initial: Initial Condition Response for Linear Systems
In control: A Control Systems Toolbox

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 initialplot, the same arguments are allowed

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

step impulse ramp

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))