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Given the following nonlinear state equation, x₁ = (x₁+7) - (x₂ + 6) + 9 + (x₂ + 12). u x₂ = − (x₂ + 2) - (x₁ +23) obtain an approximate LTI model, by linearizing it at the following point of operation XºP = [-7,-21¹ u" =−0.9 You are required to submit your working part, in a file. In addition to that, you are required to input the A matrix in the text boxes which are offered at the end of this question. Hint: A good procedure is the one we applied in class and in one of the tutorial problems, for obtaining the 1 st order Taylor approximation of the nonlinear state equation of the pendulum Considering that the A matrix follows this convention, [all an] 921 input the values you have obtained for the matrix A, in this vector, [a₁1 912 921 922]

Given the following nonlinear state equation, x₁ = (x₁+7) - (x₂ + 6) + 9 + (x₂ + 12). u x₂ = − (x₂ + 2) - (x₁ +23) obtain an approximate LTI model, by linearizing it at the following point of operation XºP = [-7,-21¹ u" =−0.9 You are required to submit your working part, in a file. In addition to that, you are required to input the A matrix in the text boxes which are offered at the end of this question. Hint: A good procedure is the one we applied in class and in one of the tutorial problems, for obtaining the 1 st order Taylor approximation of the nonlinear state equation of the pendulum Considering that the A matrix follows this convention, [all an] 921 input the values you have obtained for the matrix A, in this vector, [a₁1 912 921 922]

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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Given the following nonlinear state equation, x₁ = (x₁+7) ⋅ (x₂ + 6) + 9 + (x₂ + 12). u x₂ = (x₂ + 2) - (x₁ +23) obtain an approximate LTI model, by linearizing it at the following point of operation XºP=[-7,-21¹ u = –09 You are required to submit your working part, in a file. In addition to that, you are required to input the A matrix in the text boxes which are offered at the end of this question. Hint: A good procedure is the one we applied in class and in one of the tutorial problems, for obtaining the 1 st order Taylor approximation of the nonlinear state equation of the pendulum. Considering that the A matrix follows this convention, 912 A = 922 a₂1 input the values you have obtained for the matrix A, in this vector, [9₁1 912 a21 922
Transcribed Image Text:Given the following nonlinear state equation, x₁ = (x₁+7) ⋅ (x₂ + 6) + 9 + (x₂ + 12). u x₂ = (x₂ + 2) - (x₁ +23) obtain an approximate LTI model, by linearizing it at the following point of operation XºP=[-7,-21¹ u = –09 You are required to submit your working part, in a file. In addition to that, you are required to input the A matrix in the text boxes which are offered at the end of this question. Hint: A good procedure is the one we applied in class and in one of the tutorial problems, for obtaining the 1 st order Taylor approximation of the nonlinear state equation of the pendulum. Considering that the A matrix follows this convention, 912 A = 922 a₂1 input the values you have obtained for the matrix A, in this vector, [9₁1 912 a21 922
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