lsim: Time response of a Linear system
In benubah/control: A Control Systems Toolbox

Description Usage Arguments Details Value See Also Examples

lsim Computes the time response of a Linear system described by:

x = Ax + Bu

y = Cx + Du

to the input time history u.

1	lsim(sys, u, t, x0)

`sys`	An LTI system of `tf`, `ss` and `zpk` class
`u`	A row vector for single input systems. The input `u` must have as many rows as there are inputs in the system. Each column of U corresponds to a new time point. `u` could be generated using a signal generator like `gensig`
`t`	time vector which must be regularly spaced. e.g. `seq(0,4,0.1)`
`x0`	a vector of initial conditions with as many rows as the rows of `a`

lsim(sys, u, t) provides the time history of the linear system with zero-initial conditions.

lsim(sys, u, t, x0) provides the time history of the linear system with initial conditions. If the linear system is represented as a model of tf or zpk it is first converted to state-space before linear simulation is performed. This function depends on c2d and ltitr

Returns a list of two matrices, x and y. The x values are returned from ltitr call.

ltitr lsimplot

signal <- gensig('square',4,10,0.1)
H <- tf(c(2, 5, 1),c(1, 2, 3))
response <- lsim(H, signal$u, signal$t)
plot(signal$t, response$y, type = "l", main = "Linear Simulation Response", col = "blue")
lines(signal$t, signal$u, type = "l", col = "grey")
grid(5,5, col = "lightgray")
## Not run:  based on example at: https://www.mathworks.com/help/ident/ref/lsim.html 

## Not run:  MIMO system response 
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))
response <- lsim(ss(A,B,C,D), cbind(signal$u, signal$u), signal$t)
plot(signal$t, response$y[1,], type = "l",
 main = "Linear Simulation Response", col = "blue"); grid(7,7)
plot(signal$t, response$y[2,], type = "l",
main = "Linear Simulation Response", col = "blue"); grid(7,7)