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Question 1. Consider a mechanical system shown in the figure below, where F₁ (t) and F₂(t) are the inputs. k₁ m m1 mm The equations of motion are derived as follows, → Fi(t) b m₂ x2 F₂(t) m₁x₁ + k₁x₁ − k₂(x2 − x₁) – b(x₂ − x₁) = F₁(t) m₂x₂ + k₂(x₂ − x₁) + b( x2 − x₁) = F2(t) a) Obtain the state-space form to represent this system. For the output equations, assume that the variables of interest (outputs) are x₁ and x₂. b) Re-write the state-space model obtained in Part a in the matrix-vector form, that is x Ax+ Bu, y = Cx + Du Clearly show the state vector, input vector, output vector, and the state, input, output and transition matrices.

Question 1. Consider a mechanical system shown in the figure below, where F₁ (t) and F₂(t) are the inputs. k₁ m m1 mm The equations of motion are derived as follows, → Fi(t) b m₂ x2 F₂(t) m₁x₁ + k₁x₁ − k₂(x2 − x₁) – b(x₂ − x₁) = F₁(t) m₂x₂ + k₂(x₂ − x₁) + b( x2 − x₁) = F2(t) a) Obtain the state-space form to represent this system. For the output equations, assume that the variables of interest (outputs) are x₁ and x₂. b) Re-write the state-space model obtained in Part a in the matrix-vector form, that is x Ax+ Bu, y = Cx + Du Clearly show the state vector, input vector, output vector, and the state, input, output and transition matrices.

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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Question 1. Consider a mechanical system shown in the figure below, where F₁ (t) and F₂(t) are the inputs. k₁ m m1 mm The equations of motion are derived as follows, → Fi(t) b m₂ x2 F₂(t) m₁x₁ + k₁x₁ − k₂(x2 − x₁) – b(x₂ − x₁) = F₁(t) m₂x₂ + k₂(x₂ − x₁) + b( x2 − x₁) = F2(t) a) Obtain the state-space form to represent this system. For the output equations, assume that the variables of interest (outputs) are x₁ and x₂. b) Re-write the state-space model obtained in Part a in the matrix-vector form, that is x Ax+ Bu, y = Cx + Du Clearly show the state vector, input vector, output vector, and the state, input, output and transition matrices.
Transcribed Image Text:Question 1. Consider a mechanical system shown in the figure below, where F₁ (t) and F₂(t) are the inputs. k₁ m m1 mm The equations of motion are derived as follows, → Fi(t) b m₂ x2 F₂(t) m₁x₁ + k₁x₁ − k₂(x2 − x₁) – b(x₂ − x₁) = F₁(t) m₂x₂ + k₂(x₂ − x₁) + b( x2 − x₁) = F2(t) a) Obtain the state-space form to represent this system. For the output equations, assume that the variables of interest (outputs) are x₁ and x₂. b) Re-write the state-space model obtained in Part a in the matrix-vector form, that is x Ax+ Bu, y = Cx + Du Clearly show the state vector, input vector, output vector, and the state, input, output and transition matrices.
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