A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems

A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization

Attenuation of Persistent L∞-Bounded Disturbances for Nonlinear Systems

A version of nonlinear generalization of the L1-control problem, which deals with the attenuation of persistent bounded disturbances in L∞-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the L1-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. The concepts from viability theory, nonsmooth analysis, and set-valued analysis play important roles. In addition, the relation between the L1-control of a continuous-time system and the l1-control of its Euler approximated discrete-time systems is established

Hydrogen Peroxide Wound Irrigation in Orthopaedic Surgery.

As the burden of deep hardware infections continues to rise in orthopaedics, there is increasing interest in strategies for more effective debridement of colonized tissues and biofilm. Hydrogen peroxide has been used medically for almost a century, but its applications in orthopaedic surgery have yet to be fully determined. The basic science and clinical research on the antiseptic efficacy of hydrogen peroxide have demonstrated its efficacy against bacteria, and it has demonstrated potential synergy with other irrigation solutions such as chlorhexidine and povidone-iodine. While hydrogen peroxide is effective in infection reduction, there are concerns with wound healing, cytotoxicity, and embolic phenomena, and we recommend against hydrogen peroxide usage in the treatment of partial knee replacements, hemiarthroplasties, or native joints. Additionally, due to the potential for oxygen gas formation, hydrogen peroxide should not be used in cases of dural compromise, when pressurizing medullary canals, or when irrigating smaller closed spaces to avoid the possibility of air embolism. Finally, we present our protocol for irrigation and debridement and exchange of modular components in total joint arthroplasty, incorporating hydrogen peroxide in combination with povidone-iodine and chlorhexidine

Adaptive ℋ∞-control for nonlinear systems: a dissipation theoretical approach

The adaptive ℋ∞-control problem for parameter-dependent nonlinear systems with full information feedback is considered. The techniques from dissipation theory as well as the vector and parameter projection methods are used to derive the adaptive ℋ∞-control laws. Both of the projection techniques are rigorously treated. The adaptive robust stabilization for nonlinear systems with ℒ2-gain hounded uncertainties is investigated

H∞ Control of Nonlinear Systems: A Class of Controllers

The standard state space solutions to the H∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear H∞-controllers are parameterized as nonlinear fractional transformations on contractive, stable free nonlinear parameters. As in the linear case, the H∞ control problem is solved by its reduction to four simpler special state space problems, together with a separation argument. Another byproduct of this approach is that the sufficient conditions for H∞ control problem to be solved are also derived with this machinery. The solvability for nonlinear H∞-control problem requires positive definite solutions to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy an additional coupling condition. An illustrative example, which deals with a passive plant, is given at the end

Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background

In this letter, via the Darboux transformation method we construct new analytic soliton solutions for the Sasa-Satsuma equation which describes the femtosecond pulses propagation in a monomode fiber. We reveal that two different types of femtosecond solitons, i.e., the anti-dark (AD) and Mexican-hat (MH) solitons, can form on a continuous wave (CW) background, and numerically study their stability under small initial perturbations. Different from the common bright and dark solitons, the AD and MH solitons can exhibit both the resonant and elastic interactions, as well as various partially/completely inelastic interactions which are composed of such two fundamental interactions. In addition, we find that the energy exchange between some interacting soliton and the CW background may lead to one AD soliton changing into an MH one, or one MH soliton into an AD one.Comment: 12 pages, 6 figure

ℋ∞ control of nonlinear systems via output feedback: controller parameterization

The standard state space solutions to the ℋ∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) ℋ∞ controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the ℋ∞ control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for ℋ∞-control problem to be locally solved are also derived with this machinery

H∞ control of nonlinear systems: a convex characterization

The nonlinear H∞-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to H∞-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed

Experimental and computational study of two-phase slug flow

This thesis presents a computational and experimental investigation of horizontal gas-liquid two-phase slug flow. The overall aim of the present project was to carry out analytical and computational studies to model the processes of slug initiation, growth and collapse in horizontal pipes. The literature of two-phase flow, with a focus on slug flow, is reviewed. A “Benchmark exercise” of predicting the horizontal two-phase slug flow on the WASP (Water, Air, Sand and Petroleum) facility was set up for CFD simulations with the aim of investigating the capability of CFD codes in the prediction of slug flow characteristics in large scale pipe (78 mm ID, 37 m long). Six CFD codes (TRIOMPH, LedaFlow, STAR-CD, TransAT, FLUENT and CFX) were participated in this exercise. The complex nature of the slug flow mechanism and the relatively large-scale of the associated modelling domain contribute to the challenges of this CFD exercise; this is particularly challenging for three-dimensional simulations. It has proven difficult to carry out direct comparisons between the performances of the various codes; this is due to the difference in the assumptions and approximations made in each case. Successive slugging was captured by most of the CFD codes, apart from CFX in which the flow was remaining stratified. In terms of flow characteristics, comparison against the measurements was mainly focused on the distribution of slug frequency at various locations. Satisfactory agreement was obtained by the 1D code TRIOMPH, whereas the rest of the codes were failed to reproduce the observed trend of slug frequency distribution. The ability of the TRIOMPH code in the prediction of horizontal slug flow is limited in a restrain region, where the two-fluid equations employed in the code has to be well-posed, therefore a validation case study was examined. For a well-posed system, a unique solution can be obtained, whereas for an ill-posed system, the solution would become mesh dependent. However, the lack of unique solution of the ill-posed case can be altered by applying unsteady inlet condition prescribed in terms of a train of slugs, which can be generated by an alternative code namely slug-tracking code. CFD prediction of horizontal slug flow in a channel with rectangular cross-section (100 mm x 30 mm x 8000 mm) was systematically studied using STAR-CCM+. The experimental data was provided by Forschungszentrum Rossendorf (FZD) from Germany. Mesh sensitivity and parametric study were conducted to determine the settings that optimise accuracy and stability. The polyhedral mesh was found to give a fast and better convergence of the numerical solutions. A sufficient small grid size is important in order to resolve the velocity gradient throughout the two fluids. The onset of interfacial instability, wave growth, and slug generation processes were captured in the simulation. However, the predicted slug initiation site was shifted further downstream than the actual site observed in the experiment, leading to the discrepancy in the prediction of the flow characteristics. Experimental studies on slug initiation and their subsequent development were carried out on the LOWPRSS (Low Pressure) facility at Imperial College London. The motion of the slug is followed using high-speed imaging and conductivity probes for air-oil and air-water systems, respectively. The slug frequency results demonstrate that rapid initiation events occur near the inlet region, and the slug frequency exhibits a maximum at intermediate axial distances before eventually reaching an approximately constant value at sufficiently large distances downstream of the inlet. Particular attention was given to the slug initiation mechanism observed using the LOWPRESS facility. Together with a set of air-water slug flow data obtained on the WASP facility, the influence of inlet geometry was examined. It was shown that the inlet geometry significantly influences slug initiation; however, the effect of inlet geometry on the slug development reduces along the pipe length. Beyond a certain distance, slug frequency approaches a constant value invariant with inlet geometry.Open Acces