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.
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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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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