Derive the plant transfer function, , for the DC motor position system in terms of the motor gain constant, K, and the time constant, τ.Consider PD-Control with set-point weighting by setting ki = 0 in Equation 6.4.1. Determine the closed-loop transfer function from the position reference, r, to the angular position output, θ in radians, i.e., Y(s)/R(s), in terms of K, τ, bsp, kp and kd.Determine kp and kd in terms of the closed-loop natural frequency, ωn, damping ratio, ζ, motor time constant, τ, and motor gain constant, K.Determine the steady-state error to a unit step input. Given bsp = 1, determine the DC Gain of the closed-loop motor position system. Pre-Lab ReadingThe block diagram of the closed-loop system for control of motor position is shown in the figure.Motor1Iy=e1PIDS+DC Motor PID position control closed-loop block diagram with set point weight bsp 1The two-degree of freedom PID compensator with set point weighting isu) ( () y(t)) +r(T)y(T) dtk(t)6.4.1]sd41-...

Write the expression of the PID controller in Laplace transform:-

Answered: Pre-Lab Reading The block diagram of…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter12: Power System Controls

Section: Chapter Questions

Problem 12.4P

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Question

Derive the plant transfer function, , for the DC motor position system in terms of the motor gain constant, K, and the time constant, τ.
Consider PD-Control with set-point weighting by setting k_i = 0 in Equation 6.4.1. Determine the closed-loop transfer function from the position reference, r, to the angular position output, θ in radians_,i.e., Y(s)/R(s), in terms of K, τ, b_sp, k_pand k_d.
Determine k_pand k_d in terms of the closed-loop natural frequency, ω_n, damping ratio, ζ, motor time constant, τ, and motor gain constant, K.
Determine the steady-state error to a unit step input. Given b_sp = 1, determine the DC Gain of the closed-loop motor position system.

Pre-Lab Reading
The block diagram of the closed-loop system for control of motor position is shown in the figure.
Motor
1
Iy=e
1
PID
S+
DC Motor PID position control closed-loop block diagram with set point weight bsp 1
The two-degree of freedom PID compensator with set point weighting is
u) ( () y(t)) +
r(T)y(T) dtk
(t)
6.4.1]
sd
41-.
..

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