, sys; 0, sys2]
M
hinfnorm(M)
M = [0, sys; 0, sys]
hinfnorm(M)
#ref(2018.11.15-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.15-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.15-3.jpg,left,noimg,whiteboard #3);
#ref(2018.11.15-4.jpg,left,noimg,whiteboard #4);
-Q:
\[ \sigma_i u_i = M v_i
\]
が証明できれば
\[
\bar \sigma(M) = \max_{a\neq 0}\frac{\| b\|_2}{\|a\|_2}
\]
がいえるということで合っていますか?
-A: 合っています。(厳密には、ベクトル a を
\[ a = \Sigma_{i=1}^m \alpha_i v_i
\]
のように、ベクトル vi の線形結合で表して実数 αi を振って2...
-Q:
\[ \|M\|_\infty < 1
\]
をたしかめる時
\[ \bar \sigma(M) \]
を計算して出しますが 1より大きいかどうか考えるなら最後の√...
-A: その通りです。
-Q: Σは M の大きさによっては、
//\[
//\Sigma = \left[ \begin{mat}{c} \begin{mat}{cccc} \sigma...
//\]
\[
\Sigma = \left[ \begin{array}{c} \begin{array}{ccc} \sigm...
\]
のゼロ行列はなくなりますか?
また、
\[ M^{p\times m} \]
が p < m のときは Σ はどうなりますか?
-A: Mが正方行列つまりp=mのときゼロ行列はなくなります。ま...
** &color(green){[lecture #11]}; 2018.11.22 Robust perfor...
+ review: R.S. prob. for Delta hat and Delta tilde
+ scaled H infinity control problem
+ how to determine structure of scaling matrix
+ design example &ref(ex1122_1.m);
ex1108_1
gam2 = gam_opt
K2 = K_opt;
ex1122_1
gam_opt
+ mini report #2 &ref(report2.pdf);
+ mini exam #1 (10 min.)
%-- 2018/11/22 13:37 --%
ex1108_1
gam2 = gam_opt
K2 = K_opt
ex1122_1
gam_opt
gam2
d_opt
#ref(2018.11.22-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.22-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.22-3.jpg,left,noimg,whiteboard #3);
#ref(2018.11.22-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #12]}; 2018.11.29 Robust perfor...
+ return of mini exam #1 and mini report #2
+ review of scaling &ref(ex1129_1.m);
+ introduction of a practical system: Speed control of tw...
-- experimental setup &br;
&ref(授業/制御工学特論2014/setup.pdf); ... ``spring plate...
&ref(photo1.png,left,noimg);
-- objective of control system = disturbance attenuation ...
-- frequency response experiment and physical model of sp...
#ref(ex1129_2.m);
#ref(servo1.dat);
#ref(servo2.dat);
-- room 374 @ Dept. Mech. Bldg. 2
%-- 2018/11/29 13:07 --%
ex1129_1
gam2
gam3
clp2.b
format long
norm(M3_d, 'inf')
ex1129_2
#ref(2018.11.29-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.29-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #13]}; 2018.12.6 Control system...
+ mini exam #2
-- [[schedule2018]]
+ review of the experimental system
-- closed-loop system of 2-by-2 plant G and controller K
-- closed-loop gain is desired to be minimized
-- how to handle modeling error of G ?
+ design example
-- frequency response experiment data&br;
[[servo1.dat>/:~exp/seigyokougakutokuron_2018/exp/freqres...
[[servo2.dat>/:~exp/seigyokougakutokuron_2018/exp/freqres...
-- determination of plant model(nominal plant and additiv...
&ref(nominal.m);&br;
&ref(weight.m);
-- configuration of generalized plant and controller desi...
&ref(cont.m);
-- comparison of closed-loop gain characteristics with an...
&ref(compare.m);
-- result of control experiment&br;
[[result.dat>/:~exp/seigyokougakutokuron_2018/exp/design_...
&ref(perf.m);
//+ room 157 @ Dept. Mech. Bldg.2
+ final report and remote experimental system
++design your controller(s) so that the system performanc...
++Draw the following figures and explain the difference b...
+++bode diagram of controllers
+++gain characteristic of closed-loop system from w to z
+++time response of control experiment
++Why is the performance of your system improved(or unfor...
--&size(30){&color(red){due date: 4th(Fri) Jan 17:00};};
--submit your report(pdf or doc) by e-mail to kobayasi@na...
--You can use Japanese
--maximum controller order is 20
--submit your &size(25){&color(red){controller.dat, contr...
//--Your login password will be e-mailed on Dec 16.
--the system will be started until next lecture
--You can send up to %%5%%&color(red){10}; controllers
--&size(30){&color(black){[[control experimental results ...
--freqresp ... frequency response will be measured and up...
