National Instruments 370753C-01

Chapter 6 State-Space Design

poleplace( ) is unusual among Xmath’s modern control design

functions in that only the A and B matrix variables are used as input,

rather than a complete system variable. This is done because the other

state-space matrices are not needed in the computation, and in many cases

it is desirable to change or perturb the elements of the A and B matrices

slightly to simulate actual conditions, without having to reformat the entire

system. For an example of an arbitrary pole placement for a controllable

system, refer to Example 6-4.

Example 6-4 Arbitrary Pole Placement for a Controllable System

A = [0,1,0,0;21,0,0,0.8;0,0,0,1;0,0,0,-4];

B = [0,-2,0,1]';

C = eye(4,4);

D = zeros(4,1);

ipsys = system(A,B,C,D);

If you want to place the system poles in a Butterworth pattern:

Kc = poleplace(A,B,[-5+8.66*jay, -8.66+5*jay]);

You then can use this new gain vector as a feedback gain to create a new

system,

ipsysfb = feedback(ipsys, system([],[],[],Kc));

and verify that the poles of this new system are at the designated locations:

poles(ipsysfb)

ans (a column vector) =

-8.66 + 5 j

-8.66 - 5 j

-5 + 8.66 j

-5 - 8.66 j

You need specify only one complex pole in a conjugate pair of desired pole

locations. poleplace( ) checks for conjugate pairs and adds conjugates

as necessary to the input poles( ) vector.

Then the system matrix S is created:

r is a random row vector with as many rows as A has columns. You then

create a random complex row vector with as many elements and conjugate

SAB