The Gamma-Ray imaging Device (GRID) is a NASA experiment to be flown on a long-duration, high-altitude balloon

Question:

The Gamma-Ray imaging Device (GRID) is a NASA experiment to be flown on a long-duration, high-altitude balloon during the coming solar maximum. The GRID on a balloon is an instrument that will qualitatively improve hard X-ray imaging and carry out the first gamma-ray imaging for the study of solar high-energy phenomena in the next phase of peak solar activity. From its long-duration balloon platform, GRID will observe numerous hard X-ray bursts, coronal hard X-ray sources, "superhot" thermal events, and micro flares [2]. Figure CP12.8(a) depicts the GRID payload attached to the balloon. The major components of the GRID experiment consist of a 5.2- meter canister and mounting gondola, a high-altitude balloon, and a cable connecting the gondola and balloon. The instrument-sun pointing requirements of the experiment are 0.1 degree pointing accuracy and 0.2 arc second per 4 ms pointing stability.
An optical sun sensor provides a measure of the sun-instrument angle and is modeled as a first-order system with a DC gain and a pole at s = -500. A torque motor actuates the canister/gondola assembly. The azimuth angle control system is shown in Figure CP12.8(b). Tlie PID controller is selected by the design team so that

where a and b are to be selected. A prefilter is used as shown in Figure CP12.8(b). Determine the value of KD, a, and b so that the dominant roots have a £ of 0.8 and the overshoot to a step input is less than 3%. Develop a simulation to study the control system performance. Use a step response to confirm the percent overshoot meets the specification.