+ how to improve the performance ?
-- %%order of the nominal plant%% accuracy of the nominal...
-- weighting for robust stability
//+ detailed explanation of m-files in the previous lecture
+ specifications of the experimental system
++ program sources for frequency response experiment
--- [[freqresp.h>/:~exp/seigyokougakutokuron_2018/freqres...
--- [[freqresp_module.c>/:~exp/seigyokougakutokuron_2018/...
--- [[freqresp_app.c>/:~exp/seigyokougakutokuron_2018/fre...
--- format of servo1.dat (w is used instead of u for serv...
1st column ... frequency (Hz)
2nd column ... gain from u(Nm) to y(rad/s)
3rd column ... phase (deg) from u to y
4th column ... gain from u to z
5th column ... phase (deg) from u to z
++ program sources for control experiment
--- [[hinf.h>/:~exp/seigyokougakutokuron_2018/hinf.h]]
--- [[hinf_module.c>/:~exp/seigyokougakutokuron_2018/hinf...
--- [[hinf_app.c>/:~exp/seigyokougakutokuron_2018/hinf_ap...
--- format of result.dat
1st column: time (s)
2nd column: y (rad/s)
3rd column: z (rad/s)
4th column: u (Nm)
5th column: w (Nm)
++ configuration of control experiment
--- disturbance signal w is specified as described in hin...
w = 0; // disturbance torque for driven motor ...
if((t > 2)&&(t < 3)){
w = RATED_TORQ * -0.15;
}
if((t > 4)&&(t < 5)){
w = RATED_TORQ * -0.1 * sin(2*M_PI*5.0 * (t-4.0));
}
da_conv(torq_volt_conv_1(w), 1);
--- control signal u is limited as specified in hinf.h an...
#define U_MAX (RATED_TORQ / 3.0)
if(u > U_MAX) u = U_MAX;
if(u < -U_MAX) u = -U_MAX;
u is generated by PI control for t < 1(s). Your designed ...
++ calculation of rotational speed
--- The rotational speed is approximately calculated by u...
theta_rad[0] = (double)read_theta(0) / (double)Pn212 * 2...
theta_rad[1] = (double)read_theta(1) / (double)Pn212 * 2...
y = (theta_rad[0] - theta_rad_before[0]) / msg->sampling...
z = (theta_rad[1] - theta_rad_before[1]) / msg->sampling...
theta_rad_before[0] = theta_rad[0];
theta_rad_before[1] = theta_rad[1];
where the sampling period is given as 0.25 ms.
%-- 2018/12/06 12:53 --%
nominal
w
size(w)
servo1
size(servo1)
nupwd
pwd
cd data
ls
cd ..
nominal
size(w)
size(resp)
size(servo2)
size(servo1)
n
nominal
n
k
resp
k
w
clear all
nominal
weight
cont
compare
perf
nominal
#ref(2018.12.06-1.jpg,left,noimg,whiteboard #1);
#ref(2018.12.06-2.jpg,left,noimg,whiteboard #2);
-Q: コントローラは何で書くのか?
-A: 説明が曖昧でしたが、コントローラの状態空間実現(のフ...
具体的には、これらのファイルが実験機で動作しているC言語の...
** &color(green){[lecture #14]}; 2018.12.13 Control syste...
- return of mini exam #2
- review & supplemental explanations
-- final report
--- control objective is to suppress speed fluctuation of...
--- unstable controller is admitted
--- no strict control objective is given ( there is a fre...
--- c2d() is used to discretize the resultant continuous-...
-- web based remote experiment system
--- now you can login after registration
--- room temperature is displayed and stored in temp.txt ...
--- the system will be unavailable from %%21(Fri)%% &colo...
- preparation of your own controller(s) by using the remo...
#ref(nominal_ave.m);
#ref(sub.m);
%-- 2018/12/13 13:58 --%
help subspace
nominal_ave
pwd
cd ..
pwd
nominal_ave
G_g
G1_g
G2_g
(G_g + G10_g)/2
bode((G_g + G10_g)/2)
figure(2)
bode((G_g + G10_g)/2)
figure(2)
#ref(2018.12.13-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #15]}; 2018.12.20 Control syste...
- preparation of your own controller(s)
-- use [[design example #3>/:~exp/seigyokougakutokuron_20...
-- discuss relationship between the required figures (a),...
-- driving and driven torque are set to zero when driven-...
