Question 1) Antenna Control System: Physical Modeling, Actuators/Sensors Modeling and Real-time Control Implementation

a) Figure 1-a shows the original analog system for an antenna azimuth control problem, while Figure 1-b represents its digital implementation (with the computer in the loop with gain K). Design gain K in Figure 1-b to yield a closed-loop damping ratio of 0.5.

Assume a sampling interval of T = 0.1 seconds.

Figure 1. Antenna control system: a) analog implementation; and b) digital implementation.

b) Now consider the antenna azimuth position control system shown in the following pages (Layout, Schematic, Block Diagram, and Schematic Parameters).

i) Using "Layout" and "Schematic" pages, develop a complete physical model of the system and implement it using Simscape® in Matlab. Use the numerical values for Configuration 1 given in "Schematic Parameters" page.

ii) Compare your modeling results obtained in Part b-i above with the ones obtained from digital implementation in Part a.

iii) Convert the system developed in Part b-i into a digital system with sampling interval of T = 0.1 seconds. For the purpose of conversion, assume that the potentiometers are replaced with unity gain transducers. Also, neglect the power amplifier dynamics.

iv) Using the converted system in Part b-iii, design the gain, K, for 16.3% overshoot. For your designed value of gain, find the steady-state error for a unit ramp input.