Develop a MATLAB/Simulink model for controlling...

The two axes of an X-Y table are driven by DC motors. The motor shaft for each axis is coupled to a leadscrew whose rotation is directly related to the linear motion of the X-Y table along the direction of the leadscrew axis. The relation between the angular displacement of the leadscrew and the linear motion of the X-Y table is given by x(t) = p (t) where x(t) is the linear displacement of the table and 6(1) is the angular displacement of the leadscrew. x(t) and (t) are defined in meters and degrees, respectively. p is the leadscrew pitch. It is assumed to be 0.01 m i rev Assume that the dynamics of the DC motor along with its inertia loading stemming from the leadscrew and the X-Y table can be represented by the following second order model: 0(s) k V(s) s(rs+1) where r(1) is the input voltage to the motor. k-9360 deg/Volt*sec) and = 0.025 sec The objective of this assignment is to automatically position the X-Y table at the mid range of the x-axis. This task can be accomplished by driving the x-axis in the following three modes 1) Open-loop mode 1: Apply a positive input voltage signal, V-Vou, to move the X-Y table in the positive direction until it reaches a switch located at the end of the positive range of the x-axis. Consider that the X-Y table moves 1 meter from its initial position x(t=0-0 before it comes in contact with the switch. The latter yields the following output values: a. Value of"1" when the X-Y table is in contact with the switch b. Value of "" when the X-Y table is not in contact with the switch 2) Open-loop mode 2: Apply a negative input voltage signal, , V-VoL2, to move the X-Y table in the negative direction until it reaches a switch located at the end of the negative range of the x-axis, which is assumed to be located at x =-0.4 m 3) Closed-loop mode: a. Based on the above open-loop modes, determine the appropriate value for ref that will position the X-Y table at the mid-range of the x-axis b. Apply a "Proportional Controller or P-Controller" to move the table from x(t)--0.4 mt to x(t)=xref with a zero steady-state error and no overshoot. Note that for a P-Controller, the control voltage V-Vo, is given by