A servovalve is a transducer that regulates flow to a hydraulic actuator. It takes electrical current i in Amps as input and converts it to fluid flow q in m³/s, with dynamics that can be modeled as a second order system with a transfer function W Q(s) = k- I(s) s² + 2(wns + w (1) where k = 2.4, w₁ = 2π√n with √n = 160 Hz, and 0.2. Suppose the output flow of the servovalve is routed into a hydraulic cylinder connected to a mass. The resulting transfer function from fluid flow rate to velocity v in m/s of the mass is V(s) Q(s) 1 1 = Ams+b' (2) where A = 0.25 m² is the area of the cylinder, b = 10 Ns/m is viscous damping due to friction between piston and cylinder, and the mass m = 20 kg. (a) Find the transfer function relating current input I(s) to velocity output V(s), that is, give II(s) = of the two cascaded systems V(8) I(8) (b) Sketch its Bode magnitude plot, using decibels as the unit of magnitude (c) Your boss tells you you need to increase the frequency range of the constant magnitude band that exists at low frequencies. Suppose you can only change (, wn, or m. What parameter would you change and would you make it larger or smaller? Why did you pick this parameter?
A servovalve is a transducer that regulates flow to a hydraulic actuator. It takes electrical current i in Amps as input and converts it to fluid flow q in m³/s, with dynamics that can be modeled as a second order system with a transfer function W Q(s) = k- I(s) s² + 2(wns + w (1) where k = 2.4, w₁ = 2π√n with √n = 160 Hz, and 0.2. Suppose the output flow of the servovalve is routed into a hydraulic cylinder connected to a mass. The resulting transfer function from fluid flow rate to velocity v in m/s of the mass is V(s) Q(s) 1 1 = Ams+b' (2) where A = 0.25 m² is the area of the cylinder, b = 10 Ns/m is viscous damping due to friction between piston and cylinder, and the mass m = 20 kg. (a) Find the transfer function relating current input I(s) to velocity output V(s), that is, give II(s) = of the two cascaded systems V(8) I(8) (b) Sketch its Bode magnitude plot, using decibels as the unit of magnitude (c) Your boss tells you you need to increase the frequency range of the constant magnitude band that exists at low frequencies. Suppose you can only change (, wn, or m. What parameter would you change and would you make it larger or smaller? Why did you pick this parameter?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Please solve this fully for me, I need help on this fast :)
Transcribed Image Text:A servovalve is a transducer that regulates flow to a hydraulic actuator. It takes electrical
current i in Amps as input and converts it to fluid flow q in m³/s, with dynamics that can be modeled
as a second order system with a transfer function
W
Q(s)
= k-
I(s)
s² + 2(wns + w
(1)
where k = 2.4, w₁ = 2π√n with √n = 160 Hz, and 0.2. Suppose the output flow of the servovalve
is routed into a hydraulic cylinder connected to a mass. The resulting transfer function from fluid flow
rate to velocity v in m/s of the mass is
V(s)
Q(s)
1
1
=
Ams+b'
(2)
where A = 0.25 m² is the area of the cylinder, b = 10 Ns/m is viscous damping due to friction between
piston and cylinder, and the mass m = 20 kg.
(a) Find the transfer function relating current input I(s) to velocity output V(s), that is, give II(s) =
of the two cascaded systems
V(8)
I(8)
(b) Sketch its Bode magnitude plot, using decibels as the unit of magnitude
(c) Your boss tells you you need to increase the frequency range of the constant magnitude band that
exists at low frequencies. Suppose you can only change (, wn, or m. What parameter would you
change and would you make it larger or smaller? Why did you pick this parameter?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY