Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Reference frame re-alignment for vector control of the brushless doubly-fed machine

Vector control provides stability and performance when applied to the brushless doubly-fed machine, however cross-coupling effects can arise between inputs and outputs. To address these effects, a procedure is proposed to both visualize and minimize the cross-coupling by means of steady-state mapping and a re-alignment of the dq reference frame. With this method implemented, gain-response tests show improved decoupling across the operating region. © 2013 EUCA.

Gain saturation in 60-fs mode-locked semiconductor laser

A passively mode-locked optically-pumped InGaAs/GaAs quantum well laser with an intracavity semiconductor saturable absorber mirror emits sub-100-fs pulses. Pulse energy declines steeply as pulse duration is reduced below 100 fs due to gain saturation. © 2010 Optical Society of America.

Gain bandwidth characterization of surface-emitting quantum well laser gain structures for femtosecond operation

We present a method to experimentally characterize the gain filter and calculate a corresponding parabolic gain bandwidth of lasers that are described by "class A" dynamics by solving the master equation of spectral condensation for Gaussian spectra. We experimentally determine the gain filter, with an equivalent parabolic gain bandwidth of up to 51 nm, for broad-band InGaAs/GaAs quantum well gain surface-emitting semiconductor laser structures capable of producing pulses down to 60 fs width when mode-locked with an optical Stark saturable absorber mirror. © 2010 Optical Society of America.

Optimization of dynamic properties and link performance for directly-modulated gain-coupled DFB lasers

This paper demonstrates the respective roles that combined gain- and index-coupling play in the dynamic properties and overall link performance of DFB lasers. It is shown that for datacommunication applications, modest gain-coupling enables optimum transmission at 10Gbit/s.