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# Documentation

## Response from Initial Conditions

This example shows how to compute and plot the response of a state-space (ss) model to specified initial state values using initialplot and initial.

Load a state-space model.

```load ltiexamples sys_dc
sys_dc.InputName = 'Volts';
sys_dc.OutputName = 'w';
sys_dc.StateName = {'Current','w'};
sys_dc```
```sys_dc =

a =
Current        w
Current       -4    -0.03
w           0.75      -10

b =
Volts
Current      2
w            0

c =
Current        w
w        0        1

d =
Volts
w      0

Continuous-time state-space model.
```

This example uses the SISO, 2-state model sys_dc. This model represents a DC motor. The input is an applied voltage, and the output is the angular rate of the motor ω. The states of the model are the induced current i (x1), and ω (x2).

Plot the undriven evolution of the motor's angular rate from an initial state in which the induced current is 1.0 amp and the initial rotation rate is 5.0 rad/s.

```x0 = [1.0 5.0];
initialplot(sys_dc,x0)```

initialplot plots the time evolution from the specified initial condition on the screen. Unless you specify a time range to plot, impulse automatically chooses a time range that illustrates the system dynamics.

Calculate the time evolution of the output and the states of sys_dc from t = 0 (application of the step input) to t = 1 s.

```t = 0:0.01:1;
[y,t,x] = initial(sys_dc,x0,t);```

The vector y contains the output at each time step in t. The array x contains the state values at each time step. Therefore, in this example x is a 2-by-101 array. Each row of x contains the values of the two states of sys_dc at the corresponding time step.