Problem-5. The figure below on the left shows an armature controlled de servomotor driving a load through a gear train,

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Problem 5 The Figure Below On The Left Shows An Armature Controlled De Servomotor Driving A Load Through A Gear Train 1 (204.83 KiB) Viewed 26 times

Problem-5. The figure below on the left shows an armature controlled de servomotor driving a load through a gear train, which is commonly used in a closed-loop control system. The schematic diagram below on the right represents the armature circuit rotating simply due to the voltage eact) applied and the fixed magnetic field B by a permanent magnet. The armature voltage as an electrical parameter ea(t) is considered to be the input to the system. The resistance and inductance of the armature circuit are Rą and La, respectively. vy(t) is the back emf and directly proportional to the rotational speed of the armature as vy(t) = K W,n(t), where K, is a constant of proportionality called the back emf constant. The torque developed by the motor is proportional to the armature current, Im(t) = Kla(t), where K, is the constant of proportionality and called the motor torque constant. When the motor drives a load, the equivalent inertia and viscous damping at the armature are Jm and Dm, respectively. These entities include the corresponding armature and load parameters. (a) Obtain the transfer function of G (s) = m(s) G2(s) = @_(s) wm(s) G3(S) = in terms of Ea(s) Ea(s) Ea(s) Ea(s) electrical and mechanical parameters Kt, KoJm, Dm, Ra, La (b) Represent this de servomotor with a negative feedback block diagram that produces the transfer functions of G(s) and G3(s). Hint: The expected block diagram is given below with labelled blocks and signals for your convenience. Hence, all you need to do is determining the functions of each block. (c) Obtain a state-space representation of the system choosing the state variables as x1 = Wm (motor shaft's angular speed in rad/s) and X2 = ia (armature current in Amps), the input u is the applied voltage eq and the output y is the angular speed (Wm) in terms of electrical and mechanical parameters Ky, Kb.Jm,Dm, Ra, La 0.(1) = and G3(s) = wz(s) eo Motor Ni = 12 at - 1-21 R La W-0000 llll N2 = 25 N3 = 25 Rotor (1) Armature ) circuit 1.00 0.00 8.(1) N4 = 72 elfo Load Electrical parameters (5) Torque Constant Mechanical parameters Integrator E.(S) Tm(s) Wm(s) Om(s) V.() back emf constant