PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL3(81)

曝光台 注意防骗 网曝天猫店富美金盛家居专营店坑蒙拐骗欺诈消费者

as rapidly as possible so that,in the limit, the estimated states approach the actual
states. The schematic diagram of such a full-state observer is shown in Fig. 5.43.
     Suppose the dynamics of the plant and output are given by
x - Ax + Bu
y = Cx
Let the observer dynanucs and the output be given by
so that
x = Ax + Bu + L(y - y)
y -. Cx
y - y = C(x - x)
(5.285)
(5.286)
(5.287)
(5.288)
(5.289)
Fig. 5.43    Schematic diagram of fall-state obsener.
LINEAR SYSTEMS, THEORY, AND DESIGN:A BRIEF REVIEW      523
ex -x -x = A(x -x) - L(y - y)
- (A - LC)(x -- x)
          ey = C(x - x)
(5.290)
(5.291)
(5.292)
    P/ant given in dual phase-variable form.    Suppose that the given plant A is
in dual p~ase-variable form
Then,let us assume that the matrix A - LC has the following form
A - LC -
The characteristic equation of the observer system is then given by
(5.293)
(5.294)
s" + (an -i  +/i)s   -1  + (a,, _2 +/2)Sn -2 + ...+ (t/0 + /n) = 0          (5.295)
   Let the characteristic equation that gives the desired transient response of the
observer be given by
s I + Ltn - IS i-I  + dr._ 2S r -2 + .. . + do = 0                    (5.296)
Equating the coefficients oflike powers of s, we obtain
ll  - dn -i  - an -i, l2  -. d,, _ 2 - an -2,- - -, 1,,  -. do - ao                  (5.297)
Here, /1,12,...,/n are the elements of the feedback gain matrix to achieve the
desired performance of the full-state observer.
Here, x is the estimated state vector, and y is the estimated output. Let e.  - x - x
be the error between the actual states and the estimated states and ey = y - y be
the error between the measured and estimated outputs. Then,
I

    i
The objective of the design is to choose the observer gain matrix / such that the
errors ex and ey approach zero as rapidly as possible. In other words, we choose
the observer gain matrix / so that the closed-loop eigenvalues produce the desired
transient response of the observer.
    -an_i  1 O C

A- -an_3 O O 1
               .N.
      -ai   -  .  .
     -ao  0 0 0
-(an_i+/l) 1 O O . O
-(an_2+/2) 0 1 O . 0
-(an_3+/3) 0 O 1 . O
                     ...
-(ai+/n)  .    . . 1
~(aO+ln)  0 O 0 . O
524           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
P/ant not given in dual phase-variable form.    Suppose the given plant
                                    x = Ax + BU .                           (5.298)
                                       y = Cx                              (5.299)
is not in dual phase-variable form. Then we assume that there exists a matrix P
where x - Pz that transforms this plant into a dual phase-variable form as given
by
                                       z = Azz + Bzu                             (5.300)
                                         y = Czz                               (5.301)
　
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