ExampleLPV.m
2afd4b553794master

ExampleLPV.m
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			Ts = 5e-2; % sampling time
			% Specify damping coefficient.
			c = 5;
			% Specify stiffness.
			k = 300;
			% Specify load command.
			u = 1:10;
			% Specify mass.
			m = 10u + 0.1u.^2;
			% Compute linear system at a given mass value.
			clearvars sys
			for i = 1:length(u)
			A = [0 1; -k/m(i), -c/m(i)];
			B = [0; 1/m(i)];
			C = [1 0];
			sys(:,:,i) = c2d(ss(A,B,C,0),Ts,'least-squares');
			end

			%The variable u is the scheduling input. Add this information to the model.

			sys.SamplingGrid = struct('LoadCommand',u);

			bode(sys)
			shg

			%%
			% Simultanous stabilization using a PID controller

			C0 = tunablePID('C','pid',Ts); %


			z = tf('z',Ts);
			C0.u = 'e'; C0.y = 'u';

			sys.y = 'y';
			sys.u = 'u';
			Sum1 = sumblk('e = r - y');
			T0 = connect(sys,C0,Sum1,{'r'},{'u','e','y'});


			W1 = 1/(z-1);
			W2 = 1/makeweight(2,0.05pi/Ts,0.1,Ts); % CL bandwidth off ~0.05pi/Ts

			softReq = [ TuningGoal.WeightedGain('r','e',W1,[])];


			hardReq = [ TuningGoal.WeightedGain('r','y',W2,[]);];


			opts = systuneOptions('RandomStart',0);
			[CL,fSoft,gHard,f] = systune(T0,softReq,hardReq,opts);

			C = getBlockValue(CL,'C');
			S0 = feedback(1,sys*C);

			%%


			% Get the default strutcures used for datadriven
			[SYS, OBJ, CON, PAR] = datadriven.emptyStruct();

			[num,den] = tfdata(C,'v'); % get numerator/denominator of initial controller

			orderK = 2;

			if length(num) < orderK + 1
			% The final and initial controller must have the same order. To achieve
			% this, the initial controller is simply zero-padded.
			den(orderK+1) = 0; %
			num(orderK+1) = 0; %
			end



			% Poles on unit cicle of the inital and final controller MUST be identical.
			% To do so, move all the controller's poles to the fixed part in the
			% controller (that will remain unchanged).

			Fy = [1 -1]; % fixed parts in denominator.
			den = deconv(den,Fy); % remove the fixed parts from the denominator, as they are now in the fixed part Fy.

			Q = THETA(sys(:,:,1));
			den = den(:)';
			num = num(:)';

			if length(Q) > 1
			den(numel(Q),1) = 0;
			num(numel(Q),1) = 0;
			end

			SYS.controller = struct('num',num','den',den','Ts',Ts,'Fx',1,'Fy',Fy,'theta',@THETA); % specify feedback controller strucutre

			w = logspace(-2,log10(pi/Ts),500);
			SYS.model = sys; % Specify model(s). If multiple model, stack them, eg. stack(1,G1,G2,G3,...)
			SYS.W = w; % specify frequency grid where problem is solved.

			OBJ.inf.W1 = .1/(tf('z',Ts)-1); % Only minimize \|\| W1 S \|\|_inf.
			% Ideally objective should be around 1

			CON.W1 = 1/2; % constraint \|\| W1 S \|\|_\infty <1, here we only want to guarantee a modulus margin of 2
			CON.W2 = 1/2; % constraint \|\| W2 T \|\|_\infty <1
			CON.W3 = db2mag(-60); % constraint \|\| W3 U \|\|_\infty <1

			% Optimization parameters
			PAR.tol = 1e-3; % stop when change in objective < 1e-3. (no progress, iterative algo may has stalled)
			PAR.maxIter = 50; % max Number of iterations
			PAR.radius = 0.99; % max radius eigenvalue controller poles

			%% SOVLE

			% !! REQUIRES MOSEK + MOSEK FUSION !!
			% Make sure the license is avalible, and Fusion installed.
			% type
			% >> mosekdiag
			% to check if mosek read to go
			%
			[SYS.controller,obj] = datadriven.lpv(SYS,OBJ,CON,PAR); % implementation for SISO controllers

			FB = datadriven.getController(SYS);

			%%


			figure
			S = feedback(1,sys*FB); % compute sensitivity

			step(S0,S);

			legend('Non-LPV','LPV')


			function theta = THETA(sys)

			q = sys.SamplingGrid.LoadCommand;

			theta = [1;q;q^2]; % schedule controller with 1,LoadCommand,LoadCommand^2
			end

toolbox/Examples/ExampleLPV.m2afd4b553794master

ExampleLPV.mView Options

toolbox/Examples/ExampleLPV.m
2afd4b553794master

ExampleLPV.m
View Options