#define SPEED_MAX 60.0 // driving torque becomes zero wh...
and [[hinf_module.c>/:~exp/seigyokougakutokuron_2018/hinf...
int flag_speed_excess = 0; // 2018.12.19
if(flag_speed_excess == 1) w = 0; // 2018.12.20
da_conv(torq_volt_conv_1(w), 1);
if(fabs(z) > SPEED_MAX) flag_speed_excess = 1; // ...
if(flag_speed_excess == 1) u = 0; // 2018.12.19
#ifndef NO_CONTROL
da_conv(torq_volt_conv_0(u), 0);
#endif
-- the system will be unavailable 7:30 -- 19:00 on 22(Sat)
- questionnaires
-- to university
-- for web-based experimental environment
%-- 2018/12/20 13:19 --%
nominal
weight
cont
compare
nominal
weight
ctrlpref
cont
compare
weigh
weight
cont
weight
nominal
weight
#ref(2018.12.20-1.jpg,left,noimg,whiteboard #1);
-Q: うまくいくとやっぱりたのしいですね。
-A: モチベーションが高まったところで、過去の授業の内容を...
//■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
//&color(black,red){&size(20){!!! the remaining page is u...
//
- 2018.12.20 19:00
&size(30){&color(red){due to unexpected alert occurred at...
// if(fabs(z) > SPEED_MAX) flag_speed_excess = ...
if((fabs(z) > SPEED_MAX) || (fabs(y) > SPEED_MAX)) ...
//**related links [#g1a68a2b]
//-東ティモール工学部復興支援/support of rehabilitation f...
//--[[How to control objects>/:~kobayasi/easttimor/2009/i...
//--[[Prof. Kimura's page>http://sessyu.nagaokaut.ac.jp/~...
終了行:
[[授業]]
*Advanced Automation [#x7f11daf]
[[latest lecture>#r9c48324]]
** &color(green){[lecture #1]}; 2018.9.6 outline of the l...
- outline of this lecture
-- syllabus([https://vos-lc-web01.nagaokaut.ac.jp/])
-- evaluation
--- mini report #1 ... 10%
--- mini exam #1 ... 10%
--- mini report #2 ... 10%
--- mini exam #2 ... 10%
--- final report ... 60%
-- [[schedule2018]] (tentative)
-- map &ref(授業/制御工学特論2017/map_v1.1.pdf); for revi...
- review : stabilization of SISO unstable plant by classi...
-- transfer functions / differential equations
-- poles / eigenvalues
-- impulse response / initial value response
-- ...
%-- 2018/09/06 12:48 --%
s = tf('s')
P = 1/(s-1)
pole(P)
impulse(P)
k = 2
Tyr = feedback(P*k, 1)
help feedback
Tyr = feedback(P*k, 1)
step(Tyr)
k
k = 10
Tyr = feedback(P*k, 1)
step(Tyr)
#ref(2018.09.06-1.jpg,left,noimg,whiteboard #1);
#ref(2018.09.06-2.jpg,left,noimg,whiteboard #2);
#ref(2018.09.06-3.jpg,left,noimg,whiteboard #3);
#ref(2018.09.06-4.jpg,left,noimg,whiteboard #4);
-Q: Q3とQ4で話した内容で&br;
古典制御:初期値が0である代わりにインパルスを入れる&br;
現代制御:初期値がある代わりにインパルスを入れない&br;
であっていますか?正確に聞きそびれたので教えてください
-A: 合っています。H∞制御の導入のところでまた詳しく説明す...
** &color(green){[lecture -]}; 2018.9.13 canceled [#o708b...
** &color(green){[lecture #2]}; 2018.9.20 review of class...
+ introduction of Matlab and Simulink
&ref(授業/制御工学特論2015/text_fixed.pdf); Basic usage o...
-- interactive system (no compilation, no variable difini...
-- m file
//-- example: stabilization of inverted pendulum (sorry i...
//--- [[derivation of equation of motion>http://c.nagaoka...
//--- [[stabilization of 1-link pendulum>http://c.nagaoka...
//--- [[stabilization of 2-link pendulum>http://c.nagaoka...
//
+ system representation: Transfer Function(TF) / State-Sp...
//
-- example: mass-spring-damper system
-- difinition of SSR
-- from SSR to TF
-- from TF to SSR: controllable canonical form
+ open-loop characteristic
-- open-loop stability: poles and eigenvalues
-- Bode plot and frequency response &ref(ex0920_1.m); &re...
--- cut off frequency; DC gain; -40dB/dec; variation of c
--- relation between P(jw) and steady-state response
+ closed-loop stability
-- Nyquist stability criterion (for L(s):stable)
-- Nyquist plot &ref(ex0920_2.m); &ref(mod0920_2.mdl);
--- Gain Margin(GM); Phase Margin(PM)
%-- 2018/09/20 13:05 --%
demo
t = [1, 2, 3]
who
a = t'
who
a(5) = 1
a(5,4) = 100
pwd
ex0920_1
who
P
P.den
P.den{:}
P
eig(P)
pole(P)
Pss = ss(P)
Pss
Pss.a
eig(Pss.a)
ex0920_2
#ref(2018.09.20-1.jpg,left,noimg,whiteboard #1);
#ref(2018.09.20-2.jpg,left,noimg,whiteboard #2);
#ref(2018.09.20-3.jpg,left,noimg,whiteboard #3);
#ref(2018.09.20-4.jpg,left,noimg,whiteboard #4);
#ref(2018.09.20-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #3]}; 2018.9.27 review of class...
