曝光臺 注意防騙 網曝天貓店富美金盛家居專營店坑蒙拐騙欺詐消費者

of the compensated system compare with that of the basic system?
5.12   For the unity feedback system with
                                       k
                                                                  G(s) =  (s +1) s + 3~
(a) show that the system cannot be made to operate with time for peak amplitude
of 2.0 s and 23.38% overshoot by simple gain adjustment and (b) design a suitable
compensator to achieve this performance.
'{
 "j
  j
   lj
      \

534           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
5.13   For the unity feedback system with
                 k
G(s) = ~s+ ) s+4~s+7)
design a PlOD controller that will give time for peak amplitude of 1.2 s and 15%
over~hoot with zero steady-state error for a unit-step input. Plot the unit-step
response for the basic and PID-compensated systems.
5.14   For the system shown in Fig. P5.14, deterrrune the values of gain kh and
k so that the minor loop operates with a damping ratio of 0.707 and the entire
closed-loop system has 15qo overshoot.
Fig. P5.14    Control system for Exercises 5.14 and 5.15-
5.15    Determine the rate gyro gain kr. for the system shown in Fig. P5.14 so that
the compensated system operates at one-third the settling time compared to the
basic system while continuing to have the same 15% overshoot.
5.16    Given the linear time-invariant system
                                        x(t) : Ax(t) + Bu(t)
find (a) eigenvalues of the matrix A, (b) the state transition matrix Q(t), and (c)
state vector x(t) for the foUowing cases:
(i)  A = [ 01
(ii) A=[;. -.l]
B=[:] x(0)-.
B = [:]
      .  1 -1  (
(iii) A- O 1 -j  B=
   00-
x(0) -
x,0,= [:]
LINEAR SYSTEMS, THEORY, AND-DESIGN: A BRIEF REVIEW      535
    ]+[:]u,t,
y=[l  O  0] [x-[:]
Can this system be transformed into phase-variable form? If so, find the transfor-
mation z -. Px so that the transformed system z - Azz + Bzu(t), y = Czz is ir]
phase-variable form.
5.18    Represent the following system in state-space, phase- variable form:
              d3X  2d2X  3dx
                         d~3 + dt2 + dt +5x - u(t)
5.19Giventhe O;-:l[x::l+[{lu,t,
Y=[l O 0][x-."]
Can this system be transformed to dual-phase variable form? If so, find the trans-
formation z -. Px such that the transformed system z = Azz + Bzu(t), y = Czz
is in dual phase-variable form.
5.20   Design a phase-variable, full-state feedback controller for the plant given
by
                                                                -1- 0.8)
             ~
         G(s)=~+, ;~((sS~)(s+5)
to yield a 15% overshoot with a settling time of 0.8 s.
5.21   Design a full-state feedback observer for the plant
                                                            1
　
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