control (version 0.2.5)

step: Step Response for Linear Systems

Description

step obtains the time response of the linear system:

$$dx/dt = Ax + Bu$$

$$y = Cx + Du$$

Usage

step(sys, t, input)
stepplot(sys, t, input)

Arguments

sys

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

t

Time vector. If not provided, it is automatically set.

input

For calls to step, input is a number specifying an input for a MIMO state-space system. If the system has 3 inputs, then input would be set to 1, set to 2 and then to 3 to obtain the step response from input 1, 2, and 3 to the outputs. For single input systems, input is always set to 1.

For calls to stepplot, input is a vector or range for a MIMO state-space system. For example, input <- 1:3 for a system with 3-inputs

Value

A list is returned by calling step 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 stepplot

Details

step produces the step response of linear systems using lsim

stepplot produces the step response as a plot againts time.

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

Other possible calls using step and stepplot are:

step(sys)

step(sys, t)

stepplot(sys)

stepplot(sys, t)

See Also

initial impulse ramp

Examples

# NOT RUN {
res <- step(tf(1, c(1,2,1)))
res$y
res$t
step(tf(1, c(1,2,1)), seq(0, 10, 0.1))
stepplot(tf(1, c(1,2,1)))
stepplot(tf(1, c(1,2,1)), seq(0, 10, 0.1))

# }
# NOT RUN {
  State-space MIMO systems 
# }
# NOT RUN {
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))
res1 <- step(ss(A,B,C,D), input = 1)
res2 <- step(ss(A,B,C,D), input = 2)
res1$y # has two rows, i.e. for two outputs
res2$y # has two rows, i.e. for two outputs
stepplot(ss(A,B,C,D), input = 1:2) # OR
stepplot(ss(A,B,C,D), input = 1:ncol(D))

# }