A three-axis control system for inspecting individual semiconductor wafers is shown in figure below. This system uses a DC motor to drive X axis to the desired position. The goal is to achieve smooth, accurate movement in X axis. Z-axis motor x-axis motor wafer y-axis motor To calibrate the DC motor, the change in angular velocity of the shaft (output) is recorded for the unit step change in voltage (input) and the transition response is as follows; 10 Time a) Determine delay time, rise time, and settling time, (15 points) b) Assuming DC motor in this application as the 1st-order system. determine the motor parameters K and T. (10 points) G(s) = (Ts + 1) A sensor and a proportional (P) controller with the gain K, will be added to the system. Sensor measures the actual position of the head. c) Add/draw sensor and controller in the schematic shown in figure above (10 points) The motor and moving table may be represented by the transfer function K G(s) = s(Ts + 1) The controller takes the difference of the actual and desired positions and generates an error, This error is multiplied by an amplifier K. d) Draw the proper block diagram for the entire system. (10 points) e) Is the system stable2 (20 points) ) What is the steady-state position error for a step change in the desired input? (15 points) g) Calculate the required K, in order to vield a steady-state error of 0.5 mm for a ramp input of 0.2 m/s. (20 points) Amplitude 2.