A linearized model for the water level in a system of two interconnected water tanks is 2 * = [ -1 -²] * + [i] * x u 0-2 a) Find the transfer function for the system with input u when the output, y, is the level of water in the lower tank. [Hint: you should be able to decide which state that represents the level in the lower tank from the dynamic equations.] b) Assume that we wish to control the level of water in the lower tank with a proportional controller U(s) = K (R(s) - Y(s)). What K> 0 will result in oscillations following a step response? c) What will be the period of the oscillations when K = 5? d) We now set K = 2 and assume that initially the system is at rest with x₁(0) = x₂(0) = 0. What is the maximal size of a step (i.e. r(t) = al(t) where 1 is the heaviside function) that we can make without water spilling from the lower tank which has a capacity to hold 1 unit of water? (We assume that the upper tank has unlimited capacity.)
A linearized model for the water level in a system of two interconnected water tanks is 2 * = [ -1 -²] * + [i] * x u 0-2 a) Find the transfer function for the system with input u when the output, y, is the level of water in the lower tank. [Hint: you should be able to decide which state that represents the level in the lower tank from the dynamic equations.] b) Assume that we wish to control the level of water in the lower tank with a proportional controller U(s) = K (R(s) - Y(s)). What K> 0 will result in oscillations following a step response? c) What will be the period of the oscillations when K = 5? d) We now set K = 2 and assume that initially the system is at rest with x₁(0) = x₂(0) = 0. What is the maximal size of a step (i.e. r(t) = al(t) where 1 is the heaviside function) that we can make without water spilling from the lower tank which has a capacity to hold 1 unit of water? (We assume that the upper tank has unlimited capacity.)
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
Explain the state space function
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 3 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.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