Problem statement As a part of a machine, a DC motor is used to move a metal piece in a linear motion. The metal piece s

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Problem Statement As A Part Of A Machine A Dc Motor Is Used To Move A Metal Piece In A Linear Motion The Metal Piece S 1 (167.11 KiB) Viewed 40 times

Problem statement As a part of a machine, a DC motor is used to move a metal piece in a linear motion. The metal piece slides over a roller that rotates with the motor shaft, as shown in the figure below. Assume a negligible friction through the system. The metal piece is to be controlled given the parameters for the DC motor and the metal piece in the table below. Metal Piece DC Motor Roller Parameter Mass of the metal piece (M) System Inertia (Um) Roller radius (r) Motor damping (bm) Torque constant (Km) Back emf constant (Kb) Motor resistance (Rm) Motor inductance (Lm) Value 12.653kg 10.91 x 10-3 kg.m? 31.75 X 10-3 m 0.268 N.ms/rad 0.8379N.m/amp 0.838 V s/rad 1.3612 3.6 mH 1- Mathematical Modeling Represent the given system by a schematic model, and find the state space representation of the system. If the desired controlled output is the metal piece position X(s), obtain the open loop transfer function.