initial (Control Design and Simulation Module, MathScript Function)

Member of the timeresp class.

Syntax

initial(SysIn, attributes, x0)

initial(SysIn, attributes, x0, t)

[Y, T, X] = initial(SysIn, x0)

[Y, T, X] = initial(SysIn, x0, t)

Description

Creates an initial response initial response plot of a system model. For state-space models, the initial response is output of the model due to the initial states. For transfer function and zero-pole-gain models, this function bases the initial conditions on the model outputs. You also can use this function to return the impulse response of the model outputs. If the model is in state-space form, you also can use this function to return the impulse response of the model states. If you do not specify an output, this function creates a plot.

Examples

Inputs

Name	Description
SysIn	Specifies a linear time-invariant (LTI) model in transfer function, zero-pole-gain, or state-space form.
attributes	Specifies valid plot attributes. Order the plot attributes by color, point-style, and line-style. For example, 'bo-' specifies that the plot is blue, marks points with circles, and uses solid lines. attributes is a string that can take a combination of the following values: 'b' Colors the plot blue. 'c' Colors the plot cyan. 'g' Colors the plot green. 'k' Colors the plot black. 'm' Colors the plot magenta. 'r' Colors the plot red. 'y' Colors the plot yellow. '.' Marks points with dots. 'o' Marks points with circles. 'x' Marks points with crosses. '+' Marks points with plus signs. '*' Marks points with asterisks. '-' Uses solid lines. ':' Uses dotted lines. '-.' Uses dashed and dotted lines. '--' Uses dashed lines.
x0	Specifies the initial states of the SysIn model if the SysIn model is in state-space form. If the SysIn model is in transfer function or zero-pole-gain form, x0 specifies the initial outputs. x0 is a real vector.
t	Specifies a uniformly spaced time vector that contains information about the initial time, time step, and final time. You can format t as [t0:dt:tf], where t0 is the initial time, dt is the time step, and tf is the final time. You also can format t as [tf]. You also can use the linspace function to generate t. t is a real vector.

Outputs

Name	Description
Y	Returns the time response of the outputs of the SysIn model due to the conditions you specify in the x0 input. Y is a real matrix.
T	Returns the uniformly spaced time vector this function uses to calculate the initial response and the state trajectories. T is a real vector.
X	Returns the time response of the states of the SysIn model due to the conditions you specify in the x0 input. This function returns X only if the SysIn model is in state-space form. X is a real matrix.

Examples

SysIn = zpk([1], [-1, -2], 0.5)
y0 = 2
initial(SysIn, 'rx-',y0, [0:0.1:10])

Related Topics

lsim
step