Short Questions (30 pts.): what are the poles of the following system? Is the system stable?...
1. What are the poles and zeros of G(s) ? Is the system stable? Explain. -flu 10. What are the poles of the following state space system? dt 15. G()(in(3t); what is system steady state response yss )-? x(s) (s+3)
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and the zeros on the s-plane (4) Is this system stable or unstable? Why or why not? (5) Estimate the system's response (not knowing the type of the input)
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and...
10 Marks Consider the following second-order system 56 u. (a) 2 Marks] What are the poles of the system? (b) 2 Marks] What is the meaning that the system be stable in terms of system response x(t)? Is the system stable or not? (c) [6 Marks] Design a rate-feedback PD controller u(t) — К,(r — г) - Кай so that the system response to a step input has a settling time around 2 sec and an overshoot of about 5%....
PROBLEM 1 Consider the transfer function T(S) =s5 +2s4 + 2s3 + 4s2 + s + 2 a) Using the Routh-Hurwitz method, determine whether the system is stable. If it is not stable, how many poles are in the right-half plane? b) Using MATLAB, compute the poles of T(s) and verify the result in part a) c) Plot the unit step response and discuss the results. (Report should include: Code, Figure 1.Unit step response, answers and conclusion)
PROBLEM 1 Consider...
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+200) G(s) = Do the following using Matlab: a) Sketch the root locus. b) Find the range of gain, K that makes the system stable c) Find the value of K that yields a damping ratio of 0.707 for the system's closed-loop dominant poles. d) Obtain Ts, Tp, %OS for the closed loop system in part c). e) Find the value of K that yields...
A system is given by: yt=5xt+1-3 Is the system BIBO stable? Justify Is the system memoryless? Explain Is the system causal? Explain Is the system time invariant? Justify Is the system linear? Justify What is the impulse response h(t) of the system? Is the system internally stable? If you could not figure out h(t) from part f, use the h(t) from the problem below. ht=5e-tut-u(t-4)
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no? c) H HG) were modified as follows. Determine the system stability as a function of parameter k, i.e, what is the minimal value of k required to keep the system stable? d) Sketch Bode the plot for T(s) including data 'k, derived from...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
by the differential equation What is the frequency response of the stable, causal LTI system defined by the differential equation: dy(t) dy(t) dt dt dt Use Matlab syntax for your response, assuming w is the frequency vector
(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)...