National Instruments 370753C-01

Chapter 3 Building System Connections

• By default, feedback is defined to be negative.

• The number of outputs from the first system must equal the number of

inputs to the second system.

• The number of outputs from the second system must equal the number

of inputs in the first.

• Both systems must have the same sample rate.

• Improper dynamic systems (systems with more zeros than poles) are

not allowed.

• When only one system is specified, it must be square (it must have an

equal number of inputs and outputs).

Example 3-1 Using afeedback( ) to Connect Two Systems

Sys1 = system([.5,1;0,2],[1,0]',[0,1],0);

Sys2 = system([1,-.2;1,0],[1,0]',[1,1],0);

saf = afeedback(Sys1,Sys2);

Algorithm

If only one system input (Sys1) is provided to afeedback( ), the second

input (Sys2) defaults to a zero-state system with unity gain. This is

analogous to a state-space system with NULL values for the A, B, and C

matrices, and with an identity matrix for D. Notice that you use the Xmath

definition of a non-square identity matrix. In this case, the row dimension

of D equals the number of inputs to Sys1, and the column dimension equals

the number of outputs of Sys1. In the following discussion, you denote the

state-space matrices of Sys1 by A1, B1, C1, and D1, and you follow the same

convention for Sys2.

The two systems are first internally converted to a state-space form, if

necessary, and subdivided into the A, B, C, and D state-space matrices.

Scaling matrices S1 and S2 are computed for Sys1 and Sys2 as follows:

S1 = I + D1D2

S2 = I + D2D1

Additionally, you define:

B1s = B1/S2 and D1s = D1/S2

B2s = B2/S1 and D2s = D2/S1

Matrix right-division problems must be well-posed, with the scaling

matrices S1 and S2 nonsingular. afeedback( ) displays an error message