We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping compl...

In this paper‎, ‎we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset‎ ‎of 3-dimensional space‎. ‎The place of sensor is modeled by a subdomain‎ ‎of this region of a given measure‎. ‎By using an approach based on the embedding process‎, ‎first‎, ‎the system is formulated in variational form;...

An overview of the history and current practices of laser beam shaping is presented. When diffraction effects are not important, geometrical methods for laser beam shaping (ray tracing, conservation of energy within a bundle of rays, and the constant optical path length condition) can be used to determine system configurations, including aspheric elements and spherical-surface GRIN lenses, whic...

Introduction For linear time-invariant (LTI) setpoint control systems, input shaping is a powerful technique to reduce residual vibrations in those systems as shown in [1]. The targeting trajectory can be optimized (e.g. minimize targeting time or energy consumption) through convex optimization techniques. A broad overview of real-time or nearly real-time applications has been given in [2]. Inp...

At present, the research on five-level inverters mainly involves the modulation algorithm and topology, and few articles study the five-level inverter from the control strategy. In this paper, the nonlinear passivity-based control (PBC) method is proposed for single-phase uninterruptible power supply inverters. The proposed PBC method is based on an energy shaping and damping injection idea, wh...

a 2-d heat conduction model has been solved by using the adomian decomposition method topredict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source.the laser source may operate in a continuous wave (cw) mode or repeated pulse (rp) mode and may havearbitrary, spatial and temporal profiles.a generalized solution containing five-terms approxim...

This paper, describes the second phase of an ongoing research project dealing with the implementation of an interactive interface. It is a “hands free” instrument, utilizing a non-contact tactile feedback method based on airborne ultrasound. The three main elements/components of the interface that will be discussed in this paper are: 1. Generation of audible sound by self-demodulation of an ult...

We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler–Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in...