MATLAB CONTROL SYSTEM TOOLBOX 9 Guida Utente Scaricare il pdf (Pagina 560)

100

101

place

11-170

11place

Purpose Pole placement design

Syntax K = place(A,B,p)

[K,prec,message] = place(A,B,p)

Description Given the single- or multi-input system

and a vector

p of desired self-conjugate closed-loop pole locations, place

computes a gain matrix K such that the state feedback places the

closed-loop poles at the locations

p. In other words, the eigenvalues of

match the entries of

p (up to t he ordering).

K = place(A,B,p) computes a feedback gain matrix K that achieves the

desired closed-loop pole locations

p, assuming all the i nputs of the plant are

control inputs. The length of

p must match the row size of A. place works for

multi-input systems and is based on the algorithm from [1]. This algorithm

uses the extra degrees of freedom to find a solution that minimizes the

sensitivity of the closed-loop poles to perturbations in or .

[K,prec,message] = place(A,B,p) also returns prec, an estimate of how

closely the eigenvalues of match the specified locations

p (prec

measures the number of accurate decimal digits in the actual closed-loop

poles). If some nonzero closed-loop pole is more than 10% off from the desired

location,

message contains a warning message .

You can also use

place forestimatorgainselectionby transposingthe A matrix

and substituting

C' for B.

l = place(A',C',p).'

Example Consider a state-space system (a,b,c,d) with two inputs, three outputs, and

three states. You can compute the feedback gain matrix needed to place the

closed-loop poles at

p = [1.1 23 5.0] by

p = [1 1.23 5.0];

K = place(a,b,p)

Ax Bu+=

uKx

–=

ABK

–

ABK

–

1 2 ... 555 556 557 558 559 560 561 562 563 564 565 ... 648 649

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MATLAB CONTROL SYSTEM TOOLBOX 9 Guida Utente Pagina 560

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