Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.

Moment asymptotic stability of stochastic hybrid delay systems

in this paper we investigate the moment asymptotic stability for the nonlinear stochastic hybrid delay systems. Sufficient criteria on the stabilization and robust stability are also established for linear stochastic hybrid delay systems. Copyright © 2005 IFAC.

Lyapunov's stability and operational margin of grid-connected photovoltaic modules

Analyses of photovoltaic power generation based on Lyapunov's theorems are presented. The characteristics of the photovoltaic module and the power conditioning unit are analyzed in order to establish energy functions that assess the stability of solutions and define safe regions of operation. Furthermore, it is shown that grid-connected photovoltaic modules driven at maximum power may become unstable under normal grid transients. In such cases, stability can be maintained by allowing an operational margin defined as the energy difference between the stable and the unstable solutions of the system. Simulations show that modules cope well with grid transients when a sufficiently large margin is used.

Enhancing the stability of subsonic compressors using casing grooves

Casing grooves are known to increase the stable operating range of axial compressors. The mechanism by which this stability enhancement occurs is poorly understood. This paper develops a better understanding of the behavior of casing grooves through analysis of new data. An experimental parametric study is used to demonstrate the effect of varying the axial location of a single casing groove on the stability and efficiency of the compressor. The effect that the groove has on rotor outflow blockage, blade loading, and the near-casing flow field is then investigated using both experimental and computational methods. It is found that the interaction of the groove with the flow field is different when the groove is positioned forward or aft relative to the blade. The interaction of the groove with the flow in the tip region in both of these positions is presented in detail. Finally, the implications of these findings for the design of casing grooves of different depths are discussed. © 2011 American Society of Mechanical Engineers.

Stability enhancement by casing grooves: The importance of stall inception mechanism and solidity

This paper concerns the optimisation of casing grooves and the important influence of stall inception mechanism on groove performance. Installing casing grooves is a well known technique for improving the stable operating range of a compressor, but the wide-spread use of grooves is restricted by the loss of efficiency and flow capacity. In this paper, laboratory tests are used to examine the conditions under which casing treatment can be used to greatest effect. The use of a single casing groove was investigated in a recently published companion paper. The current work extends this to multiple-groove treatments and considers their performance in relation to stall inception mechanisms. Here it is shown that the stall margin gain from multiple grooves is less than the sum of the gains if the grooves were used individually. By contrast, the loss of efficiency is additive as the number of grooves increases. It is then shown that casing grooves give the greatest stall margin improvement when used in a compressor which exhibits spike-type stall inception, while modal activity before stall can dramatically reduce the effectiveness of the grooves. This finding highlights the importance of being able to predict the stall inception mechanism which might occur in a given compressor before and after grooves are added. Some published prediction techniques are therefore examined, but found wanting. Lastly, it is shown that casing grooves can, in some cases, be used to remove rotor blades and produce a more efficient, stable and light-weight rotor. © 2010 by ASME.

Enhancing the stability of subsonic compressors using casing grooves

Casing grooves are known to increase the stable operating range of axial compressors. The mechanism by which this stability enhancement occurs is poorly understood. This paper develops a better understanding of the behaviour of grooves through analysis of new data. An experimental parametric study is used to demonstrate the effect of varying the axial location of a single casing groove on the stability and efficiency of the compressor. The effect that the groove has on rotor outflow blockage, blade loading and the near-casing flow field is then studied using both experimental and computational methods. It is found that the interaction of the groove with the flow field is different when the groove is positioned forward or aft relative to the blade. The interaction of the groove with the flow in the tip region in both of these positions is presented in detail. Finally, the implications of these findings for the design of casing grooves of different depths are discussed. Copyright © 2009 Rolls-Royce plc.

On the stability of a rod adhering to a rigid surface: Shear-induced stable adhesion and the instability of peeling

Using variational methods, we establish conditions for the nonlinear stability of adhesive states between an elastica and a rigid halfspace. The treatment produces coupled criteria for adhesion and buckling instabilities by exploiting classical techniques from Legendre and Jacobi. Three examples that arise in a broad range of engineered systems, from microelectronics to biologically inspired fiber array adhesion, are used to illuminate the stability criteria. The first example illustrates buckling instabilities in adhered rods, while the second shows the instability of a peeling process and the third illustrates the stability of a shear-induced adhesion. The latter examples can also be used to explain how microfiber array adhesives can be activated by shearing and deactivated by peeling. The nonlinear stability criteria developed in this paper are also compared to other treatments. © 2012 Elsevier Ltd. All rights reserved.

Self-regulating casing treatment for axial compressor stability enhancement

The operating range of an axial compressor is often restricted by a safety imposed stall margin. One possible way of regaining operating range is with the application of casing treatment. Of particular interest here is the type of casing treatment which extracts air from a high pressure location in the compressor and re-injects it through discrete loops into the rotor tip region. Existing re-circulation systems have the disadvantage of reducing compressor efficiency at design conditions because worked flow is unnecessarily re-circulated at these operating conditions. Re-circulation is really only needed near stall. This paper proposes a self-regulating casing treatment in which the re-circulated flow is minimized at compressor design conditions and maximized near stall. The self-regulating capability is achieved by taking advantage of changes which occur in the tip clearance velocity and pressure fields as the compressor is throttled toward stall. In the proof-of-concept work reported here, flow is extracted from the high pressure region over the rotor tips and re-injected just upstream of the same blade row. Parametric studies are reported in which the flow extraction and re-injection ports are optimized for location, shape and orientation. The optimized design is shown to compare favorably with a circumferential groove tested in the same compressor. The relationship between stall inception type and casing treatment effectiveness is also investigated. The self-regulating aspect of the new design works well: stall margin improvements from 2.2 to 6.0% are achieved for just 0.25% total air re-circulated near stall and half that near design conditions. The self-regulating capability is achieved by the selective location and orientation of the extraction hole; a simple model is discussed which predicts the optimum axial location. Copyright © 2011 by ASME.

Stability control of a railway vehicle using absolute stiffness and inerters

Work presented in this paper studies the potential of employing inerters -a novel mechanical device used successfully in racing cars- in active suspension configurations with the aim to enhance railway vehicle system performance. The particular element of research in this paper concerns railway wheelset lateral stability control. Controlled torques are applied to the wheelsets using the concept of absolute stiffness. The effects of a reduced set of arbitrary passive structures using springs, dampers and inerters integrated to the active solution are discussed. A multi-objective optimisation problem is defined for tuning the parameters of the proposed configurations. Finally, time domain simulations are assessed for the railway vehicle while negotiating a curved track. A simplification of the design problem for stability is attained with the integration of inerters to the active solutions. © 2012 IEEE.