Active Singularity Approach to Control of Nonsmooth Mechanical and Electromechanical Systems Using Wavelet-based and Impulsive Contol Methods

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Active Singularity Approach to Control of Nonsmooth Mechanical & Electromechanical Systems Using Wavelet-Based & Impulsive Control MethodsAbstractThe common feature in the behavior of systems with impacts and impulsive control actions is the presence of singularities which manifest themselves in discontinuities and nonsmoothness in system motion, jumps in system dimension, lack of continuous dependence on the initial conditions and other irregularities. This proposal focuses on the introduction of a control action into the system during the singularity phase rather than the traditional approach of control during the nonsingular phase of the system motion.The goal of the research are to a) develop a mathematical framework for representing control actions, system motions, and system dynamics during the singularity phase of system motion and combining them with the regular motion phase, b) develop the ultra-high-speed time-localized state estimation and system identification procedures, which utilize signals containing both smooth and impulsive measurement data, c) develop procedures for the design of open-loop and feedback control laws to satisfy specific control objectives with control actions applied during the singularity phase as well as during the regular system motion, and d) apply the procedures developed to the high speed fault clearing in the boiler-turbine units with fast valving, modeling and control of impact-based motions in MEMS, and control of the robotic systems for cutting and welding with impulsive endpoint return motion.