The background readgin ( if you needed) is on the screenshot Determine the closed loop transfer function from the speed reference, r, to the angular motor speed output, ω, i.e., Y(s)/R(s).Determine kp and ki in terms of the closed-loop natural frequency, ωn, damping ratio, ζ, motor time constant, τ, and motor gain constant, K.Based on your results from (1) and (2), how would large values of the controller gains, kp and ki, affect the closed-loop undamped natural frequency of the system?Explain how bsp can be used to adjust the speed and overshoot of the response to reference values. (Hint: When answering this question, explain how the value of bsp affects the locations of the closed-loop zeros and/or poles.) Read the QNET On-Off and PID Control (DC Motor Speed Control) background material in the PDF document on MoodleThe speed of the DC motor is controlled using a proportional-integral control system. The block diagram of the closed-loop system isshown below.кy=eTs+1DC Motor PI speed control closed-loop block diagram2(s)КG(s)The transfer function representing the DC motor speed-voltage relationThe input-output relation in the time-domain for a PI controller with set-point weighting is:is used to design the PI controllerk,(r-y)u-k, (br-y)+spwhere k, is the proportional gain, ki is the integral gain, and bn is the set-point weight (refer to background reading)Note: There is no tachometer sensor present on the QNET DC motor system that measures the speed. Instead the amplifier board hascircuitry that computes the derivative of the encoder signal, i.e. a digital tachometer. However to minimize the noise of the measuredsignal and increase the overall robustness of the system, the following first-order low-pass filter is used:m,measT,s+Parameter Tyis the filter time constant that determines the cutoff frequency and mmeas is the measured speed signal

Part (1):Consider only one input signal r and neglect all other input signal to obtain the transfer…

Answered: Read the QNET On-Off and PID Control…

Introductory Circuit Analysis (13th Edition)

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Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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The background readgin ( if you needed) is on the screenshot

Determine the closed loop transfer function from the speed reference, r, to the angular motor speed output, ω_, i.e., Y(s)/R(s).
Determine k_p and k_i in terms of the closed-loop natural frequency, ω_n, damping ratio, ζ, motor time constant, τ, and motor gain constant, K.
Based on your results from (1) and (2), how would large values of the controller gains, k_p and k_i, affect the closed-loop undamped natural frequency of the system?
Explain how b_sp can be used to adjust the speed and overshoot of the response to reference values. (Hint: When answering this question, explain how the value of b_sp affects the locations of the closed-loop zeros and/or poles.)

Read the QNET On-Off and PID Control (DC Motor Speed Control) background material in the PDF document on Moodle
The speed of the DC motor is controlled using a proportional-integral control system. The block diagram of the closed-loop system is
shown below.
к
y=e
Ts+1
DC Motor PI speed control closed-loop block diagram
2(s)
К
G(s)
The transfer function representing the DC motor speed-voltage relation
The input-output relation in the time-domain for a PI controller with set-point weighting is:
is used to design the PI controller
k,(r-y)
u-k, (br-y)+
sp
where k, is the proportional gain, ki is the integral gain, and bn is the set-point weight (refer to background reading)
Note: There is no tachometer sensor present on the QNET DC motor system that measures the speed. Instead the amplifier board has
circuitry that computes the derivative of the encoder signal, i.e. a digital tachometer. However to minimize the noise of the measured
signal and increase the overall robustness of the system, the following first-order low-pass filter is used:
m,meas
T,s+
Parameter Tyis the filter time constant that determines the cutoff frequency and mmeas is the measured speed signal

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