+ LQR problem
-- controllability
-- cost function J >= 0
-- (semi)-positive definiteness
+ solution of LQR problem
-- ARE and quadratic equation
-- closed loop stability ... Lyapunov criterion
-- Jmin
&ref(授業/制御工学特論2015/lqr.pdf); ≒ &ref(授業/制御工学...
+ example
&ref(ex0927_1.m); &ref(mod0927_1.mdl);
%-- 2018/09/27 13:01 --%
ex0927_1
A
B
Uc
det(Uc)
eig(Q)
P
A'*P
A'*P + P*A + Q - P*B/R*B'*P
A'*P + P*A + Q - P*B*inv(R)*B'*P
Jmin
J
plot(t, J)
#ref(2018.09.27-1.jpg,left,noimg,whiteboard #1);
#ref(2018.09.27-2.jpg,left,noimg,whiteboard #2);
#ref(2018.09.27-3.jpg,left,noimg,whiteboard #3);
#ref(2018.09.27-4.jpg,left,noimg,whiteboard #4);
-Q: 計算する時間もっとほしいです
-A: もう少し見回って進捗を見るようにします。すみません。
** &color(green){[lecture #4]}; 2018.10.4 relation betwee...
- GOAL: to learn difference in concepts between LQR probl...
//- review of LQR problem and the simple example
+ a simple example relating LQR and H infinity control pr...
-- For given plant G
\[
G = \left[\begin{array}{c|c:c} a & 1 & b \\ \hline \sqrt{...
= \left\{ \begin{array}{l} \dot x = ax + bu + w\\ z = \le...
\]
with zero initial state value x(0) = 0,
find a state-feedback controller
\[ u = -f x \]
such that
\begin{eqnarray}
(i) &&\quad \mbox{closed loop is stable} \\
(ii) &&\quad \mbox{minimize}
\left\{\begin{array}{l} \| z \|_2 \mbox{ for } w(t) = \de...
\| T_{zw} \|_\infty \mbox{($H_\infty$ control problem)}\e...
\end{eqnarray}
-- comparison of norms in (ii) (for a = -1, b = 1, q = 1,...
\[
\begin{array}{|c||c|c|}\hline
& \mbox{LQR}: f=-1+\sqrt{2} & \quad \quad H_\infty: f=1\q...
J=\|z\|_2^2 & & \\ \hline
\|T_{zw}\|_\infty & & \\ \hline
\end{array}
\]
+ an alternative description to LQR problem
++ J = (L2 norm of z)^2
++ impulse resp. with zero initial value = initial value ...
+ definition of H infinity norm (SISO)
s = tf('s');
G1 = 1/(s+1);
bode(G1);
norm(G1, 'inf')
G2 = 1/(s^2 + 0.1*s + 1);
bode(G2);
norm(G2, 'inf')
+ definition of H infinity norm (SIMO)
+ solve the problem by hand
+ solve the problem by tool(hinfsyn)
&ref(ex1004.m);
%-- 2018/10/04 12:58 --%
s = tf('s');
G1 = 1/(s+1);
bode(G1);
norm(G1, 'inf')
G2 = 1/(s^2 + 0.1*s + 1);
bode(G2);
norm(G2, 'inf')
format long e
norm(G2, 'inf')
grid on
ex1004
#ref(2018.10.04-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.04-2.jpg,left,noimg,whiteboard #2);
#ref(2018.10.04-3.jpg,left,noimg,whiteboard #3);
#ref(2018.10.04-4.jpg,left,noimg,whiteboard #4);
#ref(2018.10.04-5.jpg,left,noimg,whiteboard #5);
#ref(2018.10.04-6.jpg,left,noimg,whiteboard #6);
-Q: z を L して Z(s) = Tzw W(s) の Tzw の導出? について...
-A: その直前の話
\[X(s) = \frac{1}{s - (a - bf)}W(s) = \frac{1}{s + 1 + f}...
\]
が大丈夫とすると、
\[z = \left[ \begin{array}{c} \sqrt{q} \\ -\sqrt{r} f \en...
\left[ \begin{array}{c} 1 \\ -f \end{array}\right]x
\]
より、
\[
Z(s) = \left[ \begin{array}{c} 1 \\ -f \end{array}\right]...
\]
すなわち、
\[
T_{zw}(s) = \left[ \begin{array}{c} 1 \\ -f \end{array}\r...
