Cta Exam-Control Theory and Applications

May 5th, 2015
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State True or False a. A dynamic system can be operated at an unstable equilibrium point, if a stabilizing feedback controller is applied to it. ( ) b. A system is stable according to Lyapunov if the system converges to some equilibrium point for all initial states. ( ) c. According to Lyapunov, the domain of attraction of a nonlinear system with one stable equilibrium point is always the complete state-space.

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Cta ExamTechnische Universitt Dortmund a Department of Biochemical and Chemical Engineering Chair of Process Dynamics and Operations Prof. Dr. Sebastian EngellWritten Midterm Examination Control Theory & Application Master Program: Automation & Robotics WS 2010/11 9th of December, 2010 Duration: 75 minutesTaskAchievable ScoreScore Achieved Question 1: a) b) c) d) e) Question 2: Question 3: a) b) Question 4: a) b) c) d) e) f) Question 5: Question 6: a) b) Total2.5 0.5 0.5 0.5 0.5 0.5 3 1.5 1 0.5 3 0.5 0.5 0.5 0.5 0.5 0.5 4 (0.5x8) 3 1 2 17.0TaskAchievable ScoreScore Achieved Problem 1: a) b) Problem 2: a) b) c) Problem 3: a) b) Total9 3 6 6 2 2 2 5 2 3 20Midterm Examination: Control Theory and Applications, 9.12.2010Page 2Question 1: Stability (2.5 Points)State True or False a. A dynamic system can be operated at an unstable equilibrium point, if a stabilizing feedback controller is applied to it. ( ) b. A system is stable according to Lyapunov if the system converges to some equilibrium point for all initial states. ( ) c. According to Lyapunov, the domain of attraction of a nonlinear system with one stable equilibrium point is always the complete state-space. ( ) d. An autonomous linear system having two eigenvalues 1 = 0, 2 < 0 will always converge to the origin. ( ) e. An autonomous linear system having two eigenvalues 1 = 2 = 0 is always a simply stable system. ( )Midterm Examination: Control T

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