initial
Initial condition response of state-space model
Syntax
initial(sys,x0)
initial(sys,x0,Tfinal)
initial(sys,x0,t)
initial(sys1,sys2,...,sysN,x0)
initial(sys1,sys2,...,sysN,x0,Tfinal)
initial(sys1,sys2,...,sysN,x0,t)
[y,t,x] = initial(sys,x0)
[y,t,x] = initial(sys,x0,Tfinal)
[y,t,x] = initial(sys,x0,t)
Description
initial(sys,x0) calculates the unforced
response of a state-space (ss)
model sys with an initial condition on the states
specified by the vector x0:
This function is applicable to either continuous- or discrete-time
models. When invoked without output arguments, initial plots
the initial condition response on the screen.
initial(sys,x0,Tfinal) simulates the response
from t = 0 to the final time t = Tfinal.
Express Tfinal in the system time units, specified
in the TimeUnit property of sys.
For discrete-time systems with unspecified sample time (Ts
= -1), initial interprets Tfinal as
the number of sampling periods to simulate.
initial(sys,x0,t) uses
the user-supplied time vector t for simulation.
Express t in the system time units, specified in
the TimeUnit property of sys.
For discrete-time models, t should be of the form 0:Ts:Tf,
where Ts is the sample time. For continuous-time
models, t should be of the form 0:dt:Tf,
where dt becomes the sample time of a discrete
approximation to the continuous system (see impulse).
To plot the initial condition responses of several LTI models on a single figure, use
initial(sys1,sys2,...,sysN,x0)
initial(sys1,sys2,...,sysN,x0,Tfinal)
initial(sys1,sys2,...,sysN,x0,t)
(see impulse for details).
When invoked with output arguments,
[y,t,x] = initial(sys,x0)
[y,t,x] = initial(sys,x0,Tfinal)
[y,t,x] = initial(sys,x0,t)
return the output response y, the time vector t used
for simulation, and the state trajectories x. No
plot is drawn on the screen. The array y has as
many rows as time samples (length of t) and as
many columns as outputs. Similarly, x has length(t) rows
and as many columns as states.
Examples
Response of State-Space Model to Initial Condition
Plot the response of the following state-space model:
Take the following initial condition:
a = [-0.5572, -0.7814; 0.7814, 0]; c = [1.9691 6.4493]; x0 = [1 ; 0]; sys = ss(a,[],c,[]); initial(sys,x0)
Tips
You can change the properties of your plot, for example the units. For information on the ways to change properties of your plots, see Ways to Customize Plots.