= \left[ \begin{array}{c} \frac{1}{s + 1 + f} \\ \frac{-f...
\]
です。
** &color(green){[lecture #5]}; 2018.10.11 relation betwe...
+ complete the table in simple example
+ confirm the cost function J for both controllers by sim...
-- block diagram in the simulink model
-- how to approximate impulse disturbance
-- impulse disturbance resp. with zero initial condition ...
+ confirm the closed-loop H infinity norm for both contro...
-- H infinity norm = L2 induced norm
-- review: steady-state response; the worst-case disturba...
-- what is the worst-case disturbance in the simple examp...
+ general state-feedback case: &ref(授業/制御工学特論2015...
-- includes the simple example as a special case
-- LQR &ref(授業/制御工学特論2015/lqr.pdf); is included a...
%-- 2018/10/11 12:58 --%
sqrt(2-sqrt(2))
mod1011
f
ex1004
a
b
q
r
A
f
f = -1+sqrt(2)
x0
x0 = 0
h
h = 0.1
zz
h = 0.001
zz
f = 1
zz
x0 = 1
zz
f
h
h = 1
x0
x0 = 0
zz
zz(end)
zz(end)/ww(end)
sqrt(zz(end)/ww(end))
h
h = 100
sqrt(zz(end)/ww(end))
f = sqrt(2)-1
h
sqrt(zz(end)/ww(end))
#ref(2018.10.11-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.11-2.jpg,left,noimg,whiteboard #2);
-Q: LQR は外乱を考慮しない制御理論という認識でよいか
-A: 元の問題に外乱の項が無い、という意味ではそうです。が...
一方、明示的に外乱(ノイズ)の項を加えたLQG問題もあります。
** &color(green){[lecture #6]}; 2018.10.18 Mixed sensitiv...
+ outline: &ref(授業/制御工学特論2017/map_v1.1_mixedsens1...
-- sensitivity function S and complementary sensitivity f...
+ H infinity control problem (general case)
-- with generalized plant G
-- including the state-feedback case)
+ reference tracking problem
-- corresponding generalized plant G ?
-- how to translate the condition (ii) into one with H in...
-- introduction of weighting function for sensitivity fun...
+ design example &ref(ex1018_1.m); &ref(ex1018_2.m);
+ the small gain theorem
-- proof: Nyquist stability criterion
//+ from performance optimization to robust stabilization
%-- 2018/10/18 12:58 --%
ex1018_1
P
pole(P)
eig(P)
ex1018_2
G
who
K_hinf
eig(K.a)
eig(K_hinf.a)
ex1018_2
K_hinf
figure(5)
bode(K_hinf)
-Q: \[
{}^\forall \ \omega
\] とか \[ {}^\forall \ \Delta \] とかの ∀って何でしたっ...
-A: 「すべての」です。
-Q: ex1018_2.m の 13行目の説明がはやくて分からなかった。
-A: hinfsyn ... H∞制御問題を解きます。第一引数に一般化プ...
#ref(2018.10.18-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.18-2.jpg,left,noimg,whiteboard #2);
#ref(2018.10.18-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #7]}; 2018.10.25 Mixed sensitiv...
+ review: the small gain theorem ... robust stability = H...
+ outline: from point to set &ref(授業/制御工学特論2017/m...
+ normalized uncertainty Delta
+ uncertainty model
+ how to determine P0 and WT
-- example: frequency response of plant with perturbation...
-- frequency response based procedure for P0 and WT &ref(...
+ robust stabilization problem and equivalent problem
-- design example and simulation &ref(ex1025_3.m); &ref(m...
%-- 2018/10/25 13:25 --%
ex1025_1
ex1025_2
ex1025_3
mod1025
c
c = 0.8
c = 1.3
c = 2
#ref(2018.10.25-1.jpg,left,noimg,whiteboard #1);
#ref(2018.10.25-2.jpg,left,noimg,whiteboard #2);
#ref(2018.10.25-3.jpg,left,noimg,whiteboard #3);
#ref(2018.10.25-4.jpg,left,noimg,whiteboard #4); ... sorr...
-Q: additive uncertainty model は multiplicative 〜 を含...
-A: 確かに今日説明したように、W(s) = P0(s)WT(s) とおけば...
-Q:
-Q: ex1025_1.m で
\[ \tilde P(s) = \frac{1}{(s-1)(cs+1)}
\]
の (cs+1) の部分が不安定にならない理由がよく分かりません...
-A: その部分に対応する極は cs + 1 = 0 より、s = -1/c です...
** &color(green){[lecture #8]}; 2018.11.1 Mixed sensitivi...
- review: &ref(授業/制御工学特論2017/map_v1.1_mixedsens2....
- outline:
++ how to design controllers considering both conditions ...
