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Consider a second-order nonlinear system described by à1 = a – x2, i2 = -1 - a1 + (1+ x3)u, y = x1 + 2x1x2. (a) Find all q equilibrium points xe,1, Xe,2;,..., xe.g of the system and the corresponding outputs Y0,1, Y0,2, . , Y0,g when the input u has a nominal value uo = 1. (b) For each i E {1,2,...,q}, linearize the system around the operating point (xe,i, u0, Yo,i).

Consider a second-order nonlinear system described by à1 = a – x2, i2 = -1 - a1 + (1+ x3)u, y = x1 + 2x1x2. (a) Find all q equilibrium points xe,1, Xe,2;,..., xe.g of the system and the corresponding outputs Y0,1, Y0,2, . , Y0,g when the input u has a nominal value uo = 1. (b) For each i E {1,2,...,q}, linearize the system around the operating point (xe,i, u0, Yo,i).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a second-order nonlinear system described by i1 = x – 02, i2 = -1 – x1 + (1+x²)u, = X1 - y = x1 + 2x1x2. (a) Find all q equilibrium points xe,1, Xe,2, ..., xe,g of the system and the corresponding outputs Y0,1, Yo,2, . .. , Y0,g when the input u has a nominal value uo = 1. (b) For each i E {1,2, ..., q}, linearize the system around the operating point (xe,i, u0, Yo,i).
Transcribed Image Text:Consider a second-order nonlinear system described by i1 = x – 02, i2 = -1 – x1 + (1+x²)u, = X1 - y = x1 + 2x1x2. (a) Find all q equilibrium points xe,1, Xe,2, ..., xe,g of the system and the corresponding outputs Y0,1, Yo,2, . .. , Y0,g when the input u has a nominal value uo = 1. (b) For each i E {1,2, ..., q}, linearize the system around the operating point (xe,i, u0, Yo,i).
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