www.pudn.com > nnctrl_v5.zip > predtest.m, change:1997-06-06,size:6358b


% PROGRAM DEMONTRATION OF NEURAL NETWORK BASED PREDICTIVE CONTROL 
% 
% Programmed by Magnus Norgaard, IAU/IMM, Technical Univ. of Denmark 
% LastEditDate: Feb. 20, 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','Predictive control'); 
 
  % >>>>>>>>>>>>>>>>  SCREEN 1  <<<<<<<<<<<<<<<<< 
  s0='1'; 
  s1='The purpose of this program is to demonstrate'; 
  s2='neural network based predictive control of a'; 
  s3='nonlinear process. Two types of controller designs'; 
  s4='will be investigated: "true" nonlinear generalized'; 
  s5='predictive control and approximate generalized predictive'; 
  s6='control. The process in question is a spring-mass-damper'; 
  s7='system with a hardening spring:'; 
  s8=' y"(t) + y''(t) + y(t) + y(t)^{3} = u(t)'; 
  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 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 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(Y); 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 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)'],'yhat(t)'); 
  title('Network architecture') 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6);  
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end 
   
   
  % >>>>>>>>>>>>>>>>  SCREEN 4  <<<<<<<<<<<<<<<<< 
  % ----- Train network ----- 
  s0='4'; 
  s1=[]; 
  s2='    >> Training process in action!! <<'; 
  s3=[]; 
  s4=[]; 
  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); 
  drawnow 
  trparms = [200 0 1 0]; 
  NetDef  = ['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)'],'yhat(t)'); 
  title('Trained network') 
  if StopDemo==1, close all, break; end 
   
  % >>>>>>>>>>>>>>>>  SCREEN 5  <<<<<<<<<<<<<<<<< 
  s0='5'; 
  s1='The network has now been trained and we are ready to'; 
  s2='simulate nonlinear predictive control of the process.'; 
  s3='We will use the program "npcinit1" which implements'; 
  s4='a Quasi-Newton search for the minimum of the GPC criterion'; 
  s5='The design parameters are selected as follows:'; 
  s6='Minimum and maximum output horizon: N1=1 and N2=7'; 
  s7='Control horizon and penalty factor: Nu=1 and rho=0.03'; 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7); 
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end 
   
  % >>>>>>>>>>>>>>>>  SCREEN 6  <<<<<<<<<<<<<<<<< 
  figure('Units','Centimeters','Position',[1.5 1.5 10 1.5]); 
  npccon1 
  close 
  subplot(411) 
  plot([0:samples-1],[ref_data y_data]); grid 
  axis([0 samples -2.2 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)') 
  drawnow 
  s0='6'; 
  s1='It appears that we obtain a reasonably close'; 
  s2='tracking of the reference trajectory. However, you'; 
  s3='probably noticed that the simulation was extremely'; 
  s4='time consuming. The reason for this is the iterative'; 
  s5='minimization algorithm executed at each sample to'; 
  s6='determine the optimal control. Alternatively we may thus'; 
  s7='apply the instantaneous linearization principle to reduce'; 
  s8='the amount of computations. This is simulated with "apccon"'; 
  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 7  <<<<<<<<<<<<<<<<< 
  figure('Units','Centimeters','Position',[1.5 1.5 10 1.5]); 
  apccon 
  close 
  subplot(411) 
  plot([0:samples-1],[ref_data y_data]); grid 
  axis([0 samples -2.2 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)') 
  drawnow 
  s0='7'; 
  s1='The simulation was obviously considerably faster than'; 
  s2='before but the reference tracking still looks OK.'; 
  s3='The response differs slightly from the one produced by'; 
  s4='the nonlinear predictive controller. This is not alone'; 
  s5='due to the linearization but also has to do with the future'; 
  s6='predictions being calculated in a different fashion'; 
  s7='(see the manual).'; 
  smat=str2mat(s0,s1,s2,s3,s4,s5,s6,s7);  
  pmnshow(smat,guihand,edmulti,contbut,quitbut); 
  if StopDemo==1, close all, break; end  
   
  % >>>>>>>>>>>>>>>>  SCREEN 9  <<<<<<<<<<<<<<<<< 
  s0='9'; 
  s1=[]; 
  s2='                  >> THE END <<'; 
  smat=str2mat(s1,s1,s1,s1,s2); 
  set(edmulti,'String',smat); 
  drawnow 
end