Function: LSIM_MOD

Purpose. Simulation of the modal decomposition.

Synopsis.

[p_dom,l2_norm] = lsim_mod(sys,u,t,x0,ixy[,npol[,sbplot1[,sbplot2[,sbplot3]]]])

Description. This function simulates the modal decomposition of a state or of a measurement signal. If it is invoked with output argument(s), the simulation is not plotted but the poles are sorted out, ordered with respect to their L₂ contribution. Dominant modes can be identified in that way.

Input arguments.

`sys,u,t,x0`	Same as for the function `lsim` or alternatively `u = 'u1'` (or `'u2'`,...) for an unit step demand at the first (or second,...) input. In this case `t` indicates the length of the simulation.
`ixy`	String like `'x1'` (or `'x2'`,...), `'y1'` (or `'y2'`,...) which indicates the signal (only one at a time) which is plotted. `'xi'` stands for `i`th state, `'yi'` for `i`th output.
`npol`	Is the number of modes which are plotted. The selection is made by considering the largest L₂ norms during the simulation interval. If `npol` has 2 entries the modes from rank `npol(1)` to rank `npol(2)` are plotted.
`sbplot1`	Is a 1 by 3 integer matrix giving the sub-plot box for displaying the modal simulation result.
`sbplot2`	Similar for the legend.
`sbplot3`	Similar for the global simulation. The exact global simulation corresponds to the solid line. The sum of the `npol` dominant modes corresponds to the dashed line.

For example sbplot1=[1,2,1], sbplot2=[2,2,2], sbplot3=[2,2,4].

Output arguments.

`p_dom`	If there is an output argument the simulation is not plotted. `p_dom` is the vector of the `npol` dominant poles (ordering in decreasing dominance).
`l2_norm`	Is the vector of the L₂ contribution measures of the modes.

See also:lsim, plot_res

Examples. The following commands lines illustrate a standard modal analysis, note that we close the feedback loop before using lsim_mod.

  sys = rcamdata('lat',0,2,0);
  Klat = fb_prop(sys,0,[-1+%i;-.6;-1.7;-1.4;-1.2],'n',...
                                           [4 4 1 1 1]);
  sysfb = sys /. (-Klat);

  lsim_mod(sysfb,'u1',10,0,'y1')

The resulting modal decomposition is given in the following figure (the signal 'y1', sum of all modes, is given on the right hand side).