take the inverse Laplace transform of the expression and find zeros and poles
Take the inverse Laplace transforms of the expression and Write the zeros and poles of the systems.
17. For each of the dynamical systems shown below (1) find the poles and the zeros (2) write an expression for the general form of the step response without solving for the inverse Laplace transform 20 c) G(s) +6S +144 d) G(s)- s +-9 e +10) (s + 5) 2
i. For the transfer function s+2 T(S) - 2 +9 a. find the locations of the poles and zeros (3 marks) b. plot them on the s-plane (3 marks) c. write an expression for the general form of the step response without solving for the inverse Laplace transform (2 marks) d. State the nature of the response (2 marks)
(20 pts) Pole-zero cancellation: common poles and zeros will bring us some issues in the system design and analysis. In this problem, we will analyze how to properly handle common poles and zeros. 2.1 Consider the following two systems System 1: G(s)~5+2 System 2: G(s) S+2 (s+1.99) (s+20) Using inverse Laplace transform, determine the step response and discuss whether you can use a first-order system to approximate the step response. 2.2 Now consider the following system G(s) = (s -1.99)...
3. Solve the following ditferential equations analytically by using Laplace transform] d2x dt2 d2x +163x 5cos3t where x(0)=0, =0 dt where x(0) = 0, 의@ = 0 dt CHECK YOUR ANSWER BY MATLAB 4. By using MATLAB find poles and zeros for the following transfer function. Then find inverse Laplace. 100 (s 5)(s 70) s(s+45) (s 55)(s2 7s 110)(s2 + 6s + 95) G(s)
1) Laplace transforms/Transfer functions Use Laplace transform tables!!!! 1.1: Find the Laplace transform of - 4t) f(t) = lc + e *).u(t) (simplify into one ratio) 1.2.. Find the poles and zeros of the following functions. Indicate any repearted poles and complex conjugate poles. Expand the transforms using partial fraction expansion. 20 1.2.1: F(s) = (s + 3).(52 + 8 + 25) 1.2.2: 252 + 18s + 12 F(s) =- 54 + 9.5? + 34.5² + 90-s + 100
Problem#3 (16 points) Consider a system that has R(S) as the input and Y (S) as the output. The transfer function is given by: Y(S) R(S) 45+12 What are the poles of the system? For r(t) output in the time-domain y(t) For r(t) = t, t output in the time-domain y(t) 1- 2- 1,t 0, use partial fraction expansion and inverse Laplace transform to find the 3- 0, use partial fraction expansion and inverse Laplace transform to find the
9-8 Find the Laplace transform of f(t)=54cos(100 3sin(10t)] u(t). Locate the poles and zeros of F(s).
Question 1: [25 pts] S+1 a) Find the inverse Laplace transform of the expression $2+4 b) Find the inverse Laplace transform of the expression (s-5)(s2+4) c) Use the information from the parts a) and b) to find the solution of the IVP y" + 4y = 6e5t, y(0) = 1, y'(0) = 1.