(a) The control input is the elevator deflection angle u(t) = 8(t). Define the output as y(t) = 0(t),the pitch angle. The following linear time-invariant ODE expresses the relationship between u(t)and y(t) under certain conditions (it is derived from linearized equations of motion of the aircraft):ÿ +0.74 ÿ + 0.92 yState the order of this ODE. Use the ODE and a Laplace transform table to derive the open-loop(or forward-path) transfer function, H(s) = Y(s)/U(s) = (s)/A(s). Submit your calculations.R(s):C(s):(b) Compute the finite zeros and finite poles of H(s) and state the number of infinite zeros ofH(s). Is the transfer function H(s) stable, marginally stable, or unstable? Justify your answer.== 1.2 0.18 uParts (c) (e) pertain to the unity negative feedback controller shown below, in whichOdes (s) is the desired pitch angle, H(s) is the transfer function computed in part (a), andK(s+1)-, a proportional-integral (PI) controller with a single control gain K.SR(s) 0C(s)H(s)- Y(s) (a) The control input is the elevator deflection angle u(t) = 8(t). Define the output as y(t) = 0(t),the pitch angle. The following linear time-invariant ODE expresses the relationship between u(t)and y(t) under certain conditions (it is derived from linearized equations of motion of the aircraft):ÿ +0.74 ÿ + 0.92 yState the order of this ODE. Use the ODE and a Laplace transform table to derive the open-loop(or forward-path) transfer function, H(s) = Y(s)/U(s) = (s)/A(s). Submit your calculations.R(s):C(s):(b) Compute the finite zeros and finite poles of H(s) and state the number of infinite zeros ofH(s). Is the transfer function H(s) stable, marginally stable, or unstable? Justify your answer.== 1.2 0.18 uParts (c) (e) pertain to the unity negative feedback controller shown below, in whichOdes (s) is the desired pitch angle, H(s) is the transfer function computed in part (a), andK(s+1)-, a proportional-integral (PI) controller with a single control gain K.SR(s) 0C(s)H(s)- Y(s)

Solution of question (1): The given linear time-invariant ODE is y...+0.74y..+0.92y=1.2u.+0.18u. The…

(a) The control input is the elevator deflection angle u(t) = 8(t). Define the output as y(t) = 0 (t), the pitch angle. The following linear time-invariant ODE expresses the relationship between u(t) and y(t) under certain conditions (it is derived from linearized equations of motion of the aircraft): = 1.2 ÿ + 0.74 ÿ + 0.92 ý 0.18 u State the order of this ODE. Use the ODE and a Laplace transform table to derive the open-loop (or forward-path) transfer function, H(s) = Y(s)/U(s) = 0(s)/A(s). Submit your calculations. (b) Compute the finite zeros and finite poles of H(s) and state the number of infinite zeros of H(s). Is the transfer function H(s) stable, marginally stable, or unstable? Justify your answer.

(a) The control input is the elevator deflection angle u(t) = 8(t). Define the output as y(t) = 0 (t), the pitch angle. The following linear time-invariant ODE expresses the relationship between u(t) and y(t) under certain conditions (it is derived from linearized equations of motion of the aircraft): = 1.2 ÿ + 0.74 ÿ + 0.92 ý 0.18 u State the order of this ODE. Use the ODE and a Laplace transform table to derive the open-loop (or forward-path) transfer function, H(s) = Y(s)/U(s) = 0(s)/A(s). Submit your calculations. (b) Compute the finite zeros and finite poles of H(s) and state the number of infinite zeros of H(s). Is the transfer function H(s) stable, marginally stable, or unstable? Justify your answer.

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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