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lintest.m - 《神经网络控制工具箱》（nnct
源码下载: &
% PROGRAM FOR DEMONTRATING CONTROL BASED ON INSTANTANEOUS LINEARIZATION
% Programmed by Magnus Norgaard, IAU/IMM, Technical Univ. of Denmark
% LastEditDate: Feb. 20, 1996
StopDemo=0;
for k=1:1, %dummy loop
% &&&&&&&&&&&&&&&&
BUILD GUI INTERFACE
&&&&&&&&&&&&&&&&&
[guihand,edmulti,contbut,quitbut]=
set(guihand,'Name','Control based on instantaneous linearization');
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
s1='The purpose of this demo is to show how the instantaneous';
s2='linearization principle can be used in the design of';
s3='control systems for nonlinear processes. Two types of';
s4='designs will be investigated: pole placement with zero';
s5='cancellation and pole placement without zero cancellation.';
s6='The process in question is a spring-mass-damper system';
s7='with a hardening spring: y&(t) + y''(t) + y(t) + y(t)^{
} = u(t)';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7);
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
% -- Generate data --
N2=length(U);
N1=floor(N2/2);
Y1 = Y(1:N1)';
U1 = U(1:N1)';
Y2 = Y(N1+1:N2)';
U2 = U(N1+1:N2)';
s1='Before we can apply the controller design we need a neural';
s2='network model of the process. To create this we must make';
s3='an experiment and collect a set of data describing the';
s4='process over its entire range of operation. Such an';
s5='experiment has been simulated in advance with the function';
s6='&experim.& The plot above shows the data set.';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6);
subplot(411)
plot(U1); grid
axis([0 N1 min(U1) max(U1)])
title('Input and output sequence')
subplot(412)
plot(Y1); grid
axis([0 N1 min(Y1) max(Y1)])
xlabel('time (samples)')
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
s1='To identify the neural network model we will use the';
s2='function &nnarx& from the NNSYSID-toolbox. Since it''s';
s3='a second order process we will use as regressors two';
s4='past outputs and two past controls. Furthermore we choose';
s5='a network architecture with five hidden &tanh& units and';
s6='one linear output.';
subplot(411);delete(gca);subplot(412);delete(gca)
subplot('position',[0.1 0.55 0.45 0.38]);
drawnet(ones(7,5),ones(1,8),eps,{
'y(t-1)' 'y(t-2)' 'u(t-1)' 'u(t-2)'
title('Network architecture')
smat=str2mat(s0,s1,s2,s3,s4,s5,s6);
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
% ----- Train network -----
&& Training process in action!! &&';
s5='We run up to 200 iterations so you may have to';
s6='wait for a while.';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6);
set(edmulti,'String',smat);
trparms = settrain(trparms,'maxiter',200);
= ['HHHHH';'L----'];
NN=[2 2 1];
[W1,W2]=nnarx(NetDef,NN,[],[],trparms,Y1,U1);
save forward2 W1 W2 NetDef NN
delete(gca);
subplot('position',[0.1 0.55 0.45 0.38]);
drawnet(W1,W2,eps,{
'y(t-1)' 'y(t-2)' 'u(t-1)' 'u(t-2)'
title('Trained network')
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
s1='The network has now been trained and we are ready to';
s2='simulate the control system. First we will try a';
s3='pole placement strategy where we cancel the zero.';
s4='Let''s choose the desired closed loop system as:';
s6='H(z)=----------------------------';
} - 1.4z^{
} + 0.49z';
s8='corresponding to two poles in z=0.7 and one in z=0.';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7,s8);
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
figure('Units','Centimeters','Position',[1.5 1.5 10 1.5]);
subplot(411)
plot([0:samples-1],[ref_data y_data ym_data]); grid
axis([0 samples -2 2])
title('Reference, output and desired output')
subplot(412)
plot([0:samples-1],u_data);
axis([0 samples min(u_data) max(u_data)]); grid
title('Control signal')
xlabel('time (samples)')
s1='Very nice model-following is clearly achieved. However';
s2='the control signal is very active because the zero we';
