Answer Happy

An armature-controlled DC motor is coupled with a gear wheel and used to slide cart on well lubricated surface (as shown in figure) via a gear rack attached to the cart. hy Vata b.C. Motor al -Oil Bed a) Draw a block diagram that represents the system b) Determine the closed loop transfer function of the system when displacement of the cart, x(t), is the system output and input voltage to the DC motor, Valt), is the reference input. c) Determine the displacement of the cart as a function of time if an input voltage of 10 V is applied to the motor for a duration of 5 seconds. How far the cart moves as the result of this input. d) Determine the angular velocity of the motor as a function of time for the same input. Electrical and mechanical parameters of the system are given in the following table.
Table of Parameter Values Value 0.08 H 0.25 92 1.1 V.s/rad Parameter Description La Armature (rotor) Inductance Ra Armature resistance Кь Electromotive force constant Km Torque constant J Moment of inertia of armature and gear B Coefficient of viscous friction torque of armature R Gear radius m Mass of cart and gear rack b Coefficient of viscous friction of the cart M Coefficient of dynamic friction of the cart 1.05 N.m/A 0.8 kg.m? 0.14 N.m.s 0.08 m 50 kg 0.3 N.s/m 0