Showing papers by "Richard H. Middleton published in 2015"

Disturbance rejection via control by interconnection of port-Hamiltonian systems

Abstract: In this paper we present a new result on rejection of unmatched external disturbances on port-Hamiltonian systems using Control by Interconnection (CbI). The PHS structure is used to design a controller that rejects unmatched constant disturbances from non-passive outputs. In the PHS framework, the disturbance rejection problem has been addressed adding integral action and using a change of coordinates. In our approach, we avoid a change of coordinates keeping the original state vector, which contains variables with physical interpretation. The methodology proposed in this paper is illustrated on an electrical circuit and on a permanent magnet synchronous motor. Simulation of the later example shows the performance of the control design.

${\cal H}_{\infty}$ and ${\cal H}_{2}$ Norms of 2-D Mixed Continuous-Discrete-Time Systems via Rationally-Dependent Complex Lyapunov Functions

Abstract: This paper addresses the problem of determining the ${\cal H}_{\infty}$ and ${\cal H}_{2}$ norms of 2-D mixed continuous-discrete-time systems The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs) The second contribution is to show that the upper bounds provided are nonconservative by using Lyapunov functions in the chosen class with sufficiently large degree The third contribution is to provide conditions for establishing the tightness of the upper bounds The fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient LMI condition for establishing positive semidefiniteness of even Hermitian matrix polynomials This result is also exploited to derive an improved necessary and sufficient LMI condition for establishing exponential stability of 2-D mixed continuous-discrete-time systems Some numerical examples illustrate the proposed approach It is worth remarking that nonconservative LMI methods for determining the ${\cal H}_{\infty}$ and ${\cal H}_{2}$ norms of 2-D mixed continuous-discrete-time systems have not been proposed yet in the literature

Planning Models to Optimize the Agri-Fresh Food Supply Chain for Loss Minimization: A Review

Abstract: This article aims to present a comprehensive and structured review on recent studies in the field of agribusiness planning models, aiming to optimize agri-fresh food supply chain, with a focus on loss minimization in the fruits and vegetables supply chains. The studies are classified according to six research streams, namely modeling approaches, functional area (decision variables), objective functions, solution approaches, product type/country, and case study. From the literature, it is concluded that the importance of food loss minimization is increasing. However, in most of the reviewed papers, food loss minimization is considered as a secondary scope with the main scope of cost decrease or profit increase. This article shows directions and opportunities to researchers and practitioners trying to identify the existing state of the art, gaps in current research, and future studies on the topic.

Distributed Load Management Using Additive Increase Multiplicative Decrease Based Techniques

Abstract: Due to the expected increase in penetration levels of Plug-in Electric Vehicles (PEVs), the demand on the distribution power grid is expected to rise significantly during PEV charging. However, as PEV charging in many cases may not be time critical, they are suitable for load management tasks where the power consumption of PEVs is controlled to support the grid. Additionally, PEVs may also be enabled to inject power into the grid to lower peak demand or counteract the influence of intermittent renewable energy generation, such as that produced by solar photovoltaic panels. Further, PEV active rectifiers can be used to balance reactive power in a local area if required, to reduce the necessity for long distance transport of reactive power. To achieve these objectives, we adapt a known distributed algorithm, Additive Increase Multiplicative Decrease, to control both the active and reactive power consumption and injection. Here, we present this algorithm in a unified framework and illustrate the flexibility of the algorithm to accommodate different user objectives. We illustrate this with three scenarios, including a domestic scenario and a workplace scenario. In these scenarios the various objectives allow us to define a type of “fairness” for how the PEVs should adapt their power consumption, i.e. equal charging rates, or charging rates based on energy requirements. We then validate the algorithms by simulations of a simple radial test network. The simulations presented use the power simulation tool OpenDSS interlinked with MATLAB.

On the modified AIMD algorithm for distributed resource management with saturation of each user's share

Abstract: Recently the additive increase multiplicative decrease (AIMD) algorithm has been applied in fields other than congestion control in communications networks. A major attribute of these new applications is that the share of each user is bounded. Simulations suggest that AIMD performs well, even in the case of individual constraints on each user. In this paper, we provide a formal proof of exponential convergence to a unique fixed-point for the AIMD algorithm under individual user constraints.

Beyond synchronization: String instability in coupled harmonic oscillator systems

Abstract: Summary In this paper, we consider the problem of disturbance response and error amplification for a simple system of coupled harmonic oscillators. We first suppose that identical oscillators are connected in a string in which each oscillator attempts to track its predecessor by using the same control law that depends on the relative position information from its immediate predecessor. Such an oscillator string is called a homogeneous oscillator string with predecessor-following architecture. Motivated by terminology from the problem of vehicle platooning, we say that the synchronized oscillator system is string unstable if the effect of a disturbance to the lead oscillator is amplified as it propagates along the string. With the use of a new Bode-like integral relation that must be satisfied by the complementary sensitivity function, we provide sufficient conditions for string instability. The sufficient conditions show that any string of oscillators that satisfies certain time domain performance specifications and bandwidth limitations must necessarily be string unstable. We further introduce a concept of time headway for the oscillator system and extend our analysis of string instability to consider the heterogeneous oscillator string and a more general communication range. Copyright © 2014 John Wiley & Sons, Ltd.

Consensus of a class of second-order nonlinear heterogeneous multi-agent systems with uniform time delay

Abstract: In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, stability conditions and solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities (LMIs) apart from a small number of scalar parameters that appear nonlinearly. The effectiveness of the proposed control protocol is illustrated by numerical examples.

Static feedback design for 2D mixed continuous-discrete-time systems via LMIs

Abstract: This paper addresses the problem of designing static feedback controllers for 2D mixed continuous-discrete-time systems via linear matrix inequalities (LMIs). It is shown that a necessary and sufficient condition can be obtained by solving two LMI problems. The first LMI problem aims at determining a polynomial whose positivity domain corresponds to stabilizing controllers. The second LMI problem aims at identifying one controller in such a domain. The condition is sufficient for any size of the LMI problems, and is necessary for a sufficiently large one. Some numerical examples illustrate the proposed methodology.

AIMD in a discrete time implementation or with a non-constant shared resource

Abstract: The additive increase multiplicative decrease (AIMD) algorithm, that is commonly used for congestion avoidance in communication networks, has recently been suggested in other fields such as load management in electric power networks. As for congestion avoidance, in such systems a large number of agents are required to share a given resource. In recent work by Shorten, Wirth and Leith on congestion control in networking a stochastic model has been developed to analyse AIMD algorithms. However, the analysis assumes a continuous implementation of the algorithm and a constant available resource. These assumptions are no longer useful if the AIMD algorithm is applied in fields such as load management in electric power networks, where a discrete implementation is often required, and the available resource shared may be inherently variable. In this paper we develop a disturbed AIMD model based on the model introduced by Shorten et al. that includes discrete time implementation and time varying resource availability. Further, we use that model to bound the influence of these disturbances, caused by either a discrete implementation or small variations in the available resource.