Answer Happy

Dont use block diagram please. solve it analytically.
PROJECT PROBLEM O O o o O This project; is about modeling and control of the system described below, consists of multiple parts, which will be assigned and collected weekly, must be done individually by each student. some parts require the use of MATLAB/Simulink or Scilab/Xcos. Tutorials for both options are provided in LMS. Feel free to use books, lecture notes etc. For the written parts; o use the provided Paper Template, read the instructions carefully and follow them completely, use as many pages as you like but combine them into a single PDF file. For the software parts; comment your code such that each line is clearly described, make sure that Simulink or Xcos models are free from clutter and ready to run. o make sure to display your results as clear as possible. You models will not be modified/enhanced in any way and they will be graded in their submitted form. For submission; o combine all you files (PDF and code/model) in a folder, o zip or rar the folder, submit via the link provided on LMS. There is no late policy. O o O O O x(t) R ܠܠܠܠܠܠ i 0,(t) 0,(t) k + vt V M K., K. m f(t) The physical model of a lathe axis is shown above. The system consists of an electric motor, a flexible coupling, a rigid leadscrew, and a carriage attached to the nut of the leadscrew. The inputs of the system are the motor supply voltage V(t), and the cutting force F(t) applied to the carriage. The electric motor is modeled with armature resistance R, armature inductance L, torque constant Km and back-emf constant Ke. Torsional stiffness of the coupling is k. Mass of the carriage is m. Pitch of the rigid leadscrew is 2. All the frictional effects are modeled as if they are accumulated at the right-hand-side bearing as a rotational viscous friction (damping) with coefficient b. The model parameters are as follows: R L = 0.1 Ω = 0.01 H Km = 0.1 N.m/A Ke = 0.1 V.s/rad ki = 5000 N.m/rad b = 0.01 N.m.s/rad 2 = 0.02 m m = 50 kg
1. In order to simplify the model, neglect the armature inductance L, and assume that the coupling is infinitely stiff (i.e. 0. = 62). Write the continuity equations for the simplified model and show that the simplified transfer function is: = X(s) 1 V(s) s? +5.5s 2. Assume you have a perfect sensor (H(s)=1). Use the simplified transfer function and control the position of the carriage x(t) when f(t) = 0 with a proportional (P) controller. Find the value range for the controller gain K, to achieve less than 10% overshoot (Mp < 0.1) within 1 s (tp < 1) of a unit-step input. <