111 1/1 You are designing a position control system. A DC motor is driving an inertial load J (a big disk) with no damping. The motor is driven by a servoamplifier in a controlled-current mode such that the command to the servoamp results in a proportional current to the motor which in turn results in a proportional torque at the motor shaft. In other words, T(t) = Ka * v(t) where T(t) is the torque on the inertial load J, Ka is a constant and v(t) is the voltage command input to the servo amp. Thus, the plant Gp for this system has the servoamp command v(t) as input and angular position of the disk as the output. The angular position of the inertial load is measured, fed back and subtracted from a reference position to form an error signal that is fed into the controller Gc. The input of Gp is v(t) and the output of Gp is theta(t) (a) Show that plant Gp has the transfer Ka function G, (s) = = 2 Js + Gc Gp (b) Using whatever design tools you like, including Matlab, explore P and PD control forms in order to design a closed loop system that has a good step response (you get to define "good") that is relatively fast without too much overshoot nor too many oscillations nor too much of a steady-state error. Report your findings so that the reader can understand exactly what you are proposing for your design and why. In your report, state the specifications you are trying to meet with your control system. For this problem, let J = 0.01 kg-m^2 and Ka = 0.1 N-m/Volt. The position feedback signal scaling is 1 V/rad. Keep track of and report your units.