Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
7.39 This problem is intended to give you more insight into controllability and observability. Consider the circuit in Fig. 7.92, with an input voltage u(t) and an output current y(t). Source (a) Using the capacitor voltage and inductor current as state-variables, write state and output equations for the system Figure 7.92 y(t) Electric circuit for Problem 7.39 + u(t) R2 (b) Find the conditions relating R1, R2, C, and L that render the system uncon- trollable. Find a similar set of conditions that result in an unobservable system (c) Interpret the conditions found in part (b) physically in terms of the time constants of the system (d) Find the transfer function of the system. Show that there is a pole-zero cancellation for the conditions derived in part (b) (that is, when the system is uncontrollable or unobservable)

7.39 This problem is intended to give you more insight into controllability and observability. Consider the circuit in Fig. 7.92, with an input voltage u(t) and an output current y(t). Source (a) Using the capacitor voltage and inductor current as state-variables, write state and output equations for the system Figure 7.92 y(t) Electric circuit for Problem 7.39 + u(t) R2 (b) Find the conditions relating R1, R2, C, and L that render the system uncon- trollable. Find a similar set of conditions that result in an unobservable system (c) Interpret the conditions found in part (b) physically in terms of the time constants of the system (d) Find the transfer function of the system. Show that there is a pole-zero cancellation for the conditions derived in part (b) (that is, when the system is uncontrollable or unobservable)

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

Feedback Control of Dynamic Systems (7th edition) - Problem 7.39

7.39 This problem is intended to give you more insight into controllability and observability. Consider the circuit in Fig. 7.92, with an input voltage u(t) and an output current y(t). Source (a) Using the capacitor voltage and inductor current as state-variables, write state and output equations for the system Figure 7.92 y(t) Electric circuit for Problem 7.39 + u(t) R2 (b) Find the conditions relating R1, R2, C, and L that render the system uncon- trollable. Find a similar set of conditions that result in an unobservable system (c) Interpret the conditions found in part (b) physically in terms of the time constants of the system (d) Find the transfer function of the system. Show that there is a pole-zero cancellation for the conditions derived in part (b) (that is, when the system is uncontrollable or unobservable)
Transcribed Image Text:7.39 This problem is intended to give you more insight into controllability and observability. Consider the circuit in Fig. 7.92, with an input voltage u(t) and an output current y(t). Source (a) Using the capacitor voltage and inductor current as state-variables, write state and output equations for the system Figure 7.92 y(t) Electric circuit for Problem 7.39 + u(t) R2 (b) Find the conditions relating R1, R2, C, and L that render the system uncon- trollable. Find a similar set of conditions that result in an unobservable system (c) Interpret the conditions found in part (b) physically in terms of the time constants of the system (d) Find the transfer function of the system. Show that there is a pole-zero cancellation for the conditions derived in part (b) (that is, when the system is uncontrollable or unobservable)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Routh Hurwitz Criteria
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
  • SEE MORE 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