++ gap between nominal performance and robust performance
+ mixed sensitivity problem ---> (1) and (2) : proof
+ generalized plant for mixed senstivity problem
+ design example &ref(ex1101_1.m); minimize gamma by hand
+ gamma iteration by bisection method &ref(ex1101_2.m);
+ nominal performance and robust performance &ref(ex1101_...
+ introduction of robust performance problem
%-- 2018/11/01 12:59 --%
ex1101_1
gam
ex1101_1
K
ex1101_2
ex1101_3
#ref(2018.11.01-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.01-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.01-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #9]}; 2018.11.8 robust performa...
-- [[schedule2018]] mini report #1 and exam #1
+ review
-- mixed sensitivity problem : N.P. but not R.P.
-- robust performance problem (R.P.)
c.f. the last whiteboard
+ an equivalent robust stability (R.S.) problem to R.P.
-- with structured uncertainty Delta hat
+ definition of H infinity norm for general case (MIMO)
-- definition of singular values and the maximum singular...
M = [1i, 1i; 0, 1]
M'
eig(M'*M)
svd(M)
-- mini report #1 &ref(report1.pdf); ... You will have a ...
+ proof of ||Delta hat||_inf <= 1
+ design example: &ref(ex1108_1.m);
-- robust performance is achieved but large gap
-- non structured uncertainty is considered ... the desig...
%-- 2018/11/08 13:03 --%
ex1101_1
ex1101_2
ex1101_3
1i
j
M = [1i, 1i; 0, 1]
M'
eig(M'*M)
svd(M)
(3+sqrt(5))/2
sqrt((3+sqrt(5))/2)
ex1108_1
#ref(2018.11.08-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.08-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.08-3.jpg,left,noimg,whiteboard #3);
#ref(2018.11.08-4.jpg,left,noimg,whiteboard #4);
-Q: 共役複素数の~(バー)と最大を表す~(バー)は行列がR(...
-A: そういうことではなく、単に、複素共役にも最大にも同じ...
-Q: λ(M*M)が実数の証明レポートにしません?
-A: 「mini」レポートにならなさそうなので、今年度はレポー...
** &color(green){[lecture #10]}; 2018.11.15 Robust perfor...
+ return of mini report #1
+ review
-- robust performance but too conservative
ex1108_1
-- robust stability problem for Delta hat and its equival...
-- structured unertainty Delta hat and unstructured uncer...
+ SVD: singular value decomposition
-- definition
-- meaning of the largest singular value
-- 2-norm of vectors (Euclidean norm)
-- SVD for 2-by-2 real matrix &ref(ex1115_1.m);
%-- 2018/11/15 13:01 --%
M = [1, 2; 3, 4]
[U, S, V] = svd(M)
M = [1, 1i/sqrt(2); 1, -1i/sqrt(2)]
[U, S, V] = svd(M)
U'*U
format long e
U'*U
V'*V
M = [1, 2; 3, 4]
[U, S, V] = svd(M)
fomat short
format short
[U, S, V] = svd(M)
ex1115_1
S
sys = tf(1, [1, 1])
sys2 = tf(1, [1, 1])
sys2 = tf(1, [1, 2])
sys = tf(1, [1, 1])
sys
sys2
M = [0, sys; 0, sys2]
M
hinfnorm(M)
M = [0, sys; 0, sys]
hinfnorm(M)
#ref(2018.11.15-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.15-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.15-3.jpg,left,noimg,whiteboard #3);
#ref(2018.11.15-4.jpg,left,noimg,whiteboard #4);
-Q:
\[ \sigma_i u_i = M v_i
\]
が証明できれば
\[
\bar \sigma(M) = \max_{a\neq 0}\frac{\| b\|_2}{\|a\|_2}
\]
がいえるということで合っていますか?
-A: 合っています。(厳密には、ベクトル a を
\[ a = \Sigma_{i=1}^m \alpha_i v_i
\]
のように、ベクトル vi の線形結合で表して実数 αi を振って2...
-Q:
\[ \|M\|_\infty < 1
\]
をたしかめる時
\[ \bar \sigma(M) \]
を計算して出しますが 1より大きいかどうか考えるなら最後の√...
-A: その通りです。
-Q: Σは M の大きさによっては、
//\[
//\Sigma = \left[ \begin{mat}{c} \begin{mat}{cccc} \sigma...
//\]
\[
\Sigma = \left[ \begin{array}{c} \begin{array}{ccc} \sigm...
\]
のゼロ行列はなくなりますか?
また、
\[ M^{p\times m} \]
が p < m のときは Σ はどうなりますか?
-A: Mが正方行列つまりp=mのときゼロ行列はなくなります。ま...
