Simulates a continuous, LTI system described in state space or transfer function form, for a given set of inputs.

Syntax

output = LSim(A,B,C,D,input,sample_freq,stateIC)

output = LSim(num,den,input,sample_freq,stateIC)

Argument

Name

Description

A

The state transition matrix of the system.  Must be k x k, where k is the number of states.

B

The control vector mapping inputs to the state variables of the system.  Must be k x 1.

C

The output vector relating the system states to outputs.  Must be 1 x k.

D

The feed-forward matrix.  Must be 1 x 1.

input

A vector of input signal to the system.

sample_freq

The input signal’s sampling frequency (Hz).  This is used to discretize the system.  Must be a positive scalar.

num

A vector of the numerator coefficients of the transfer function polynomial in descending power of s.

den

A vector of the denominator coefficients of the transfer function polynomial in descending power of s.  Its length is equal to k+1.

See Comments below for restrictions.

stateIC

(optional)

Vector of initial conditions of the states.  Must be k x 1. Defaults to zeros.

Outputs

Name

Description

output

The output of the system to the given input.  It has the same size as the input.

Example

For a given system defined by the state-space model A,B,C,D, and the signal input sampled at 2 kHz with zero initial conditions, find the output response:

Syntax

A =  [-10,-2; 1, 0]; B = [1; 0]; C = [0, 1]; D=[0]

response = LSim(A,B,C,D,input,2000,[0;0])

Result

The output is the response of the system to the given input.

Comments

If the system is specified by a transfer function

bnsn + … b1s + b0 / amsm + … a1s + a0

the order of the numerator must be less than or equal to that of the denominator.  For example, n ≤ m.  The order of the denominator must be at least one, for example, m ≥ 1 and a1 must be non-zero if m = 1.

See Also:

SSFromTF