simulation (time response) of linear system
[y [,x]]=csim(u,t,sl,[x0 [,tol]])
:u function, list or string (control) : :t real vector specifying times with, t(1) is the initial time (
x0=x(t(1))).
: :sl list ( syslin) : :y a matrix such that y=[y(t(i)], i=1,..,n : :x a matrix such that x=[x(t(i)], i=1,..,n : :tol a 2 vector [atol rtol] defining absolute and relative
tolerances for ode solver (see ode)
:
simulation of the controlled linear system sl. sl is assumed to be a continuous-time system represented by a syslin list.
u is the control and x0 the initial state.
y is the output and x the state.
The control can be:
2. a list : list(ut,parameter1,....,parametern) such that: inputs=ut(t,parameter1,....,parametern) ( ut is a function)
3. the string “impuls” for impulse response calculation (here sl is assumed SISO without direct feed through and x0=0)
4. the string “step” for step response calculation (here sl is assumed SISO without direct feed-through and x0=0)
s=`poly`_(0,'s');`rand`_('seed',0);w=`ssrand`_(1,1,3);w('A')=w('A')-2*`eye`_();
t=0:0.05:5;
//impulse(w) = step (s * w)
`clf`_(0);`xset`_("window",0);`show_window`_();
`plot2d`_([t',t'],[(csim('step',t,`tf2ss`_(s)*w))',0*t'])
`clf`_(1);`xset`_("window",1);`show_window`_();
`plot2d`_([t',t'],[(csim('impulse',t,w))',0*t'])
//step(w) = impulse (s^-1 * w)
`clf`_(3);`xset`_("window",3);`show_window`_();
`plot2d`_([t',t'],[(csim('step',t,w))',0*t'])
`clf`_(4);`xset`_("window",4);`show_window`_();
`plot2d`_([t',t'],[(csim('impulse',t,`tf2ss`_(1/s)*w))',0*t'])
//input defined by a time function
`deff`_('u=input(t)','u=abs(sin(t))')
`clf`_();`plot2d`_([t',t'],[(csim(`input`_,t,w))',0*t'])