Given the following matrices σ ω A = " ω σ Determine the transition matrix eAt using the Following 3 methods: a) eigenvalues and eigenvectors method b) Laplace transforms method. c) Writing A ...continues
The dynamic behavior of linear systems can be interpreted using the eigenvectors of the A matrix. We assume that A has distinct eigenvalues. a) Show that if υ is an eigenvector of A for the eigenvalue λ then eAtυ = eλtυ b) Let υk (k=1,2,…,n) be the eigenvectors of A, with corresponding ei ...continues
Suppose x'=Ax . Two one-second experiments are performed. In the first, x(0)=[1 1]T, x(1)=[4 -2]T. In the second, x(0)=[1 2]T, x(1)=[5 -2]T a) Find x(1) and x(2), given x(0) = [3 -1]T b) Find the matrix A c) Either find x(1.5) or explain why you cannot ( x(0)=[3 -1]T) d) More generally , x' =Ax, describ ...continues
A nonlinear system has an input-output model given by: 1. y'(t) + [1 + 0.2y(t)] y(t) = u(t) + 0.2u(t)3 i) Compute the operating point(s) for uo=2 ii) Obtain a linearized model for each of the operating points above. 2. à¿(t) + y(t) à½(t) + y(t)3 − y(t) = 2àº(t) + u(t)2 iii) Compute the operating point(s) ...continues
Bandwidth of the closed-loop system
Consider the paper machine control in the attached file. Plot the bandwidth of the closed-loop system as K varies in the interval 1 ≤ K ≤ 50. What gain is required to provide a bandwidth of 10 rad/sec? See attached file for full problem description.
Peak time and percent overshoot
A system with G(s) = K/(s(s+1)(s+4)) where K = 1 Design aPI controller so that the dominant roots are at s = -0.365+j0.514 and -0.365-j0.514. If a change of K = +50% or -50% occurs. Does the system peak time increase or decrease? Does the overshoot increase or decrease?
Consider the following system whose state space representation is as follows...
Consider the following system whose state space representation is as follows: x'1 0 1 0 x1 0 x'2 = 0 0 1 x2 + 0 ...continues
(See attached files for full problem descriptions)
Please draw bode plot on logarithmic paper or graph paper. Ignore any reference to Eds chart or any other chart in the questions. (See attached file for full problem description)
Please leave out problem asking for SISO and benefit for digital system. (See attached file for full problem description)
