📄 lqgopt.m
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function [ret,x0,str]=lqgopt(t,x,u,flag);
%LQGOPT is the M-file description of the SIMULINK system named LQGOPT.
% The block-diagram can be displayed by typing: LQGOPT.
%
% SYS=LQGOPT(T,X,U,FLAG) returns depending on FLAG certain
% system values given time point, T, current state vector, X,
% and input vector, U.
% FLAG is used to indicate the type of output to be returned in SYS.
%
% Setting FLAG=1 causes LQGOPT to return state derivitives, FLAG=2
% discrete states, FLAG=3 system outputs and FLAG=4 next sample
% time. For more information and other options see SFUNC.
%
% Calling LQGOPT with a FLAG of zero:
% [SIZES]=LQGOPT([],[],[],0), returns a vector, SIZES, which
% contains the sizes of the state vector and other parameters.
% SIZES(1) number of states
% SIZES(2) number of discrete states
% SIZES(3) number of outputs
% SIZES(4) number of inputs.
% For the definition of other parameters in SIZES, see SFUNC.
% See also, TRIM, LINMOD, LINSIM, EULER, RK23, RK45, ADAMS, GEAR.
% Copyright (c) 1990-94 by The MathWorks, Inc.
% Note: This M-file is only used for saving graphical information;
% after the model is loaded into memory an internal model
% representation is used.
% the system will take on the name of this mfile:
sys = mfilename;
new_system(sys)
simver(1.3)
if(0 == (nargin + nargout))
set_param(sys,'Location',[6,50,705,494])
open_system(sys)
end;
set_param(sys,'algorithm', 'RK-23')
set_param(sys,'Start time', '0.0')
set_param(sys,'Stop time', '6')
set_param(sys,'Min step size', '0.00001')
set_param(sys,'Max step size', '0.2')
set_param(sys,'Relative error','1e-3')
set_param(sys,'Return vars', '')
add_block('built-in/Outport',[sys,'/','Outport1'])
set_param([sys,'/','Outport1'],...
'hide name',0,...
'position',[185,50,205,70])
add_block('built-in/State-space',[sys,'/','Matrix gain'])
set_param([sys,'/','Matrix gain'],...
'orientation',2,...
'A','[]',...
'B','[]',...
'C','[]',...
'D','[-1.13 1.07 -0.00291 -0.433 0 ]',...
'position',[190,205,250,245])
add_block('built-in/Note',[sys,'/','Optimization Toolbox is required.'])
set_param([sys,'/','Optimization Toolbox is required.'],...
'position',[240,413,241,414])
add_block('built-in/Note',[sys,'/',['Double click on these icons to get to start optimization or get listings.',13,'']])
set_param([sys,'/',['Double click on these icons to get to start optimization or get listings.',13,'']],...
'position',[360,395,361,396])
% Subsystem 'CLF'.
new_system([sys,'/','CLF'])
set_param([sys,'/','CLF'],'Location',[-10,380,117,533])
set_param([sys,'/','CLF'],...
'Mask Display','Cost Functions\nListing',...
'Mask Type','',...
'Mask Dialogue','eval(''type lqgcost'')',...
'Mask Translate','',...
'Mask Help','')
% Finished composite block 'CLF'.
set_param([sys,'/','CLF'],...
'hide name',0,...
'position',[470,357,571,392])
% Subsystem 'OSL'.
new_system([sys,'/','OSL'])
set_param([sys,'/','OSL'],'Location',[-10,380,117,533])
set_param([sys,'/','OSL'],...
'Mask Display','Optimization Script\nListing',...
'Mask Type','',...
'Mask Dialogue','eval(''type lqgoptm'')',...
'Mask Translate','',...
'Mask Help','')
% Finished composite block 'OSL'.
set_param([sys,'/','OSL'],...
'hide name',0,...
'position',[288,357,421,392])
% Subsystem ['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. '].
new_system([sys,'/',['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. ']])
set_param([sys,'/',['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. ']],'Location',[-10,380,117,533])
set_param([sys,'/',['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. ']],...
'Mask Display','Start\nOptimization',...
'Mask Type','')
set_param([sys,'/',['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. ']],...
'Mask Dialogue','eval(''if ~exist(''''leastsq''''),fprintf(''''\nMust be licensed for Optimization Toolbox\n''''), else, fprintf(''''\nCtrl-C to abort Optimization\n\n''''); lqgoptm, end'')')
set_param([sys,'/',['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. ']],...
'Mask Translate','',...
'Mask Help','')
% Finished composite block ['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. '].
set_param([sys,'/',['Double click here',13,'to start optimizing',13,'Matrix Gain, FF Gain, and I Gain. ']],...
'hide name',0,...
'position',[140,359,226,392])
add_block('built-in/Sum',[sys,'/','Sum3'])
set_param([sys,'/','Sum3'],...
'orientation',2,...
'hide name',0,...
