Optimal Control
481
where Qt is an n n real, symmetric, positive semidenite weighting matrix for t 2
t0 ; tf and mt is the prespecied desired path of the state vector xt. The vector
et xt mt is the er
Digital Control
Figure 12.2
517
Block diagram of a discrete-time system.
computer. In this case the signals uk and yk are number sequences (usually 0 and
1). These types of systems, as we shall see, a
Optimal Control
505
1 T
lt r22 tf ; t CT tf Sr12 tf ; t
C tf SCtf f 1 t
CT tf Smtf f 2 t
11:4-19
Finally
ut Ktxt qt
where
Kt R1 tBT tPt
and
qt R1 tBT tlt
Figures 11.5 and 11.6 give an overview of the
Optimal Control
493
As a practical example of an optimal regulator, consider a ground antenna
having a xed orientation. Assume that the antenna undergoes a disturbance, e.g.,
due to a sudden strong wi
Digital Control
Figure 12.11
529
Hold circuit block diagrams: (a) hold circuit; (b) idealized hold circuit.
hold circuit shown in Figure 12.11b. Here it is assumed that the signal ut goes
through an i
Digital Control
541
In the case where the system (12.4-1) is stable in accordance with Denition
12.4.1, the point xk0 T is called the equilibrium point. In the case where the system
(12.4-1) is asympt
Digital Control
_
!
577
d2 L
dt2 J
where is the position (angle of rotation), ! is the rate of the angle of rotation, L
is the externally applied torque, and J is the moment of inertia. If x1 and
_
x2
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565
specications: gain margin Kg ! 25 dB, phase margin p ! 708, and velocity error
constant Kv 1 sec1 . The sampling period T is chosen to be 0.1 sec.
Solution
^
Let Gs Gh sGp s. Then
Digital Control
553
The remarks above are the basic motives for the implementation of indirect
design techniques for discrete-time controllers mentioned in Sec. 12.6. Indirect techniques take advantag
System Identification
589
Example 13.2.2
Consider a discrete-time system described by the following second-order difference
equation:
yk 2 !2 yk buk
The input uk and the output yk, for N 5, are presen