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1. Consider the following nonlinear system: ài = fi(r1, r2, r3) + 91 (a1)u à2 = f2(a1, #2, 23) %3! ig = fa(a1, 2, 3) y = h(r3) where ri E IR, r2 € IR, r3 € R, u e R, y E R, fi(0, 0, 0) = f2(0,0,0) = f3(0, 0,0) = 0 %3D and g1(0) # 0. Determine the relative degree of the controlled output y with respect to the manipulated input u, design an input/output feedback linearizing controller to stabilize the input/ouput dynamics and state under what conditions on the zero dynamics of the above system this controller enforces local asymptotic stability of the origin. Assume that the relative degree is well-defined in a neighborhood of the origin.

1. Consider the following nonlinear system: ài = fi(r1, r2, r3) + 91 (a1)u à2 = f2(a1, #2, 23) %3! ig = fa(a1, 2, 3) y = h(r3) where ri E IR, r2 € IR, r3 € R, u e R, y E R, fi(0, 0, 0) = f2(0,0,0) = f3(0, 0,0) = 0 %3D and g1(0) # 0. Determine the relative degree of the controlled output y with respect to the manipulated input u, design an input/output feedback linearizing controller to stabilize the input/ouput dynamics and state under what conditions on the zero dynamics of the above system this controller enforces local asymptotic stability of the origin. Assume that the relative degree is well-defined in a neighborhood of the origin.

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 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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1. Consider the following nonlinear system: à1 = fi(r1, 22, a3) + g1(a1)u i2 = f2(*1, 2, 13) iz = fa(x1, 12, 13) y = h(r3) where a1 € R, r2 € R, r3 € R, u e R, y E R, fi(0, 0, 0) = f2(0,0,0) = fa(0,0,0) = 0 and g1(0) + 0. Determine the relative degree of the controlled output y with respect to the manipulated input u, design an input/output feedback linearizing controller to stabilize the input/ouput dynamics and state under what conditions on the zero dynamics of the above system this controller enforces local asymptotic stability of the origin. Assume that the relative degree is well-defined in a neighborhood of the origin.
Transcribed Image Text:1. Consider the following nonlinear system: à1 = fi(r1, 22, a3) + g1(a1)u i2 = f2(*1, 2, 13) iz = fa(x1, 12, 13) y = h(r3) where a1 € R, r2 € R, r3 € R, u e R, y E R, fi(0, 0, 0) = f2(0,0,0) = fa(0,0,0) = 0 and g1(0) + 0. Determine the relative degree of the controlled output y with respect to the manipulated input u, design an input/output feedback linearizing controller to stabilize the input/ouput dynamics and state under what conditions on the zero dynamics of the above system this controller enforces local asymptotic stability of the origin. Assume that the relative degree is well-defined in a neighborhood of the origin.
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