Basics1_Linear.m

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namespace demos{


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function  Basics1_Linear() {


/*  Metadata */
dim = 4;
s = RandStream(" mt19937ar "," Seed ",0);

/* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 *% %%%%%%%%%%%% Simple linear model %%%%%%%%%%%%
 *%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 *% Initialize the base model */
m = models.BaseFullModel(" LinearModelDemo ");
/*  Max simulation time */
m.T= 1.5;
/*  The desired timestepping (output) */
m.dt= 0.01;
/*  The internal maximum timestep for any solver (details later) */
m.System.MaxTimestep= m.dt;
disp(m);

/* % Set the basic components
 * Only a core linear matrix A and an initial condition are needed here. */
m.System.A= dscomponents.LinearCoreFun(s.rand(dim,dim));
m.System.x0= dscomponents.ConstInitialValue(10*(s.rand(dim,1)-.5));

/* % Run a simple simulation and plot the results */
[t,y,ct,x] = m.simulate;
fprintf(" Simulation time: %g\n ",ct);
/*  Plot the system output */
m.plot(t,y);
/*  Plot the state space - here the same, as no specific output conversion is
 * set */
m.plotState(t,x);

/* % Modify the inputs and outputs
 * Now we only want the first DoF as output */
m.System.C= dscomponents.LinearOutputConv([1; zeros(dim-1,1)]^t);
/*  And we also add some system inputs!
 * This is split into B*u(t), so we need both components. */
u1 = @(t)-200*exp(-(t-.5).^2/3);
u2 = @(t)200*sin(10*t).*(t>.3);
m.System.Inputs[1] = u1;
m.System.Inputs[2] = u2;
figure;
plot(m.Times,u1(m.Times)," r ",m.Times,u2(m.Times)," b ");
legend(" u1 "," u2 ");
/*  Lets map the inputs to the second DoF */
m.System.B= dscomponents.LinearInputConv([0; 1; zeros(dim-2,1)]);

/* % Run simulation and plot the results
 * The first argument is a parameter by convention - so leave [] for input
 * selection. */
[t,y,~,x] = m.simulate([],1);
m.plot(t,y);
m.plotState(t,x);

[t,y,~,x] = m.simulate([],2);
m.plot(t,y);
m.plotState(t,x);

/* % Lets use a different solver
 * Choose explicit Heun's method */
m.ODESolver= solvers.Heun;
[t,y_heun] = m.simulate([],2);
m.plot(t,y_heun);

/*  Choose the MatLab-builtin ode15i implicit solver */
m.ODESolver= solvers.MLode15i;
[t,y_impl] = m.simulate([],2);
m.plot(t,y_impl);
figure;
semilogy(t,abs(y_impl-y_heun));

/* % Adding a mass matrix E
 * Choose a positive definite matrix */
Mmat = diag(s.randi(20,1,dim)) + s.rand(dim,dim);
m.System.M= dscomponents.ConstMassMatrix(Mmat);
m.ODESolver= solvers.Heun;
[t,y] = m.simulate([],1);
m.plot(t,y);

m.ODESolver= solvers.MLode15i;
[t,y2] = m.simulate([],1);
m.plot(t,y2);
}
};