10-15. The telescope for tracking stars and asteroids on the space shuttle may be modeled as a pure mass M. It is suspen

[answerhappygod]

10 15 The Telescope For Tracking Stars And Asteroids On The Space Shuttle May Be Modeled As A Pure Mass M It Is Suspen 1 (88.69 KiB) Viewed 38 times

10-15. The telescope for tracking stars and asteroids on the space shuttle may be modeled as a pure mass M. It is suspended by magnetic bearings so that there is no friction, and its attitude is controlled by magnetic actuators located at the base of the payload. The dynamic model for the control of the z-axis motion is shown in Fig. 10P-15(a). Since there are electrical components on the telescope, electric power must be brought to the telescope through a cable. The spring shown is used to model the wire-cable attachment, which exerts a spring force on the mass. The force produced by the mag- netic actuators is denoted by f(t). The force equation of motion in the z direction is d²z(t) f(t)-K,z(t)= M- d²² where K, = 1 lb/ft, and M = 150 lb (mass), f(t) is in pounds, and z(t) is measured in feet. (a) Show that the natural response of the system output z(t) is oscillatory without damping. Find the natural undamped frequency of the open-loop space-shuttle system. (b) Design the PID controller: G.(s)= Kp + KDs + K₁ S shown in Fig. 10-15(b) so that the following performance specifications are satisfied: Ramp-error constant K₁ = 100 The complex characteristic equation roots correspond to a relative damping ratio of 0.707 and a natural undamped frequency of 1 rad/sec Compute and plot the until-sten response of the designed system. Find the maximum overshoot. Comment on the design resu¹ s. (c) Design the PID controlier so that the folling specifications are satisfied: Ramp-error constant K₁ = 100 Maximum overshoot < 5 percent