Question
Asked Nov 18, 2019
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  1. Derive the plant transfer function, , for the DC motor position system in terms of the motor gain constant, K, and the time constant, τ.
  2. 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.
  3. 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.
  4. 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 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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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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Expert Answer

Step 1

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

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L6)=K,K

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Step 2

The transfer function of the DC motor from the given block diagram can be expressed as:-

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1 (s) mx Vm(s) R k Jegs m R 1 1 e(s) RyJ Rm eqs+1 ө(з) Vim(5) ....() k2

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Step 3

 The transfer function of the ...

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К+ кя u(s) «. к, r(s)

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