'position',[525,209,545,236])
add_block('built-in/Note',[sys,'/',['Sensor noise',13,'input']])
set_param([sys,'/',['Sensor noise',13,'input']],...
'position',[625,218,626,219])
add_block('built-in/Sum',[sys,'/','Sum2'])
set_param([sys,'/','Sum2'],...
'hide name',0,...
'position',[420,99,440,126])
add_block('built-in/Note',[sys,'/','Noise input'])
set_param([sys,'/','Noise input'],...
'position',[400,45,401,46])
% Subsystem ['Plant',13,'and actuator'].
new_system([sys,'/',['Plant',13,'and actuator']])
set_param([sys,'/',['Plant',13,'and actuator']],'Location',[0,0,511,212])
add_block('built-in/Scope',[sys,'/',['Plant',13,'and actuator/Actual Input',13,'']])
set_param([sys,'/',['Plant',13,'and actuator/Actual Input',13,'']],...
'Vgain','3.000000',...
'Hgain','10.100000',...
'Vmax','6.000000',...
'Hmax','20.200000',...
'Window',[0,0,280,220],...
'position',[280,150,305,180])
add_block('built-in/Scope',[sys,'/',['Plant',13,'and actuator/Demanded Input',13,'']])
set_param([sys,'/',['Plant',13,'and actuator/Demanded Input',13,'']],...
'Vgain','3.000000',...
'Hgain','10.100000',...
'Vmax','6.000000',...
'Hmax','20.200000',...
'Window',[0,0,280,220],...
'position',[130,150,155,180])
add_block('built-in/State-space',[sys,'/',['Plant',13,'and actuator/Plant']])
set_param([sys,'/',['Plant',13,'and actuator/Plant']],...
'A','a',...
'B','b',...
'C','c',...
'D','d',...
'position',[255,42,335,88])
add_block('built-in/Inport',[sys,'/',['Plant',13,'and actuator/in_1']])
set_param([sys,'/',['Plant',13,'and actuator/in_1']],...
'position',[25,55,45,75])
add_block('built-in/Outport',[sys,'/',['Plant',13,'and actuator/out_1']])
set_param([sys,'/',['Plant',13,'and actuator/out_1']],...
'position',[370,55,390,75])
add_block('built-in/Outport',[sys,'/',['Plant',13,'and actuator/out_2']])
set_param([sys,'/',['Plant',13,'and actuator/out_2']],...
'Port','2',...
'position',[380,125,400,145])
add_block('built-in/Saturation',[sys,'/',['Plant',13,'and actuator/Saturation']])
set_param([sys,'/',['Plant',13,'and actuator/Saturation']],...
'Lower Limit','-5',...
'Upper Limit','5',...
'position',[95,55,120,75])
add_block('built-in/Rate Limiter',[sys,'/',['Plant',13,'and actuator/Rate Limiter']])
set_param([sys,'/',['Plant',13,'and actuator/Rate Limiter']],...
'Rising Slew Limit','10',...
'Falling Slew Limit','-10',...
'position',[180,55,205,75])
add_line([sys,'/',['Plant',13,'and actuator']],[210,65;245,65])
add_line([sys,'/',['Plant',13,'and actuator']],[220,65;220,165;270,165])
add_line([sys,'/',['Plant',13,'and actuator']],[50,65;85,65])
add_line([sys,'/',['Plant',13,'and actuator']],[65,65;65,165;120,165])
add_line([sys,'/',['Plant',13,'and actuator']],[340,65;360,65])
add_line([sys,'/',['Plant',13,'and actuator']],[125,65;170,65])
add_line([sys,'/',['Plant',13,'and actuator']],[235,65;235,135;370,135])
% Finished composite block ['Plant',13,'and actuator'].
set_param([sys,'/',['Plant',13,'and actuator']],...
'position',[460,87,490,138])
add_block('built-in/Gain',[sys,'/','FF Gain'])
set_param([sys,'/','FF Gain'],...
'Gain','1 ',...
'position',[225,87,250,113])
add_block('built-in/Sum',[sys,'/','Sum6'])
set_param([sys,'/','Sum6'],...
'orientation',2,...
'hide name',0,...
'inputs','-+',...
'position',[455,281,485,314])
add_block('built-in/Sum',[sys,'/','Sum4'])
set_param([sys,'/','Sum4'],...
'hide name',0,...
'position',[100,82,120,118])
add_block('built-in/Signal Generator',[sys,'/','Signal Gen.'])
set_param([sys,'/','Signal Gen.'],...
'Peak','1.000000',...
'Peak Range','5.000000',...
'Freq','1.000000',...
'Freq Range','5.000000',...
'Wave','Sqr',...
'Units','Rads',...
'position',[30,93,70,127])
add_block('built-in/Inport',[sys,'/','Inport'])
set_param([sys,'/','Inport'],...
'hide name',0,...
'position',[50,45,70,65])
add_block('built-in/Sum',[sys,'/','Sum1'])
set_param([sys,'/','Sum1'],...
'hide name',0,...
