Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Q2 Amplifier and motor Ua(s) Wind turbine Um(s) 0,(s) E(s) K1 U(s) 5 0(s) 0.1s + 1 s2 + 4s + 40 Desired Actual pitch pitch K.

Q2 Amplifier and motor Ua(s) Wind turbine Um(s) 0,(s) E(s) K1 U(s) 5 0(s) 0.1s + 1 s2 + 4s + 40 Desired Actual pitch pitch K.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question
Q2 Amplifier Ua(s) and motor Wind turbine Um(s) 0,(s) E(s) K1 U(s) 0(s) 0.1s + 1 s2 + 4s + 40 Desired Actual pitch pitch K2 Sensor Figure Q2 A pitch-angle control system for a wind turbine is shown in Figure Q2. The desired pitch angle is given by 6,(s), while the actual pitch angle is given by 0(s). The error between actual and desired pitch is amplified and used to actuate a motor. The wind turbine is acted upon by the torque provided by the motor Um(s), and also by torque from external wind disturbances Ua(s). The actual pitch angle is measured and fed back by a sensor which has gain K2. (a) Derive the closed-loop transfer function of the system when there are no wind disturbances. For a unit step change in 0,, it is desired that the steady state error in pitch angle should be zero. Show that the condition for this is given by (b) K1 = K,K2 + 8 In addition, it is desired that a steady-state error of exactly 0.1 rad/s is produced when the desired pitch angle is adjusted by a ramp input of 4 rad/s. By substituting the condition derived in part (b) into the closed-loop transfer function, calculate suitable values for the gains K, and K2. (c) Calculate the steady-state pitch angle resulting from a step change in wind disturbance torque Ua of 5Nm when the reference pitch angle 0, is zero. (Find an expression in terms of the gains K, and K2, and then substitute the values from part (c).) (d)
Transcribed Image Text:Q2 Amplifier Ua(s) and motor Wind turbine Um(s) 0,(s) E(s) K1 U(s) 0(s) 0.1s + 1 s2 + 4s + 40 Desired Actual pitch pitch K2 Sensor Figure Q2 A pitch-angle control system for a wind turbine is shown in Figure Q2. The desired pitch angle is given by 6,(s), while the actual pitch angle is given by 0(s). The error between actual and desired pitch is amplified and used to actuate a motor. The wind turbine is acted upon by the torque provided by the motor Um(s), and also by torque from external wind disturbances Ua(s). The actual pitch angle is measured and fed back by a sensor which has gain K2. (a) Derive the closed-loop transfer function of the system when there are no wind disturbances. For a unit step change in 0,, it is desired that the steady state error in pitch angle should be zero. Show that the condition for this is given by (b) K1 = K,K2 + 8 In addition, it is desired that a steady-state error of exactly 0.1 rad/s is produced when the desired pitch angle is adjusted by a ramp input of 4 rad/s. By substituting the condition derived in part (b) into the closed-loop transfer function, calculate suitable values for the gains K, and K2. (c) Calculate the steady-state pitch angle resulting from a step change in wind disturbance torque Ua of 5Nm when the reference pitch angle 0, is zero. (Find an expression in terms of the gains K, and K2, and then substitute the values from part (c).) (d)
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Rectangular coordinate system
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS