Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

B | y=x, y=x u(t) Bx(t) M Kx(t) Mx(t)- M u(t) K U(s) S -1 x2(t) S u(t) -1 Y(s) x(t) y(t) (5a) Consider

image

B | y=x, y=x u(t) Bx(t) M Kx(t) Mx(t)- M u(t) K U(s) S -1 x2(t) S u(t) -1 Y(s) x(t) y(t) (5a) Consider the MBK (mass-damper-spring) system, assume M = 1, B = 1, K = 4. Show that the system can be represented by the signal flow graph shown above. (3%) (5b) Write down the state-space model (A,B,C) equations of the system according to the signal flow graph, which is a state diagram in this case. (Note that this B is not the friction coefficient.) (3%) (5c) Assume x(0) = 10, x2 (0) = 0, and u(t) = 0, solve the state equation for x (t), x2(t) and plot them as functions of time using MATLAB plot command. (3%) (5d) Find the characteristic equation det(sI - A) = 0, the poles (the eigenvalues of A), the damping ratio 5, and the natural frequency @. Comment on the relevance between these parameters and the system dehavior graphs obtained in 5c (3%) (5e) Find a state feedback controller, u(t) = Fx(t) = Fx(t)+F2x2(t), so that the closed-loop system eigenvalues (the eigenvalues of A+ BF) are 1+ j and -1-j. (3%) (5f) What are the damping ratio 5 and the natural frequency @ of the closed-loop system? (3%) (5g) For the closed-loop system, let x(0) = 10, x2 (0) = 0, solve the closed-loop state equation for x(t), x2(t) and plot them as functions of time using MATLAB plot command. (2%) (5h) Comment on the performances of the open-loop and the closed-loop system. (5%)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Signals and Systems using MATLAB

Authors: Luis Chaparro

2nd edition

123948126, 978-0123948120

More Books

Students also viewed these Mechanical Engineering questions

Question

Draw a labelled diagram of the Dicot stem.

Answered: 1 week ago

Question

WHAT component integration dependencies are critical?

Answered: 1 week ago

Question

Who owns and prepares the SIVP?

Answered: 1 week ago