MATLAB 09. Animation을 이용한 시뮬레이션.pdf

M A T L A BM A T L A B

Modern Control System Lab. Changwon National University

C t t P d l - Cart type Pendulum


cx FM m ml x

2 mgl fml ml I 1 1

2

cx Fx M m mlmgl fml ml I

2

2 2 2

1( )( )

cx Fx ml I mll fM l I l l M

2 2 2( )( ) mgl fM m ml I m l ml M m


22 2 2

1( )( )

cx Fx ml I mlmgl fM m ml I m l ml M m

2

2 2 2

( )( ) ( )1( )( ) ( ) ( )( )

x ml I cx F ml mgl fM l I l l F M l f

2 2 2( )( ) ( ) ( )( )M m ml I m l ml cx F M m mgl f

2 2 2 2

2 2 2

( ) ( )1( )( ) ( ) ( )

x c ml I x m l g mlf ml I FM m ml I m l cmlx mgl M m M m f mlF


2 2 2 2

2 2 2

( ) ( )1x c ml I x m l g mlf ml I F

2 2 2( )( ) ( ) ( )M m ml I m l cmlx mgl M m M m f mlF 5, 1, 1, 9.8, 0.01, 0.01, 0.02M m l g c f I 5, 1, 1, 9.8, 0.01, 0.01, 0.02M m l g c f I

0.0102 9.8 0.01 1.021x x F

6.012 0.01 58.8 0.06x F


C t t P d l - Cart type Pendulum

0.0102 9.8 0.01 1.021x x F

6.012 0.01 58.8 0.06x F

Scope

1s

Integrator1

1s

Integrator

f(u)

Fcn

Scope1

1s

Integrator3

1s

Integrator2

-K-

Gain

f(u)

Fcn1

0

Constant


11f(u)

Scope

s

Integrator1

s

Integrator

( )

Fcn

0

Scope1

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Integrator3

1s

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-K-

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f(u)

Fcn1Constant


( ,0)r( 0)r( ,0)r

l = 5;r = 0.1;

l [ 10 10 10 10]x_plane = [-10 -10 10 10];y_plane = [-0.6 -0.5 -0.5 -0.6];x_cart = [-1 -1 1 1];y_cart = [-0.5 0.5 0.5 -0.5];

l [ ]

( , )r l

x_pole = [-r -r r r];y_pole = [-l 0 0 -l];plane = fill(x_plane, y_plane, 'k');

id( , )r l grid onhold on

cart = fill(x_cart, y_cart, 'g','EraseMode','normal');pole = fill(x_pole, y_pole, 'b','EraseMode','normal');h ld ffhold offaxis([-10 10 -8 4]);


cos , sinl l ( ,0)r

( 0)r

cos , sinl l cos , sinl l

( ,0)r

1tan rl

l

( , )r l

1 13 3cos tan , sin tan2 2

r rl ll l

( , )r l

1 13 3cos tan , sin tan2 2

r rl ll l


l = 5;r = 0.1; 4

x_plane = [-10 -10 10 10];y_plane = [-0.6 -0.5 -0.5 -0.6];x_cart = [-1 -1 1 1];y_cart = [-0.5 0.5 0.5 -0.5];x pole = [-r -r r r]; 0

2

x_pole = [-r -r r r];y_pole = [-l 0 0 -l];plane = fill(x_plane, y_plane, 'k');grid onh ld

-2

hold oncart = fill(x_cart, y_cart, 'g','EraseMode','normal');pole = fill(x_pole, y_pole, 'b','EraseMode','normal');hold offaxis([-10 10 -8 4]); -6

-4

([ ])t = 0:0.01:20*pi/180;for t = 0:0.01:20*pi/180

updatedX cart = x cart + t;-10 -8 -6 -4 -2 0 2 4 6 8 10

-8

updatedX_cart = x_cart + t;temp_x = [l*cos(3/2*pi+t-atan(r/l)) r*cos(pi+t) r*cos(t) l*cos(3/2*pi+t+atan(r/l))];temp_y = [l*sin(3/2*pi+t-atan(r/l)) r*sin(pi+t) r*sin(t) l*sin(3/2*pi+t+atan(r/l))];updatedX_pole = t + temp_x;updatedY_pole = temp_y;

t( t 'Xd t ' d t dX t)set(cart, 'Xdata', updatedX_cart);set(pole, 'Xdata', updatedX_pole,'Ydata', updatedY_pole);drawnow;for i=1:5000000


temp = i;end

end

Scope

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Integrator1

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Integrator

f(u)

