Download Midterm Exam with Solution | Advanced Nonlinear Control Strategy | E C E 874 and more Exams Electrical and Electronics Engineering in PDF only on Docsity! Midterm Examination Name: ___________________________________________ Class: ECE 874 - Nonlinear Control Spring Semester - 2009 Instructor: Darren M. Dawson 1. Equilibrium Points - For the system 1 2 1 2 1 1 2 2 tan x x x x x x Find all of the equilibrium points. Find the linear approximation about each equilibrium point, find the eigenvalues of the resulting A matrix, and classify the stability of each point. Solution: Midterm Examination 2. Autonomous System - Consider the system defined by the following equations: 3 1 1 2 1 2 1 3 x x x x x x Describe the stability of the equilibrium point xe = (0, 0), in the following cases: i 0 (ii) 0 (iii) 0 3. Nonautonomous System - Study the stability of the equilibrium point xe = (0, 0) for the system: 2 2 1 1 1 2 2 2 2 2 1 2 cos sin x x x x t x x x x t 4. Backstepping Control Design - Given the following system: 3 1 1 2 2 4 2 1 2 1 x x x x x x x u Using the backstepping approach outlined in class in which intermediate tracking variables are explicitly defined, design a state feedback control law to stabilize the equilibrium point at the origin. Discuss stability and show all signals are bounded. Midterm Examination
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