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A space telescope is to be launched to carry out astronomical experiments (8). The pointing control systern is desired to achieve 0.01 minute of are and track solar objects with apparent motion up to 0.21 are minute per second. The system is illustrated in Figure P5.5(a). The control system is shown in Figure P5.5(b). Assume that r1 = 1 second and 72 = 0 (an approximation). (a) Determine the gain K = K1K2 required so that the response to a step command is as rapid as reasonable with an overshoot of less than 5%. (b) Determine the steady-state error of the system for a step and a ramp input. (C) Determine the value of K1K2 for an ITAE optimal systerm for (1) a step input and (2) a ramp input. Starlight Tracking and data relay satellite system Space shuttle Ground station (a) Controller Process Y(s) Pointing angle R(s) K;(7,3 + 1) Input 7s + 1 (b) FIGURE P5.5 (a) The space telescope. (b) The space telescope pointing control system.

A space telescope is to be launched to carry out astronomical experiments (8). The pointing control systern is desired to achieve 0.01 minute of are and track solar objects with apparent motion up to 0.21 are minute per second. The system is illustrated in Figure P5.5(a). The control system is shown in Figure P5.5(b). Assume that r1 = 1 second and 72 = 0 (an approximation). (a) Determine the gain K = K1K2 required so that the response to a step command is as rapid as reasonable with an overshoot of less than 5%. (b) Determine the steady-state error of the system for a step and a ramp input. (C) Determine the value of K1K2 for an ITAE optimal systerm for (1) a step input and (2) a ramp input. Starlight Tracking and data relay satellite system Space shuttle Ground station (a) Controller Process Y(s) Pointing angle R(s) K;(7,3 + 1) Input 7s + 1 (b) FIGURE P5.5 (a) The space telescope. (b) The space telescope pointing control system.

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A space telescope is to be launched to carry out astronomical experiments [8]. The pointing control system is desired to achieve 0.01 minute of are and track solar objects with apparent motion up to 0.21 are minute per second. The systen is illustrated in Figure P5.5(a). The control system is shown in Figure P5.5(b). Assume that r1 = 1 second and 72 = 0 (an approximation). (a) Determine the gain K = KIK2 required so that the response to a step command is as rapid as reasonable with an overshoot of less than 5%. (b) Determine the steady-state error of the system for a step and a ramp input. (C) Deterrnine the value of K1K2 for an ITAE optimal system for (1) a step input and (2) a ramp input. Starlight Tracking and data relay satellite system Space shuttle Ground station (a) Controller Process Y(s) Pointing angle R(s) K2(715 + 1) Input 72s +1 (b) FIGURE P5.5 (a) The space telescope. (b) The space telescope pointing control systern.
Transcribed Image Text:A space telescope is to be launched to carry out astronomical experiments [8]. The pointing control system is desired to achieve 0.01 minute of are and track solar objects with apparent motion up to 0.21 are minute per second. The systen is illustrated in Figure P5.5(a). The control system is shown in Figure P5.5(b). Assume that r1 = 1 second and 72 = 0 (an approximation). (a) Determine the gain K = KIK2 required so that the response to a step command is as rapid as reasonable with an overshoot of less than 5%. (b) Determine the steady-state error of the system for a step and a ramp input. (C) Deterrnine the value of K1K2 for an ITAE optimal system for (1) a step input and (2) a ramp input. Starlight Tracking and data relay satellite system Space shuttle Ground station (a) Controller Process Y(s) Pointing angle R(s) K2(715 + 1) Input 72s +1 (b) FIGURE P5.5 (a) The space telescope. (b) The space telescope pointing control systern.
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