csim simulation (time response) of linear system

## Syntax

                [y, x] = csim(u, t, sl)
                [y, x] = csim(u, t, sl, x0)
                [y, x] = csim(u, t, sl, x0, tol)

## Arguments

u

  function, list or string (control)

t

  real vector specifying times with, `t(1)` is the initial time (`x0=x(t(1))`).

sl

  A SISO or SIMO linear dynamical system, in state space, transfer function or zpk representations, in continuous time.

y

  a matrix such that `y=[y(t(i)]`, i=1,..,n

x

  an optional 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)

## Description

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` must have a single input and `x0=0`). For systems with direct feedthrough, the infinite pulse at t=0 is ignored.

4. the string `"step"` for step response calculation (here `sl` must have a single input and `x0=0`)

5. a vector giving the values of u corresponding to each t value.

## Examples

    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)
    plot2d([t',t'],[(csim('step',t,tf2ss(s)*w))',0*t'])

s=poly(0,'s'); rand('seed',0); w=ssrand(1,1,3); w('A')=w('A')-2*eye(); t=0:0.05:5; plot2d([t',t'],[(csim('step',t,tf2ss(s)*w))',0*t'])

    s=poly(0,'s');
    rand('seed',0);
    w=ssrand(1,1,3);
    w('A')=w('A')-2*eye();
    t=0:0.05:5;
    plot2d([t',t'],[(csim('impulse',t,w))',0*t'])

s=poly(0,'s'); rand('seed',0); w=ssrand(1,1,3); w('A')=w('A')-2*eye(); t=0:0.05:5; plot2d([t',t'],[(csim('impulse',t,w))',0*t'])

    s=poly(0,'s');
    rand('seed',0);
    w=ssrand(1,1,3);
    w('A')=w('A')-2*eye();
    t=0:0.05:5;
    //step(w) = impulse (s^-1 * w)
    plot2d([t',t'],[(csim('step',t,w))',0*t'])

s=poly(0,'s'); rand('seed',0); w=ssrand(1,1,3); w('A')=w('A')-2*eye(); t=0:0.05:5; plot2d([t',t'],[(csim('step',t,w))',0*t'])

    s=poly(0,'s');
    rand('seed',0);
    w=ssrand(1,1,3);
    w('A')=w('A')-2*eye();
    t=0:0.05:5;
    plot2d([t',t'],[(csim('impulse',t,tf2ss(1/s)*w))',0*t'])

s=poly(0,'s'); rand('seed',0); w=ssrand(1,1,3); w('A')=w('A')-2*eye(); t=0:0.05:5; plot2d([t',t'],[(csim('impulse',t,tf2ss(1/s)*w))',0*t'])

    s=poly(0,'s');
    rand('seed',0);
    w=ssrand(1,1,3);
    w('A')=w('A')-2*eye();
    t=0:0.05:5;
    //input defined by a time function
    deff('u=timefun(t)','u=abs(sin(t))')
    clf();plot2d([t',t'],[(csim(timefun,t,w))',0*t'])

s=poly(0,'s'); rand('seed',0); w=ssrand(1,1,3); w('A')=w('A')-2*eye(); t=0:0.05:5; deff('u=timefun(t)','u=abs(sin(t))') clf();plot2d([t',t'],[(csim(timefun,t,w))',0*t'])

## See also

- syslin
- dsimul
- flts
- ltitr
- rtitr
- ode
- impl

## History

6.0

handling zpk representation