Boundary control of flexible mechanical systems

Abstract

Flexible systems have many application areas ranging from ocean engineering to aerospace. Driven by practical needs and theoretical challenges, the control problem of flexible mechanical systems has received increasing attention in recent decades. The main objective of this thesis is to explore the advanced methodologies for the vibration control of flexible structures with guaranteed stability. By investigating four different flexible structures, i.e., nonuniform string, coupled nonlinear string, Euler-Bernoulli beam, and Timoshenko beam, boundary control combining with adaptive control is proposed to suppress the vibration of flexible systems and compensate for the system parametric uncertainties. With the proposed control, uniform ultimate boundedness of the system is proved via Lyapunov's direct method. Numerical simulations are extensively carried out to illustrate the effectiveness of the proposed control.