** &color(green){[lecture #11]}; 2018.11.22 Robust perfor...
+ review: R.S. prob. for Delta hat and Delta tilde
+ scaled H infinity control problem
+ how to determine structure of scaling matrix
+ design example &ref(ex1122_1.m);
ex1108_1
gam2 = gam_opt
K2 = K_opt;
ex1122_1
gam_opt
+ mini report #2 &ref(report2.pdf);
+ mini exam #1 (10 min.)
%-- 2018/11/22 13:37 --%
ex1108_1
gam2 = gam_opt
K2 = K_opt
ex1122_1
gam_opt
gam2
d_opt
#ref(2018.11.22-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.22-2.jpg,left,noimg,whiteboard #2);
#ref(2018.11.22-3.jpg,left,noimg,whiteboard #3);
#ref(2018.11.22-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #12]}; 2018.11.29 Robust perfor...
+ return of mini exam #1 and mini report #2
+ review of scaling &ref(ex1129_1.m);
+ introduction of a practical system: Speed control of tw...
-- experimental setup &br;
&ref(授業/制御工学特論2014/setup.pdf); ... ``spring plate...
&ref(photo1.png,left,noimg);
-- objective of control system = disturbance attenuation ...
-- frequency response experiment and physical model of sp...
#ref(ex1129_2.m);
#ref(servo1.dat);
#ref(servo2.dat);
-- room 374 @ Dept. Mech. Bldg. 2
%-- 2018/11/29 13:07 --%
ex1129_1
gam2
gam3
clp2.b
format long
norm(M3_d, 'inf')
ex1129_2
#ref(2018.11.29-1.jpg,left,noimg,whiteboard #1);
#ref(2018.11.29-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #13]}; 2018.12.6 Control system...
+ mini exam #2
-- [[schedule2018]]
+ review of the experimental system
-- closed-loop system of 2-by-2 plant G and controller K
-- closed-loop gain is desired to be minimized
-- how to handle modeling error of G ?
+ design example
-- frequency response experiment data&br;
[[servo1.dat>/:~exp/seigyokougakutokuron_2018/exp/freqres...
[[servo2.dat>/:~exp/seigyokougakutokuron_2018/exp/freqres...
-- determination of plant model(nominal plant and additiv...
&ref(nominal.m);&br;
&ref(weight.m);
-- configuration of generalized plant and controller desi...
&ref(cont.m);
-- comparison of closed-loop gain characteristics with an...
&ref(compare.m);
-- result of control experiment&br;
[[result.dat>/:~exp/seigyokougakutokuron_2018/exp/design_...
&ref(perf.m);
//+ room 157 @ Dept. Mech. Bldg.2
+ final report and remote experimental system
++design your controller(s) so that the system performanc...
++Draw the following figures and explain the difference b...
+++bode diagram of controllers
+++gain characteristic of closed-loop system from w to z
+++time response of control experiment
++Why is the performance of your system improved(or unfor...
--&size(30){&color(red){due date: 4th(Fri) Jan 17:00};};
--submit your report(pdf or doc) by e-mail to kobayasi@na...
--You can use Japanese
--maximum controller order is 20
--submit your &size(25){&color(red){controller.dat, contr...
//--Your login password will be e-mailed on Dec 16.
--the system will be started until next lecture
--You can send up to %%5%%&color(red){10}; controllers
--&size(30){&color(black){[[control experimental results ...
--freqresp ... frequency response will be measured and up...
+ how to improve the performance ?
-- %%order of the nominal plant%% accuracy of the nominal...
-- weighting for robust stability
//+ detailed explanation of m-files in the previous lecture
+ specifications of the experimental system
++ program sources for frequency response experiment
--- [[freqresp.h>/:~exp/seigyokougakutokuron_2018/freqres...
--- [[freqresp_module.c>/:~exp/seigyokougakutokuron_2018/...
--- [[freqresp_app.c>/:~exp/seigyokougakutokuron_2018/fre...
--- format of servo1.dat (w is used instead of u for serv...
1st column ... frequency (Hz)
2nd column ... gain from u(Nm) to y(rad/s)
3rd column ... phase (deg) from u to y
4th column ... gain from u to z
5th column ... phase (deg) from u to z
++ program sources for control experiment
--- [[hinf.h>/:~exp/seigyokougakutokuron_2018/hinf.h]]
--- [[hinf_module.c>/:~exp/seigyokougakutokuron_2018/hinf...
--- [[hinf_app.c>/:~exp/seigyokougakutokuron_2018/hinf_ap...
