Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

Optimizing Amplifier Placements in a Multiwavelength Optical LAN/MAN: The Unequally Powered Wavelengths Case

Optical networks based on passive-star couplers and employing WDM have been proposed for deployment in local and metropolitan areas. These networks suffer from splitting, coupling, and attenuation losses. Since there is an upper bound on transmitter power and a lower bound on receiver sensitivity, optical amplifiers are usually required to compensate for the power losses mentioned above. Due to the high cost of amplifiers, it is desirable to minimize their total number in the network. However, an optical amplifier has constraints on the maximum gain and the maximum output power it can supply; thus, optical amplifier placement becomes a challenging problem. In fact, the general problem of minimizing the total amplifier count is a mixed-integer nonlinear problem. Previous studies have attacked the amplifier-placement problem by adding the “artificial” constraint that all wavelengths, which are present at a particular point in a fiber, be at the same power level. This constraint simplifies the problem into a solvable mixed integer linear program. Unfortunately, this artificial constraint can miss feasible solutions that have a lower amplifier count but do not have the equally powered wavelengths constraint. In this paper, we present a method to solve the minimum amplifier- placement problem, while avoiding the equally powered wavelength constraint. We demonstrate that, by allowing signals to operate at different power levels, our method can reduce the number of amplifiers required.

Elimination of All-Optical Cycles in Wavelength-Routed Optical Networks

A transparent (wide-area) wavelength-routed optical network may be constructed by using wavelength cross-connect switches connected together by fiber to form an arbitrary mesh structure. The network is accessed through electronic stations that are attached to some of these cross-connects. These wavelength cross-connect switches have the property that they may configure themselves into unspecified states. Each input port of a switch is always connected to some output port of the switch whether or not such a connection is required for the purpose of information transfer. Due to the presence of these unspecified states, there exists the possibility of setting up unintended alloptical cycles in the network (viz., a loop with no terminating electronics in it). If such a cycle contains amplifiers [e.g., Erbium- Doped Fiber Amplifiers (EDFA’s)], there exists the possibility that the net loop gain is greater than the net loop loss. The amplified spontaneous emission (ASE) noise from amplifiers can build up in such a feedback loop to saturate the amplifiers and result in oscillations of the ASE noise in the loop. Such all-optical cycles as defined above (and hereafter referred to as “white” cycles) must be eliminated from an optical network in order for the network to perform any useful operation. Furthermore, for the realistic case in which the wavelength cross-connects result in signal crosstalk, there is a possibility of having closed cycles with oscillating crosstalk signals. We examine algorithms that set up new transparent optical connections upon request while avoiding the creation of such cycles in the network. These algorithms attempt to find a route for a connection and then (in a post-processing fashion) configure switches such that white cycles that might get created would automatically get eliminated. In addition, our call-set-up algorithms can avoid the possibility of crosstalk cycles.

Routing and Wavelength Assignment (RWA) with Power Considerations In All- Optical Wavelength-Routed Networks

Routing and wavelength assignment (RWA) is an important problem that arises in wavelength division multiplexed (WDM) optical networks. Previous studies have solved many variations of this problem under the assumption of perfect conditions regarding the power of a signal. In this paper, we investigate this problem while allowing for degradation of routed signals by components such as taps, multiplexers, and fiber links. We assume that optical amplifiers are preplaced. We investigate the problem of routing the maximum number of connections while maintaining proper power levels. The problem is formulated as a mixed-integer nonlinear program and two-phase hybrid solution approaches employing two different heuristics are developed

Investigation of the optical absorption of a magnetic colloid from the thermal to the electronic time-scale regime: measurement of the free-carrier absorption cross-section

The free-carrier absorption cross-section sigma of a magnetic colloid composed of magnetite nanoparticles dispersed in oil is obtained by using the Z-scan technique in different experimental conditions of the laser beam. We show that it is possible to obtain sigma with picosecond pulsed and millisecond chopped beams with pulse frequencies smaller than about 30 Hz. For higher pulse frequencies, the heating of the colloidal system triggers the appearance of the Soret effect. This effect artificially increases the value of sigma calculated from the experimental results. The limits of the different experimental setups are discussed. (C) 2012 Optical Society of America

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Femtosecond third-order nonlinear spectra of lead-germanium oxide glasses containing silver nanoparticles

This work reports on the spectral dependence of both nonlinear refraction and absorption in lead-germanium oxide glasses (PbO-GeO2) containing silver nanoparticles. We have found that this material is suitable for all-optical switching at telecom wavelengths but at the visible range it behaves either as a saturable absorber or as an optical limiter. (C) 2012 Optical Society of America

Transverse pseudo-nonlinear effects measured in solid-state laser materials using a sensitive time-resolved technique

We present a detailed study of the Baryscan technique, a new efficient alternative to the widespread Z-scan technique which has been demonstrated [Opt. Lett. 36:8, 2011] to reach among the highest sensitivity levels. This method is based upon the measurement of optical nonlinearities by means of beam centroid displacements with a position sensitive detector and is able to deal with any kind of lensing effect. This technique is applied here to measure pump-induced electronic refractive index changes (population lens), which can be discriminated from parasitic thermal effects by using a time-resolved Baryscan experiment. This method is validated by evaluating the polarizability variation at the origin of the population lens observed in the reference Cr3+:GSGG laser material.