Question

DONGGUK UNIVERSITY Division of Electronics and Electrical Engineering ENE4067-01 Modern control system Homework #2 Student ID: 1st Semester, 2020 Name: Note that you have to represent all the derivation process in detail. Problem 1. A spring-mass-friction system is described by the following differential equation. d?y(t) dy(t) dt2 + y(t) = r(t) dt (a) Define the state variables as xi(t) = y(t), x2(t) = y(t) + dy(t)/dt. Write the state equations in vector-matrix form. Find the state transition matrix of A. (b) Find the characteristic equation and the eigenvalues of A. (c) Conduct matrix diagonalization of A.

Answer 1

Let's start our discussion with State Transition Matrix, Eigenvalues & Eigenvectors, and Matrix Diagonalization.

Matrix Diagonalization: If said P is eigen eigen A = PDP-1 , then a son is to be Diagonalitable materin the materia obtained from spaces corresponding to every value and p-1 should enist.

To be clear with the matrix diagonalization once refer back to the Eigenvalues , Eigenvectors, and Eigenspaces. if you once refer back to Wikipedia or any source with that information you will get clarity about the last part of the solution.

I hope you understand the whole information, explanation, and my handwriting. I hope this will be useful to you.

Thanking You