'inputs','+-',...
'position',[350,90,375,125])
add_block('built-in/Outport',[sys,'/','Outport'])
set_param([sys,'/','Outport'],...
'hide name',0,...
'Port','2',...
'position',[585,40,605,60])
add_block('built-in/Mux',[sys,'/',['Known inputs',13,'and sensors.']])
set_param([sys,'/',['Known inputs',13,'and sensors.']],...
'orientation',2,...
'hide name',0,...
'inputs','[1,1]',...
'position',[430,194,460,236])
add_block('built-in/Mux',[sys,'/','Mux'])
set_param([sys,'/','Mux'],...
'orientation',2,...
'hide name',0,...
'inputs','[4,1]',...
'position',[265,207,290,238])
add_block('built-in/Note',[sys,'/',['Servo control with LQG controller.',13,'Try varying Integral gain and FeedForward',13,'gains.']])
set_param([sys,'/',['Servo control with LQG controller.',13,'Try varying Integral gain and FeedForward',13,'gains.']],...
'position',[320,7,321,8])
add_block('built-in/Note',[sys,'/','Integral action.'])
set_param([sys,'/','Integral action.'],...
'position',[449,320,450,321])
add_block('built-in/Integrator',[sys,'/','Integrator2'])
set_param([sys,'/','Integrator2'],...
'orientation',2,...
'hide name',0,...
'position',[405,282,425,318])
add_block('built-in/State-space',[sys,'/','State estimator'])
set_param([sys,'/','State estimator'],...
'orientation',2,...
'A','ae',...
'B','be',...
'C','ce',...
'D','de',...
'Mask Display','Kalman\nestimator',...
'Mask Type','State estimator')
set_param([sys,'/','State estimator'],...
'Mask Dialogue','Continuous Kalman state estimator.\n(Requires Control Toolbox)|Plant A matrix:|Plant B matrix:|Plant C matrix:|Plant D matrix:|State noise covar. E[ww'']:|Output noise covar. E[vv'']:')
set_param([sys,'/','State estimator'],...
'Mask Translate','[nx,nu]=size(@2); [l,p]=lqe(@1,eye(nx,nx),@3,@5,@6); [ny,nx]=size(@3); [ae,be,cexy,dexy]=estim(@1,@2,@3,@4,l,1:ny,1:nu); ce=cexy(ny+1:ny+nx,:); de=dexy(ny+1:ny+nx,:);')
set_param([sys,'/','State estimator'],...
'Mask Help','Implements a Kalman state estimator using lqe and estim commands. Mask and unmask this block to see how it works.',...
'Mask Entries','a\/b\/c\/d\/0.001*b*b''\/0.001*eye(1,1)\/')
set_param([sys,'/','State estimator'],...
'position',[340,191,400,239])
add_block('built-in/Scope',[sys,'/','Scope'])
set_param([sys,'/','Scope'],...
'Vgain','1.500000',...
'Hgain','6.100000',...
'Vmax','3.000000',...
'Hmax','12.200000',...
'Window',[553,126,833,346])
open_system([sys,'/','Scope'])
set_param([sys,'/','Scope'],...
'position',[575,85,600,115])
add_block('built-in/Scope',[sys,'/',['Floating',13,'Scope']])
set_param([sys,'/',['Floating',13,'Scope']],...
'Vgain','1.000000',...
'Hgain','10.100000',...
'Vmax','2.000000',...
'Hmax','20.200000',...
'Window',[0,0,280,220],...
'position',[70,175,95,205])
add_line(sys,[125,100;215,100])
add_line(sys,[145,100;145,60;175,60])
add_line(sys,[145,100;145,340;520,340;520,305;495,305])
add_line(sys,[575,230;555,230])
add_line(sys,[520,225;470,225])
add_line(sys,[510,225;510,290;495,290])
add_line(sys,[495,100;565,100])
add_line(sys,[560,100;560,215;555,215])
add_line(sys,[495,125;515,125;515,205;470,205])
add_line(sys,[395,70;395,105;410,105])
add_line(sys,[380,110;380,120;410,120])
add_line(sys,[445,115;450,115])
add_line(sys,[75,110;90,110])
add_line(sys,[185,225;175,225;175,170;305,170;305,115;340,115])
add_line(sys,[255,100;340,100])
add_line(sys,[400,300;305,300;305,230;300,230])
add_line(sys,[450,300;435,300])
add_line(sys,[75,55;80,55;80,90;90,90])
add_line(sys,[525,100;525,50;575,50])
add_line(sys,[425,215;410,215])
add_line(sys,[260,225;260,225])
add_line(sys,[335,215;300,215])
% Return any arguments.
if (nargin | nargout)
% Must use feval here to access system in memory
if (nargin > 3)
if (flag == 0)
eval(['[ret,x0,str]=',sys,'(t,x,u,flag);'])
else
eval(['ret =', sys,'(t,x,u,flag);'])
end
else
[ret,x0,str] = feval(sys);
end
end
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