A satellite control system is modeled as shown in Fig. P11.4-6. This system is described in Problem

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A satellite control system is modeled as shown in Fig. P11.4-6. This system is described in Problem 1.4-1.
For this problem, ignore the sensor gain and let D(z) = 1. In addition, K = 1, T = 1 s, and J = 4. As stated in Problem 9.2-4, a state model for this system is given by- [6 1] x(4) + [0.235 x(k + 1) = y(k) [10]x(k) = u(k)

where x1(k) is angular position and x2(k) is angular velocity.

(a) Determine by hand the gains required to minimize the cost functionJN = N 2010 [11](0) k=0 x(K) x(k) + 2u(k)

with N = 1. The value of N is chosen to be unity to limit the calculations.
(b) Use MATLAB to solve part (a) for N = 20. Sketch the calculated gains versus k.R(s) ro A/D ,8 Digital controller D(z) D/A Sensor Hk M(s) Amplifier and thrusters K T(s) Torque Satellite 1

Problem 1.4-1The satellite of Section 1.4 is connected in the closed-loop control system shown in Fig. P1.4-1. The torque) (s) Amplifiers and thrusters E(s) Error K T(s) Torque Js Sensor H(s) = 1 Satellite (b) (s)


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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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