Consider the reduced-order observer designed in Problem 9.4-2. In this problem, velocity [ d y / d

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Consider the reduced-order observer designed in Problem 9.4-2. In this problem, velocity [dy/dt][dy/dt] is estimated, using position [y][y] plus other information. We could simply calculate velocity, using one of the numerical differentiators described in Section 8.8. This calculated velocity would then replace the estimate of velocity in the control system. (This is the approach taken in the PID controller.)

Problem 9.4-2Consider the satellite control system of Problem 9.2-4. (a) Design a reduced-order observer for this system,

(a) Consider the plant observer as an open-loop system, as shown in Fig. 9-4. Calculate the transfer function Q(z)/Y(z)Q(z)/Y(z) with U(z)=0U(z)=0, where q(kT)q(kT) is the observer estimate of velocity.

Use (9-62) with u(k)=0u(k)=0.

(b) Plot the Bode diagram for the transfer function in part (a) versus

(c) One numerical differentiator given in Section 8.8 is

D(z)=z1TzD(z)=z1Tz

Plot the Bode diagram for this transfer function on the same graph as in part (b).

(d) Comment on the similarities and differences in the two frequency responses.

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Digital Control System Analysis And Design

ISBN: 9780132938310

4th Edition

Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty

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