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1.3. For the following questions, please provide a complete answer to the best of your ability. The expectation is that your answer will be succinct and to-the-point. 1.1. Consider the following transfer function relating an output Y(s) to an input U(s). For this transfer function and an applied input of U(s) = ½- (a step of magnitude 5), please provide: a) The value of lim y(t), if it exists. If it does not, answer "the system diverges." t-xo' b) Roughly how long it will take y(t) to reach its final value. If it diverges, answer "the system diverges." c) A sketch of y(t) (y-axis) versus t (x-axis). d) The explicit equation of the time-domain response y(t). 1.2. Y(s) U(s) = 3 S+2 Below is the SIR model of infectious diseases that we explored in tutorial activity 1. The interacting nature between the susceptible s(t) and infected I(t) populations make these ODEs nonlinear. Your task is to determine the set of linearized differential equations S'(t), I'(t) and R'(t) centered at some linearization point S, Ī, and R. Factors B, N, and y are constant. -ẞ s(t)I(t) ds(t) dt = N di(t) = dt B-S(t)I(t) N · — YI(t) = YI(t) dR(t) dt The plot below shows the complex conjugate poles for two second order systems (A) and (B) with the same gains. The simulation response of y(t) responding to a step input for u(t) is shown for you in response panel (A). Sketch the response for system (B) to the best of your ability. Parameter c is a real number such that c <-2. You may complete the sketch directly on the figure, or in your answer book. (B) (A) Im E 2 Response (A) -C -2 -1 × Ņ 1 1 2 Re Response (B)

1.3. For the following questions, please provide a complete answer to the best of your ability. The expectation is that your answer will be succinct and to-the-point. 1.1. Consider the following transfer function relating an output Y(s) to an input U(s). For this transfer function and an applied input of U(s) = ½- (a step of magnitude 5), please provide: a) The value of lim y(t), if it exists. If it does not, answer "the system diverges." t-xo' b) Roughly how long it will take y(t) to reach its final value. If it diverges, answer "the system diverges." c) A sketch of y(t) (y-axis) versus t (x-axis). d) The explicit equation of the time-domain response y(t). 1.2. Y(s) U(s) = 3 S+2 Below is the SIR model of infectious diseases that we explored in tutorial activity 1. The interacting nature between the susceptible s(t) and infected I(t) populations make these ODEs nonlinear. Your task is to determine the set of linearized differential equations S'(t), I'(t) and R'(t) centered at some linearization point S, Ī, and R. Factors B, N, and y are constant. -ẞ s(t)I(t) ds(t) dt = N di(t) = dt B-S(t)I(t) N · — YI(t) = YI(t) dR(t) dt The plot below shows the complex conjugate poles for two second order systems (A) and (B) with the same gains. The simulation response of y(t) responding to a step input for u(t) is shown for you in response panel (A). Sketch the response for system (B) to the best of your ability. Parameter c is a real number such that c <-2. You may complete the sketch directly on the figure, or in your answer book. (B) (A) Im E 2 Response (A) -C -2 -1 × Ņ 1 1 2 Re Response (B)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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1.3. For the following questions, please provide a complete answer to the best of your ability. The expectation is that your answer will be succinct and to-the-point. 1.1. Consider the following transfer function relating an output Y(s) to an input U(s). For this transfer function and an applied input of U(s) = ½- (a step of magnitude 5), please provide: a) The value of lim y(t), if it exists. If it does not, answer "the system diverges." t-xo' b) Roughly how long it will take y(t) to reach its final value. If it diverges, answer "the system diverges." c) A sketch of y(t) (y-axis) versus t (x-axis). d) The explicit equation of the time-domain response y(t). 1.2. Y(s) U(s) = 3 S+2 Below is the SIR model of infectious diseases that we explored in tutorial activity 1. The interacting nature between the susceptible s(t) and infected I(t) populations make these ODEs nonlinear. Your task is to determine the set of linearized differential equations S'(t), I'(t) and R'(t) centered at some linearization point S, Ī, and R. Factors B, N, and y are constant. -ẞ s(t)I(t) ds(t) dt = N di(t) = dt B-S(t)I(t) N · — YI(t) = YI(t) dR(t) dt The plot below shows the complex conjugate poles for two second order systems (A) and (B) with the same gains. The simulation response of y(t) responding to a step input for u(t) is shown for you in response panel (A). Sketch the response for system (B) to the best of your ability. Parameter c is a real number such that c <-2. You may complete the sketch directly on the figure, or in your answer book. (B) (A) Im E 2 Response (A) -C -2 -1 × Ņ 1 1 2 Re Response (B)
Transcribed Image Text:1.3. For the following questions, please provide a complete answer to the best of your ability. The expectation is that your answer will be succinct and to-the-point. 1.1. Consider the following transfer function relating an output Y(s) to an input U(s). For this transfer function and an applied input of U(s) = ½- (a step of magnitude 5), please provide: a) The value of lim y(t), if it exists. If it does not, answer "the system diverges." t-xo' b) Roughly how long it will take y(t) to reach its final value. If it diverges, answer "the system diverges." c) A sketch of y(t) (y-axis) versus t (x-axis). d) The explicit equation of the time-domain response y(t). 1.2. Y(s) U(s) = 3 S+2 Below is the SIR model of infectious diseases that we explored in tutorial activity 1. The interacting nature between the susceptible s(t) and infected I(t) populations make these ODEs nonlinear. Your task is to determine the set of linearized differential equations S'(t), I'(t) and R'(t) centered at some linearization point S, Ī, and R. Factors B, N, and y are constant. -ẞ s(t)I(t) ds(t) dt = N di(t) = dt B-S(t)I(t) N · — YI(t) = YI(t) dR(t) dt The plot below shows the complex conjugate poles for two second order systems (A) and (B) with the same gains. The simulation response of y(t) responding to a step input for u(t) is shown for you in response panel (A). Sketch the response for system (B) to the best of your ability. Parameter c is a real number such that c <-2. You may complete the sketch directly on the figure, or in your answer book. (B) (A) Im E 2 Response (A) -C -2 -1 × Ņ 1 1 2 Re Response (B)
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