Settling-time improvement in global convergence lagrangian networks

In this brief, a modification of Lagrangian networks given in (Xia Y., 2003) is presented. This modification improves the settling time of the convergence of Lagrangian networks to a stationary point; which is the optimal solution to the nonlinear convex programming problem with linear equality constraints. This is important because, in many real-time applications where Lagrangian networks are used to find an optimal solution, such as in signal and image processing, this settling time is interpreted as the processing time. Simulation results applied to a quadratic optimization problem show that settling time is improved from about to 2000 to 20 seconds. Lyapunov theory was used to obtain our main result.Postprint (published version

Continuous-time Proportional-Integral Distributed Optimization for Networked Systems

In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimization. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimization with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimization method. Furthermore, we establish convergence using Lyapunov stability techniques and utilizing properties from the network structure of the multi-agent system.Comment: 23 Pages, submission to Journal of Control and Decision, under review. Takes comments from previous review process into account. Reasons for a continuous approach are given and minor technical details are remedied. Largest revision is reformatting for the Journal of Control and Decisio

Design and Implementation of Model Predictive Control Strategies for Improved Power Plant Cycling

Design and Implementation of Model Predictive Control Strategies for Improved Power Plant Cycling Xin He With the increasing focus on renewable energy sources, traditional power plants such as coal-fired power plants will have to cycle their load to accommodate the penetration of renewables into the power grid. Significant overshooting and oscillatory performance may occur during cycling operations if classical feedback control strategies are employed for plantwide control. To minimize the impact when power plants are operating away from their designed conditions, model-based optimal control strategies would need to be developed for improved power plant performance during cycling. In this thesis, model predictive control (MPC) strategies are designed and implemented for improved power plant cycling. The MPC strategies addressed correspond to a dynamic matrix control (DMC)-based linear MPC, a classical sequential quadratic programming (SQP)-based nonlinear MPC, a direct transcription-based nonlinear MPC and a proposed modified SQP-based nonlinear MPC. The proposed modified SQP algorithm is based on the backtracking line search framework, which employs a group of relaxed step acceptance conditions for faster convergence. The numerical results for motivating examples, which are selected from literature problem sets, served as proof of concept to verify that the proposed modified SQP has the potential for implementation on high-dimensional systems. To illustrate the tracking performance and computational efficiency of the developed MPC strategies, three processes of different dimensionalities are addressed. The first process is an integrated gasification combined cycling power plant with a water-gas shift membrane reactor (IGCC-MR), which is represented by a first-principles and simplified systems-level nonlinear model in MATLAB. For this application, a setpoint tracking scenario simulating a step increase in power demand, a disturbance rejection scenario simulating a coal feed quality change, and a trajectory tracking scenario simulating a wind power penetration into the power grid are presented. The second application is an aqueous monoethanolamine (MEA)-based carbon capture process as part of a supercritical pulverized coal-fired (SCPC) power plant, whose model is built in Aspen Plus Dynamics. For this system, disturbance rejection scenarios considering a ramp decrease in the flue gas flow rate as well as wind power penetration, and a scenario considering a combination of disturbance rejection and setpoint tracking are addressed. The third process is the entire SCPC power plant with MEA-based carbon capture (SCPC-MEA), which simulation is also built in Aspen Plus Dynamics. Trajectory tracking and disturbance rejection scenarios associated with wind and solar power penetrations are presented for this process. The MPC implementations on the three processes for the different scenarios addressed are successful. The closed-loop results show that the proposed modified SQP-based nonlinear MPC enhances the tracking performance by up to 96% when compared to the DMC-based linear MPC in terms of integral squared error results. The novel approach also improves the MPC computational efficiency by 20% when compared to classical SQP-based and direct transcription-based nonlinear MPCs

The Optimisation of Hydrodynamic Vortex Separators for Removal of Solids from Wastewater, using the Continuous Adjoint Method with Topology Modification

Hydrodynamic vortex separators (HDVSs) are used in wastewater treatment to separate solids from wastewater. The aim of this research is to devise a CFD-based methodology that optimises their performance through modification of their design. A validation study is performed to assess whether OpenFOAM can be used to reliably model the flow of water in an HDVS. The results of the simulations are compared with experimental readings, showing a good fit when the appropriate boundary layer height and turbulence model are used. The continuous adjoint method is employed to derive the adjoint equations, associated with the drift flux equations used to model the flow of wastewater. They are specialised to the typical boundary conditions of ducted flows and are coded using OpenFOAM. An optimal design is found for boundary conditions, corresponding to typical values used in practice, and is shown to improve the performance of a simplified initial design by 40%. This optimal design is subsequently subjected to a different hydraulic loading rate and dispersed-phase volume fraction at the inlet, to assess the performance variation in these circumstances. Though the optimal design removes all the solids when the dispersed-phase fraction is reduced at the inlet, initial results suggest that the design is sensitive to hydraulic loading rate and further tests are recommended before drawing more explicit conclusions. This is the first time the adjoint drift flux equations have been derived. It is also the first time they have been coded and applied to an HDVS to optimise its performance. The methodology developed in this thesis could be applied to any device that separates solids from liquid or two immiscible liquids, in order to optimise its performance.EPSRCHydro Internationa

Design and Stability of Load-Side Primary Frequency Control in Power Systems

We present a systematic method to design ubiquitous continuous fast-acting distributed load control for primary frequency regulation in power networks, by formulating an optimal load control (OLC) problem where the objective is to minimize the aggregate cost of tracking an operating point subject to power balance over the network. We prove that the swing dynamics and the branch power flows, coupled with frequency-based load control, serve as a distributed primal-dual algorithm to solve OLC. We establish the global asymptotic stability of a multimachine network under such type of load-side primary frequency control. These results imply that the local frequency deviations at each bus convey exactly the right information about the global power imbalance for the loads to make individual decisions that turn out to be globally optimal. Simulations confirm that the proposed algorithm can rebalance power and resynchronize bus frequencies after a disturbance with significantly improved transient performance.Comment: 14 pages, 13 figures. To appear in IEEE Transactions on Automatic Contro

Observational Tests and Predictive Stellar Evolution II: Non-standard Models

We examine contributions of second order physical processes to results of stellar evolution calculations amenable to direct observational testing. In the first paper in the series (Young et al. 2001) we established baseline results using only physics which are common to modern stellar evolution codes. In the current paper we establish how much of the discrepancy between observations and baseline models is due to particular elements of new physics. We then consider the impact of the observational uncertainties on the maximum predictive accuracy achievable by a stellar evolution code. The sun is an optimal case because of the precise and abundant observations and the relative simplicity of the underlying stellar physics. The Standard Model is capable of matching the structure of the sun as determined by helioseismology and gross surface observables to better than a percent. Given an initial mass and surface composition within the observational errors, and no additional constraints for which the models can be optimized, it is not possible to predict the sun's current state to better than ~7%. Convectively induced mixing in radiative regions, seen in multidimensional hydrodynamic simulations, dramatically improves the predictions for radii, luminosity, and apsidal motions of eclipsing binaries while simultaneously maintaining consistency with observed light element depletion and turnoff ages in young clusters (Young et al. 2003). Systematic errors in core size for models of massive binaries disappear with more complete mixing physics, and acceptable fits are achieved for all of the binaries without calibration of free parameters. The lack of accurate abundance determinations for binaries is now the main obstacle to improving stellar models using this type of test.Comment: 33 pages, 8 figures, accepted for publication in the Astrophysical Journa