s3='cancel is close to -1. To avoid this we instead';
s4='choose not to let the controller cancel the zero.';
s5='Let''s use the same desired model as before but introduce';
s6='a dead-beat observer polynomial for causality reasons:';
s7='Ao(z)=z';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7);
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
figure('Units','Centimeters','Position',[1.5 1.5 10 1.5]);
subplot(411)
plot([0:samples-1],[ref_data y_data]); grid
axis([0 samples -2 2])
title('Reference and output signal')
subplot(412)
plot([0:samples-1],u_data);
axis([0 samples min(u_data) max(u_data)]); grid
title('Control signal')
xlabel('time (samples)')
s1='It is seen that the response looks more or less as';
s2='before but that the control signal now is much more';
s3='smooth.';
smat=str2mat(s0,s1,s2,s3);
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
subplot(411)
plot([0:samples-1],B_data); grid
axis([0 samples min(min(B_data(3:samples,:))) max(max(B_data))])
title('Numerator (above) and denominator (below) coefficients')
subplot(412)
plot([0:samples-1],A_data(:,2:3));
axis([0 samples min(min(A_data(3:samples,2:3))) max(max(A_data))]); grid
title('Control signal')
xlabel('time (samples)')
s1='A very nice feature of instantaneous linearization is';
s2='that it provides an excellent understanding of the';
s3='dynamics of the process. As shown above we can, for';
s4='example, plot the coefficients of the extracted linear';
s5='models.';
Another possibility is to plotpoles and zeros in';
s7='the complex plane.';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7);
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
subplot(411);delete(gca);subplot(412);delete(gca)
subplot('position',[0.1 0.55 0.45 0.38]);
Zmat = zeros(samples-2,nb-1);
for k=3:samples,
Zmat(k-2,:)=roots(B_data(k,:))';
ZPmat = zeros(samples-2,na);
for k=3:samples,
ZPmat(k-2,:)=roots(A_data(k,:))';
plot(ZPmat,'x');
title('Poles (x) and zeros (o) of extracted linear models');grid
axis([-1 1 -1 1])
axis('equal')
plot(Zmat,Zmat*0,'o');
t=-pi:0.05:
plot(sin(t),cos(t))
s1='From this plot it is quite clear why there were problems';
s2='when the controller canceled the zero. Obviously it is';
s3='very close to the unity circle. We can also see that the';
s4='poles varies quite a lot. To get a better understanding';
s5='of how the pole locations affect the behavior of the';
s6='process we can calculate damping factor and natural';
s7='frequency.';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7);
pmnshow(smat,guihand,edmulti,contbut,quitbut);
if StopDemo==1, close all, end
% &&&&&&&&&&&&&&&&
&&&&&&&&&&&&&&&&&
Cmat = zeros(samples-2,na-1);
for k=3:samples,
r=roots(A_data(k,:))';
[n,m]=sort(real(r));
[MAG,a1,a2]=ddamp(r(m)',0.2);
Cmat(k-2,1)=a1(1);
Cmat(k-2,2)=a2(1);
Cmat=real(Cmat);
subplot(411)
plot(2:samples-1,Cmat(:,1));grid
title('Natural frequency (rad/s) and damping factor')
axis([0 samples min(Cmat(:,1)) max(Cmat(:,1))])
subplot(412)
plot(2:samples-1,Cmat(:,2));grid
axis([0 samples 0 1])
xlabel('time (samples)')
s1='Obviously the process becomes less damped and the';
s2='natural frequency larger when the magnitude of';
s3='the output increases.';
THE END &&';
smat=str2mat(s0,s1,s2,s3,s4,s5,s6);
set(edmulti,'String',smat);
源码下载: &
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&initopt.mat579.00 B06-05-97 07:27
&inverse.mat632.00 B12-18-02 10:46
&inverse2.mat580.00 B06-05-97 07:27
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&6.25 kB01-28-00 14:10
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Lin tao and I live in the same building.But he lives two floors ( ) me.有选项:A.on B.over C.under D.above
Lin tao and I live in the same building.But he lives two floors ( ) me.有选项:A.on B.over C.under D.above
选D.ON 表示紧紧贴在……上.over和 above意思差不多,都是在……上.但因为我住的楼是固定的.所以只能用above.至于under,表示在……正下方,我觉得用below更好,因为below不是一定在正下方的.
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