Question

4. You want to design an orientation controller for a satellite system whose thrusters provide a torque T to modify the angular position 0 with transfer function (s) 0.1 G(s) T(s) $2 Y() R(s) G(s) C(s) You want to add damping to the system to minimize any oscillations (%OS < 5%) but still maintain a 1% settling time of less than 60 s to a unit step input. I(a) Sketch the allowable pole locations in the complex plane to meet the %OS and settling time requirements. (b) Which type of controller is more likely to improve the damping: PI or PD? Why? (c) Import your plant transfer function G(s) into Matlab's sisotool and insert a real zero at an arbitrary value (if you answered PD) or a real pole at 0 and a real zero at an arbitrary value (if you answered PI). Move your arbitrary zero and change your closed-loop gain until you have achieved the required specifications. Submit your root locus, your final C(s), and your step response from sisotool (showing the specifications have been met) as part of your homework.