--- format of result.dat
1st column: time (s)
2nd column: y (rad/s)
3rd column: z (rad/s)
4th column: u (Nm)
5th column: w (Nm)
++ configuration of control experiment
--- disturbance signal w is specified as described in hin...
w = 0; // disturbance torque for driven motor ...
if((t > 2)&&(t < 3)){
w = RATED_TORQ * -0.15;
}
if((t > 4)&&(t < 5)){
w = RATED_TORQ * -0.1 * sin(2*M_PI*5.0 * (t-4.0));
}
da_conv(torq_volt_conv_1(w), 1);
--- control signal u is limited as specified in hinf.h an...
#define U_MAX (RATED_TORQ / 3.0)
if(u > U_MAX) u = U_MAX;
if(u < -U_MAX) u = -U_MAX;
u is generated by PI control for t < 1(s). Your designed ...
++ calculation of rotational speed
--- The rotational speed is approximately calculated by u...
theta_rad[0] = (double)read_theta(0) / (double)Pn212 * 2...
theta_rad[1] = (double)read_theta(1) / (double)Pn212 * 2...
y = (theta_rad[0] - theta_rad_before[0]) / msg->sampling...
z = (theta_rad[1] - theta_rad_before[1]) / msg->sampling...
theta_rad_before[0] = theta_rad[0];
theta_rad_before[1] = theta_rad[1];
where the sampling period is given as 0.25 ms.
%-- 2018/12/06 12:53 --%
nominal
w
size(w)
servo1
size(servo1)
nupwd
pwd
cd data
ls
cd ..
nominal
size(w)
size(resp)
size(servo2)
size(servo1)
n
nominal
n
k
resp
k
w
clear all
nominal
weight
cont
compare
perf
nominal
#ref(2018.12.06-1.jpg,left,noimg,whiteboard #1);
#ref(2018.12.06-2.jpg,left,noimg,whiteboard #2);
-Q: コントローラは何で書くのか?
-A: 説明が曖昧でしたが、コントローラの状態空間実現(のフ...
具体的には、これらのファイルが実験機で動作しているC言語の...
** &color(green){[lecture #14]}; 2018.12.13 Control syste...
- return of mini exam #2
- review & supplemental explanations
-- final report
--- control objective is to suppress speed fluctuation of...
--- unstable controller is admitted
--- no strict control objective is given ( there is a fre...
--- c2d() is used to discretize the resultant continuous-...
-- web based remote experiment system
--- now you can login after registration
--- room temperature is displayed and stored in temp.txt ...
--- the system will be unavailable from %%21(Fri)%% &colo...
- preparation of your own controller(s) by using the remo...
#ref(nominal_ave.m);
#ref(sub.m);
%-- 2018/12/13 13:58 --%
help subspace
nominal_ave
pwd
cd ..
pwd
nominal_ave
G_g
G1_g
G2_g
(G_g + G10_g)/2
bode((G_g + G10_g)/2)
figure(2)
bode((G_g + G10_g)/2)
figure(2)
#ref(2018.12.13-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #15]}; 2018.12.20 Control syste...
- preparation of your own controller(s)
-- use [[design example #3>/:~exp/seigyokougakutokuron_20...
-- discuss relationship between the required figures (a),...
-- driving and driven torque are set to zero when driven-...
#define SPEED_MAX 60.0 // driving torque becomes zero wh...
and [[hinf_module.c>/:~exp/seigyokougakutokuron_2018/hinf...
int flag_speed_excess = 0; // 2018.12.19
if(flag_speed_excess == 1) w = 0; // 2018.12.20
da_conv(torq_volt_conv_1(w), 1);
if(fabs(z) > SPEED_MAX) flag_speed_excess = 1; // ...
if(flag_speed_excess == 1) u = 0; // 2018.12.19
#ifndef NO_CONTROL
da_conv(torq_volt_conv_0(u), 0);
#endif
-- the system will be unavailable 7:30 -- 19:00 on 22(Sat)
- questionnaires
-- to university
-- for web-based experimental environment
%-- 2018/12/20 13:19 --%
nominal
weight
cont
compare
nominal
weight
ctrlpref
cont
compare
weigh
weight
cont
weight
nominal
weight
#ref(2018.12.20-1.jpg,left,noimg,whiteboard #1);
-Q: うまくいくとやっぱりたのしいですね。
-A: モチベーションが高まったところで、過去の授業の内容を...
//■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
//&color(black,red){&size(20){!!! the remaining page is u...
//
- 2018.12.20 19:00
&size(30){&color(red){due to unexpected alert occurred at...
// if(fabs(z) > SPEED_MAX) flag_speed_excess = ...
if((fabs(z) > SPEED_MAX) || (fabs(y) > SPEED_MAX)) ...
//**related links [#g1a68a2b]
//-東ティモール工学部復興支援/support of rehabilitation f...
//--[[How to control objects>/:~kobayasi/easttimor/2009/i...
//--[[Prof. Kimura's page>http://sessyu.nagaokaut.ac.jp/~...
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