Chapter 2 Linear System Representation
© National Instruments Corporation 2-5 Xmath Control Design Module
State-Space System Models
State-space models comprise the second category of linear system
representations in Xmath. In state-space form, first-order differential
(continuous-time) and difference (discrete-time) equations are represented
as a set of state and output updates. The states are represented by a vector
x; u and y are vectors with as many elements as there are inputs and outputs,
respectively. This system model is useful for representing multi-input,
multi-output (MIMO) systems.
continuous time:
discrete time:
A straightforward mathematical transformation from the state-space form
to the transfer function form is as follows:
All of the forms represented in these equations can be represented using
Xmath’s system objects, as shown in Example2-2.
Example 2-2 Creating a Discrete State-Space System
Suppose you have a system which you describe in state-space form as:
and you know that the sample period of the system is 0.5 seconds between
samples—that is, the states and outputs are updated at every discrete
interval k, consisting in this case of 0.5 seconds.
x
·Ax Bu+=
yCxDu+=
xk1+AxkBuk
+=
ykCxkDuk
+=
Hq() CqI A–()
1–BD+=
xk1+
01
0.75–0
xk
1
0
uk
+=
yk01xk
=