csim — simulation (time response) of linear system
[y [,x]]=csim(u,t,sl,[x0 [,tol]])
function, list or string (control)
real vector specifying times with, t(1) is the initial time (x0=x(t(1))).
list (syslin)
a matrix such that y=[y(t(i)], i=1,..,n
a matrix such that x=[x(t(i)], i=1,..,n
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:
1. a function : [inputs]=u(t)
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)
5. a vector giving the values of u correponding to each t value.
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);xselect();
plot2d([t',t'],[(csim('step',t,tf2ss(s)*w))',0*t'])
clf(1);xset("window",1);xselect();
plot2d([t',t'],[(csim('impulse',t,w))',0*t'])
//step(w) = impulse (s^-1 * w)
clf(3);xset("window",3);xselect();
plot2d([t',t'],[(csim('step',t,w))',0*t'])
clf(4);xset("window",4);xselect();
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'])