Description Usage Arguments Details Value See Also Examples

`initial`

obtains the time response of the linear system:

*dx/dt = Ax + Bu*

*y = Cx + Du*

to an initial condition.

1 2 | ```
initial(sys, x0, t)
initialplot(sys, x0, t)
``` |

`sys` |
LTI system of transfer-function, state-space and zero-pole classes |

`x0` |
initial conditions as a column vector. Should have as many rows as the rows of A. where x0 is not specified, random values are assigned |

`t` |
regularly spaced time vector. If not provided, it is automatically set. For calls to |

`initial`

produces the time response of linear systems to initial conditions using `lsim`

`initialplot`

produces the time response to initial conditions as a plot againts time.

The functions can handle both SISO and MIMO (state-space) models.

Other possible calls using `initial`

and `initialplot`

are:

`initial(sys)`

`initial(sys, x0)`

`initialplot(sys)`

`initialplot(sys, x0)`

A list is returned by calling `initial`

containing:

`x`

Individual response of each x variable

`y`

Response of the system

`t`

Time vector

The matrix `y`

has as many rows as there are outputs, and columns of the same size of `length(t)`

.
The matrix X has as many rows as there are states. If the time
vector is not specified, then the automatically set time
vector is returned as `t`

A plot of `y`

vs `t`

is returned by calling `initialplot`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
res <- initial(tf(1, c(1,2,1)))
res$y
res$t
A <- rbind(c(-2, -1), c(1,0)); B <- rbind(1,0);
C <- cbind(0,1); D <- as.matrix(0);
x0 <- matrix(c( 0.51297, 0.98127))
initialplot(ss(A,B,C,D), x0)
initialplot(tf(1, c(1,2,1)), t = seq(0, 10, 0.1))
## Not run: State-space MIMO systems
A <- rbind(c(0,1), c(-25,-4)); B <- rbind(c(1,1), c(0,1));
C <- rbind(c(1,0), c(0,1)); D <- rbind(c(0,0), c(0,0))
res <- initial(ss(A,B,C,D))
res$y # has two rows, i.e. for two outputs
initialplot(ss(A,B,C,D))
``` |

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