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.

An experimental study of loss sources in a fan operating with continuous inlet stagnation pressure distortion

The viability of Boundary Layer Ingesting (BLI) engines for future aircraft propulsion is dependent on the ability to design robust, efficient engine fan systems for operation with continuously distorted inlet flow. A key step in this process is to develop an understanding of the specific mechanisms by which an inlet distortion affects the performance of a fan stage. In this paper, detailed full-annulus experimental measurements of the flow field within a low-speed fan stage operating with a continuous 60-degree inlet stagnation pressure distortion are presented. These results are used to describe the three-dimensional fluid mechanics governing the interaction between the fan and the distortion and to make a quantitative assessment of the impact on loss generation within the fan. A 5.3 percentage point reduction in stage total-to-total efficiency is observed as a result of the inlet distortion. The reduction in performance is shown to be dominated by increased loss generation in the rotor due to off-design incidence values at its leading edge, an effect which occurs throughout the annulus despite the localised nature of the inlet distortion. Increased loss generation in the stator row is also observed due to flow separations that are shown to be caused by whirl angle distortion at rotor exit. By addressing these losses, it should be possible to achieve improved efficiency in BLI fan systems. Copyright © 2012 by ASME.

An experimental study of loss sources in a fan operating with continuous inlet stagnation pressure distortion

The viability of boundary layer ingesting (BLI) engines for future aircraft propulsion is dependent on the ability to design robust, efficient engine fan systems for operation with continuously distorted inlet flow. A key step in this process is to develop an understanding of the specific mechanisms by which an inlet distortion affects the performance of a fan stage. In this paper, detailed full-annulus experimental measurements of the flow field within a low-speed fan stage operating with a continuous 60 deg inlet stagnation pressure distortion are presented. These results are used to describe the three-dimensional fluid mechanics governing the interaction between the fan and the distortion and to make a quantitative assessment of the impact on loss generation within the fan. A 5.3 percentage point reduction in stage total-to-total efficiency is observed as a result of the inlet distortion. The reduction in performance is shown to be dominated by increased loss generation in the rotor due to off-design incidence values at its leading edge, an effect that occurs throughout the annulus despite the localized nature of the inlet distortion. Increased loss in the stator row is also observed due to flow separations that are shown to be caused by whirl angle distortion at rotor exit. By addressing these losses, it should be possible to achieve improved efficiency in BLI fan systems. © 2013 by ASME.