Fcn

1s

1s

-K-f(u)0

Constant

Click HereTerminator

Scope1

MATLABFunction

Integrator3Integrator2 GainFcn1

pole

cart

TerminatorMATLAB Fcnp


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f(u)

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11

Integrator1Integrator

Kf( )

Fcn

0

Scope1

MATLAB

1s

Integrator3

1s

Integrator2

-K-

Gain

f(u)

Fcn1

cart

Constant


MATLABFunction

MATLAB Fcnpole


l = 5;r = 0.1;x plane = [-10 -10 10 10];x_plane [ 10 10 10 10];y_plane = [-0.6 -0.5 -0.5 -0.6];x_cart = [-1 -1 1 1];y cart = [-0.5 0.5 0.5 -0.5];y_ca t [ 0.5 0.5 0.5 0.5];x_pole = [-r -r r r];y_pole = [-l 0 0 -l];plane = fill(x_plane, y_plane, 'k');p ( p y p )grid onhold oncart = fill(x_cart, y_cart, 'g','EraseMode','normal');pole = fill(x_pole, y_pole, 'b','EraseMode','normal');hold offaxis([-10 10 -8 4]);


1s

1s

f(u)

Scope

11

Integrator1Integrator

Kf( )

Fcn

0

Scope1

MATLAB

1s

Integrator3

1s

Integrator2

-K-

Gain

f(u)

Fcn1

cart

Constant


MATLABFunction

MATLAB Fcnpole


function y = test1(pos cart theta cart pole)function y = test1(pos_cart, theta, cart, pole)l = 5;r = 0.1;r 0.1;x_cart = [-1 -1 1 1];updatedX cart = x cart + pos cart;p _ _ p _ ;temp_x = [l*cos(3/2*pi+theta-atan(r/l)) r*cos(pi+theta) r*cos(theta) l*cos(3/2*pi+theta+atan(r/l))];temp_y = [l*sin(3/2*pi+theta-atan(r/l)) r*sin(pi+theta) r*sin(theta) p y p pl*sin(3/2*pi+theta+atan(r/l))];updatedX_pole = pos_cart + temp_x;updatedY_pole = temp_y;set(cart, 'Xdata', updatedX_cart);set(pole, 'Xdata', updatedX_pole,'Ydata', updatedY_pole);drawnow;y = 1;


M A T L A BM A T L A BLQR


LQR - LQR

0 0102 9 8 0 01 1 021x x F 0.0102 9.8 0.01 1.0216.012 0.01 58.8 0.06

x x Fx F

0 1 0 0 0x x 0 0.0017 1.6301 0.0017 0.16970 0 0 1 0

x xF

0 0.0017 9.7804 0.01 0.1663 A BA B


0 1 0 0 0 0 1 0 0 00 0.0017 1.6301 0.0017 0.1697

,0 0 0 1 0

A B

0 0 0 1 00 0.0017 9.7804 0.01 0.1663

1 0 0 00 0 0 0 0 0 0 0 , 0.010 0 5 00 0 0 0

Q R 0 0 0 0

K = lqr(A,B,Q,R)


>> A = [0 1 0 0; 0 -0.0017 -1.6301 -0.0017; 0 0 0 1; 0 -0.0017 -9.7804 -0.01];[ ; ; ; ];>> B = [0 0.1697 0 0.1663]';>> Q = [1 0 0 0; 0 0 0 0; 0 0 5 0; 0 0 0 0];>> R = 0.01;>> K=lqr(A,B,Q,R)K =

10.0000 13.0808 12.7367 3.2320


Click HereClick Here

Scope

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f(u)

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T i

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MATLABFunction

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cart

TerminatorMATLAB FcnK*u pole


2Click Here

11f( )

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MATLAB FcnK*u

Gain1

pole

cart


Click Here

Signal 1

Signal Builder

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MATLABFunction

MATLAB Fcn

Integrator3Integrator2

K*u

Gain1

GainFcn1

l

cart

MATLAB Fcnpole


22.5Signal 1

test/Signal Builder : Group 1

0.5

1

1.5

-1

-0.5

0

2 5

-2

-1.5

1

0 2 4 6 8 10 12 14 16 18 20 22-2.5

Time (sec)


Documents

MATLAB 09. Animation을 이용한 시뮬레이션.pdf