www.pudn.com > nnctrl_v5.zip > fbltest.m, change:1997-06-06,size:5606b


% PROGRAM DEMONTRATION OF CONTROL USING FEEDBACK LINEARIZATION 
% 
% Programmed by Magnus Norgaard, IAU/IMM, Technical Univ. of Denmark 
% LastEditDate: Feb. 21, 1996 
close all 
StopDemo=0; 
figure 
guihand=gcf; 
for k=1:1, %dummy loop 
 
  % >>>>>>>>>>>>>>>>  BUILD GUI INTERFACE  <<<<<<<<<<<<<<<<< 
  [guihand,edmulti,contbut,quitbut]=pmnshow; 
  set(guihand,'Name','Control by feedback linearization'); 
 
  % >>>>>>>>>>>>>>>>  SCREEN 1  <<<<<<<<<<<<<<<<< 
  s0='1'; 
  s1='The purpose of this demo is to show how a simple kind'; 
  s2='of discrete feedback linearization can be used for'; 
  s3='controlling a nonlinear process. The feedback linearizes'; 
  s4='the process by introduction of a "virtual" control input'; 
  s5='and assigns the closed-loop poles to a desired location.'; 
  s6='The process in question is a spring-mass-damper system'; 
  s7='with a hardening spring: y"(t) + y''(t) + y(t) + y(t)^{3} = u(t)'; 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7); 
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end 
 
 
  % >>>>>>>>>>>>>>>>  SCREEN 2  <<<<<<<<<<<<<<<<< 
  % -- Generate data -- 
  load expdata; 
  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)'; 
  s0='2'; 
  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 plots above show 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)') 
  drawnow 
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end 
   
   
  % >>>>>>>>>>>>>>>>  SCREEN 3  <<<<<<<<<<<<<<<<< 
  s0='3'; 
  s1='To perform discrete feedback linearization we require'; 
  s2='that the process can be described by a particular model'; 
  s3='structure:'; 
  s4='             y(t)=f(phi(t)) + g(phi(t))*u(t-1)'; 
  s5='where'; 
  s6='             phi(t)=[y(t-1),..,y(t-n),u(t-2),..,u(t-m)].'; 
  s7='When the process is unknown we can let two neural'; 
  s8='networks model "f" and "g", respectively.'; 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7,s8);  
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end 
   
   
  % >>>>>>>>>>>>>>>>  SCREEN 4  <<<<<<<<<<<<<<<<< 
  s0='4'; 
  s1='The NNSYSID-toolbox contains a function called "nniol"'; 
  s2='which does this. Let''s use a network with five hidden units'; 
  s3='for approximating "f" and a network with three hidden units for'; 
  s4='approximating "g". Since we are dealing with a second'; 
  s5='order process we will use as regressors two past outputs'; 
  s6='and two past controls.'; 
  subplot(411);delete(gca);subplot(412);delete(gca) 
  subplot('position',[0.1 0.60 0.40 0.38]); 
  drawnet(ones(5,4),ones(1,6),eps,['y(t-1)';'y(t-2)';'u(t-2)'],'fhat(t)'); 
  subplot('position',[0.50 0.45 0.40 0.38]); 
  drawnet(ones(3,4),ones(1,4),eps,['y(t-1)';'y(t-2)';'u(t-2)'],'ghat(t)'); 
  title('Network architectures') 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6);  
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end 
   
  % >>>>>>>>>>>>>>>>  SCREEN 5  <<<<<<<<<<<<<<<<< 
  % ----- Train network ----- 
  s0='5'; 
  s1=[]; 
  s2='    >> Training process in action!! <<'; 
  s3=[]; 
  s4=[]; 
  s5='We run up to 100 iterations so you may have to'; 
  s6='wait for a while.'; 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6); 
  set(edmulti,'String',smat); 
  drawnow 
  trparms = [100 0 1 0]; 
  NN=[2 2 1]; 
  NetDeff = ['HHHHH'        
           'L----']; 
  NetDefg = ['HHH' 
           'L--']; 
  NN = [2 2 1]; 
  [W1f,W2f,W1g,W2g]=... 
       nniol(NetDeff,NetDefg,NN,[],[],[],[],trparms,Y1,U1);       
  save forward3 NetDeff W1f W2f NN NetDefg W1g W2g 
  delete(gca); delete(gca); 
  subplot('position',[0.1 0.60 0.40 0.38]); 
  drawnet(W1f,W2f,eps,['y(t-1)';'y(t-2)';'u(t-2)'],'fhat(t)'); 
  subplot('position',[0.50 0.45 0.40 0.38]); 
  drawnet(W1g,W2g,eps,['y(t-1)';'y(t-2)';'u(t-2)'],'ghat(t)'); 
  title('Trained network') 
  if StopDemo==1, close all, break; end 
 
  % >>>>>>>>>>>>>>>>  SCREEN 6  <<<<<<<<<<<<<<<<< 
  s0='6'; 
  s1='The network has now been trained and we are ready to'; 
  s2='simulate the control system. Let''s select as our'; 
  s3='desired characteristic polynomial:'; 
  s4=[]; 
  s5='        Am(z)=z^{2} - 1.4z + 0.49'; 
  s6=[]; 
  s7='corresponding to two poles in z=0.7'; 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7); 
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end 
   
  % >>>>>>>>>>>>>>>>  SCREEN 7  <<<<<<<<<<<<<<<<< 
  figure('Units','Centimeters','Position',[1.5 1.5 10 1.5]); 
  pp=1; 
  fblcon 
  close 
  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)') 
  drawnow 
  s0='7'; 
  s1='Obviously we have achieved a reasonably accurate'; 
  s2='model-following.'; 
  s3='              >>  THE END <<'; 
  smat=str2mat(s0,s1,s2,[],[],[],s3); 
  set(edmulti,'String',smat); 
  drawnow 
end