Question: Consider the system i = Ax + Bu with S=C -1]. B=19 (a) Find the feedback gain K to assign the closed-loop eigenvalues at (-1

Consider the system i = Ax + Bu with S=C -1].

Consider the system i = Ax + Bu with S=C -1]. B=19 (a) Find the feedback gain K to assign the closed-loop eigenvalues at (-1 =jV3)w. (b) For x(0) = [1,1]? and u = -Kx, plot x1, x2 and u for w = 1 and w = 10. Comment on the results. (c) Via simulation, find the largest w for which \u(t) 0. Find the optimal controller u* that minimizes J. For the given initial condition, compute J*. Consider the system i = Ax + Bu with S=C -1]. B=19 (a) Find the feedback gain K to assign the closed-loop eigenvalues at (-1 =jV3)w. (b) For x(0) = [1,1]? and u = -Kx, plot x1, x2 and u for w = 1 and w = 10. Comment on the results. (c) Via simulation, find the largest w for which \u(t) 0. Find the optimal controller u* that minimizes J. For the given initial condition, compute J*

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

Consider the system x = Ax + Bu where A = [ 0 1 0 1 ] , B = [ 0 1 ] ( a ) Find the feedback gain F to assign the closed - loop eigenvalues at ( 1 j 3 ) . ( b ) For x ( 0 ) = [ 1 1 ] and u = Fx , plot...

Problem 1 Reconsider the vibration control problem of the SDOF oscillator: x + 2n x + 2nx(t) = 2nu(t) (1) and the PID control u(t) = kP (r(t) x(t)) + kD( x) + kI t 0 (r() x())d (2) where r(t) is the...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Reconsider the vibration control problem of the SDOF oscillator: x + 2 nx + n 2 x ( t ) = n 2 u ( t ) ( 1 ) and the PID control u ( t ) = kP ( r ( t ) x ( t ) ) + kD ( x ) + kI Z t 0 ( r ( ) x ( ) )...

Consider the system x (t) * (t) and the performance measure = J = = x (t) 4x(t) + 4x(t) + u(t) = [20x (1) + 5x2 (1) + u(1)]dt 0 ) (a) Find the eigenvalues of the open-loop system (Hint: x = Ax+ Bu....

Page 1 of 9 SIT787 -Mathematics for Al Assignment 3 Related to the content of Weeks 6-10 Trimester 2, 2024 Important notes: e Submission deadline can be found on the unit website. Your submission can...

Consider the closed-loop system composed of the feedback interconnection of: the state-space system with matrices += ( 0 ) . B = ( 2 ). C = ( 0 ). D=0 10 the dynamic observer x (t) =Ax (t) + Bu (1) +...

^^^^^ solve please Postopening Scenario: Your angel investors are silent in relation to the business; however, they require board meetings. for status updates on the company's nancial health....

Mass Communication is filtered communication. Discuss

The temperature distribution T(r) at a distance r, measured from one end, along a bar of length L is given by T(x)= Kr(L-x), for 0xL, K = constant. (a) Express T(r) as a half-range sine series...

1 8 fre: Which one of the following will increase the cash flow from assets for a tax - paying firm, all else Multiple Choice ot: 3 8 . 5 8 cBook An increase in the change in net working capital A...

Projects A and B are mutually exclusive and both have an initial cost of $88,000. Project A has annual cash flows for three years of $18,300, $34,500, and $52,300, respectively. Project B has annual...

(Appendices) Search magazines, newspapers, and the Internet for advertisements. Collect or print out ads that offer the following: (a) something for nothing, (b) bonus for early reply, (c) offers of...

(Appendices) Visit the Federal Trade Commissions website to learn about the latest frauds and schemes being carried out against consumers. Write a onepage report on a new scheme that is not discussed...

(Appendices) Social Studies Conduct a survey of at least three people of varied ages based on the following question. How is the U.S. economy impacting your life? As a class, compare and discuss the...