Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Choose as state variables: x,(t) =u,(1) and x,()-(1). Obtain the following state space model R, + R, L. y-l - +Ou and calculate the system matrices for L 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 =-1 and 1f -2. By using observability matrix, check if the system representation R(A, B,C) is observable. Design a reduced-order state observer with desired poles 2d = -2.

Choose as state variables: x,(t) =u,(1) and x,()-(1). Obtain the following state space model R, + R, L. y-l - +Ou and calculate the system matrices for L 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 =-1 and 1f -2. By using observability matrix, check if the system representation R(A, B,C) is observable. Design a reduced-order state observer with desired poles 2d = -2.

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
icon
Concept explainers
Question

Please review only the 3 problems inside the red box.

Consider the following electrical system: R L C= uc u R The equations describing the system dynamics are the following: u(1) = 1 di(e) dt 2+(R, + R, i() + u,(1) cdu, 0 - i(1) Choose as state variables: x,(1) = u,(1) and x,(t) = i(t). Obtain the following state space model R, +R, + Ou and calculate the system matrices for L = 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 = -1 and 14 = -2. By using observability matrix, check if the system representation R(A,B,C) is observable. Design a reduced-order state observer with desired poles 24 = -2. 2.
Transcribed Image Text:Consider the following electrical system: R L C= uc u R The equations describing the system dynamics are the following: u(1) = 1 di(e) dt 2+(R, + R, i() + u,(1) cdu, 0 - i(1) Choose as state variables: x,(1) = u,(1) and x,(t) = i(t). Obtain the following state space model R, +R, + Ou and calculate the system matrices for L = 0.5, R, = 1, R2 = land C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on desired locations: 14 = -1 and 14 = -2. By using observability matrix, check if the system representation R(A,B,C) is observable. Design a reduced-order state observer with desired poles 24 = -2. 2.
Expert Solution
steps

Step by step

Solved in 7 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Thermistors
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