Question

please solve this problem with detail description.

A simple but practical feedback control system is shown below. It is a positioning system or position servo for a large video satellite antenna modeled as a mass having a large moment of inertia, J. An output potentiometer measures the output shaft position, converting the position to a proportional voltage according to vo-Kye. where, e is the output shaft angle in radians and vo is the output potentiometer voltage; Kp is the constant of proportionality between shaft position and potentiometer voltage, is the total voltage V divided by the maximum rotation of the ntiometer: Kp-v/e,nax. The input potentiometer slider position rís converted to a voltage with a potentiometer identical t potentiometer signals is then amplified with gain A1 o the potentiometer, vr -Kp r. The difference between the two where v, is the error voltage output of the difference amplifier. This voltage is then further amplified with gain A2 and is applied to the motor terminals, where v2 is the motor voltage. The second amplifier is the power amplifier, which is capable of supplying the electrical power necessary to drive the motor. The motor is coupled to the antenna with a gear train, of ratio, θ-(N1/N2).0rn, where Pn is the motor shaft angle and θ is the angular position of the antenna with moment of inertia J. N is much smaller than N2 since the high-speed shaft of the motor must drive the antenna at low speed but with a much higher torque. The control motor has negligible armature inductance and negligible internal damping ½(s) s(TLS+1) Output Antenna potentiometer Gear angular train position θ Power difference amplifier amplifier Motor Input potentiometer Vo voltage supply Angular position A Position servo Draw the block diagram and find the transfer function of R(s) to the θ(s).

Answer 1

Vts)P RIS) V (S) .V2L) r) θ(s) K-n(n/nJ . A2 A1 1<p //s(71 s +リ S (7s 1) RUS)