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Assuming initial conditions to be zero: Part 1: a) Determine the overall open-loop transfer function (G₂(s)) of the system illustrated in Figures2 (The transfer function should be in standard form and denoted as G₂ (s)). b) Design a new block diagram for the aforementioned system (G₂(s)), assuming unity feedback. Illustrate the system's response to a unit step function. c) Compute the steady-state error for unit step function, unit ramp function and unit parabolic function.

Assuming initial conditions to be zero: Part 1: a) Determine the overall open-loop transfer function (G₂(s)) of the system illustrated in Figures2 (The transfer function should be in standard form and denoted as G₂ (s)). b) Design a new block diagram for the aforementioned system (G₂(s)), assuming unity feedback. Illustrate the system's response to a unit step function. c) Compute the steady-state error for unit step function, unit ramp function and unit parabolic function.

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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The mass spring damper system of a plant assembly can be represented using the following differential equation: m F V(s) F-b- Figure 1: Mass spring damper system with differential equation Ka dx -- Kx = m. dt The transfer function, defined as the ratio of output displacement to input force, is given by: x(s) G(s) F(s) Where mass (m) = 1 kg, spring constant (K) = 40 N/m and compressor element (b) = 10 Ns/m d²x dt² = Assuming initial conditions to be zero: Part 1: Mass Spring Damper System [G₁(s)] Feedback Controller [H(s)] Figure2: Plant with feedback system e(s) The mass spring damper system is assembled with a gain "Ka" and a feedback controller (H(s)). Where, H (s) is the transfer function of the feedback controller. H(s) = 24s² + 150s + 710 Ka = 625 a) Determine the overall open-loop transfer function (G₂(s)) of the system illustrated in Figures2 (The transfer function should be in standard form and denoted as G₂(s)). b) Design a new block diagram for the aforementioned system (G₂(s)), assuming unity feedback. Illustrate the system's response to a unit step function. c) Compute the steady-state error for unit step function, unit ramp function and unit parabolic function.
Transcribed Image Text:The mass spring damper system of a plant assembly can be represented using the following differential equation: m F V(s) F-b- Figure 1: Mass spring damper system with differential equation Ka dx -- Kx = m. dt The transfer function, defined as the ratio of output displacement to input force, is given by: x(s) G(s) F(s) Where mass (m) = 1 kg, spring constant (K) = 40 N/m and compressor element (b) = 10 Ns/m d²x dt² = Assuming initial conditions to be zero: Part 1: Mass Spring Damper System [G₁(s)] Feedback Controller [H(s)] Figure2: Plant with feedback system e(s) The mass spring damper system is assembled with a gain "Ka" and a feedback controller (H(s)). Where, H (s) is the transfer function of the feedback controller. H(s) = 24s² + 150s + 710 Ka = 625 a) Determine the overall open-loop transfer function (G₂(s)) of the system illustrated in Figures2 (The transfer function should be in standard form and denoted as G₂(s)). b) Design a new block diagram for the aforementioned system (G₂(s)), assuming unity feedback. Illustrate the system's response to a unit step function. c) Compute the steady-state error for unit step function, unit ramp function and unit parabolic function.
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