National-instruments Xmath Interactive Control Design Module ICDM Instrukcja Użytkownika Pobierz pdf (Strona 17)

Chapter 2 Introduction to SISO Design

Xmath Interactive Control Design Module 2-2 ni.com

The equations describing this system are as follows:

where y denotes the plant output or sensor signal

u denotes the plant input or actuator signal

r denotes the reference or command input signal

e denotes the error signal

P denotes the plant transfer function

C denotes the controller transfer function

In ICDM, the plant and controller transfer function are required to be

rational, that is, the ratio of two polynomials:

where n

, d

, n

, and d

are polynomials called the plant numerator,

plant denominator, controller numerator, and controller denominator,

respectively. The symbols n and d are mnemonics for numerator and

denominator. The degree of d

is the plant order or plant degree. Similarly,

the degree of d

is the controller order or controller degree.

The poles and zeros of these transfer functions are the zeros (roots) of the

denominator and numerator polynomials, respectively.

In ICDM, P and C are required to be proper polynomials; that is, they have

at least as many poles as zeros. In other words, the degree of n

is less than

or equal to the degree of d

(which is N) and similarly for n

and d

. In some

situations, the plant and controller are required to be strictly proper, which

means that there are more poles than zeros.

Other important terms include:

• The loop transfer function L is defined as L = PC. The loop gain is the

magnitude of the loop transfer function.

• The sensitivity transfer function is denoted as S and given by

S =1/(1+PC). The sensitivity transfer function is the transfer function

from the reference input r to the error signal e.

yPu=

uCe=

ery–=

Ps()

s()

-----------= Cs()

s()

-----------=

1 2 ... 12 13 14 15 16 17 18 19 20 21 22 ... 128 129

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