1 / 4

At t=0, x=0, v=20 and c 1 , is the step input with value 2. Find V(s)

ÖDEV 08. Problem 1:. The mathematical model of a system is given as below : k=2. At t=0, x=0, v=20 and c 1 , is the step input with value 2. Find V(s). Answer:. D(s)=s 2 +2s+0.1. s 1 =-0.0513, s 2 =-1.9487. Problem 2:. The mathematical model of a system is:.

khoi
Download Presentation

At t=0, x=0, v=20 and c 1 , is the step input with value 2. Find V(s)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ÖDEV 08 Problem 1: The mathematical model of a system is given as below : k=2. At t=0, x=0, v=20 and c1, is the step input with value 2. Find V(s) Answer: D(s)=s2+2s+0.1 s1=-0.0513, s2=-1.9487

  2. Problem 2: The mathematical model of a system is: T(t) is input, θ(t) and ω(t) are the output. a) Find the eigenvalues of a system. Is the system stationary or not? b) At t=0 θ=0.1 and ω=-6. T(t), is the step input with value -5. Find the solution of ω(t) with Laplace transform depending on initial conditions. Find Laplace transform of solutions for θ(t) input. c) If T(t) = 3e-tcos(4t+2.7) , find θ(t). Answer: a) s1,2=-1±2i, stationary s=-1+4i;hs=0.5/(s^2+2*s+5);abs(hs),angle(hs) θ(t) = (0.0417) (3) e-tcos(4t+2.7-3.1416)

  3. Find the solution of Laplace transform based on initial conditions for d) Problem 3: The mathematical model of a system is: a) V(t) input, q1(t) ve q2(t) ouput Write the euations interms of variables form. b) Write MatLAB codes to find the eigenvalues of system. c) Find the matrix [sI-A]-1 by writing MatLAB codes. d) The results for (b) and (c) obtained with computer are given below: s1,2=-0.75±1.7854i, s3=0. and V(t), is the step function with magnitude 2. Find the Laplace transform solution depending on q1 input Answer: b) a=[-1.5,1.5,0; 0,0,1; 3.75,-3.75,0];eig(a) c) a=[-1.5,1.5,0; 0,0,1; 3.75,-3.75,0]; syms s; i1=eye(3); a1=inv(s*i1-a); pretty(a1)

  4. Problem 4: Find eigenvalues of matrix. Write the program codes to find eigenvalues by using MatLAB. b) a=[2,-4;-2,5];eig(a) Answer: a) 0.2984, 6.7016 For the system the matematical model is given below. Find the eigen values of a system by using MatLAB codes. Problem 5: Answer: Variables: x, θ, v, ω. At MatLAb : a=[0,0,1,0; 0,0,0,1; -20,-10,-2,-1; -8,-10,-2,-4]; eig(a) Eigenvalues: -1.8±4.3163i, -1.19±2.015i

More Related