16 research outputs found
Robust Simulation for Hybrid Systems: Chattering Path Avoidance
The sliding mode approach is recognized as an efficient tool for treating the
chattering behavior in hybrid systems. However, the amplitude of chattering, by
its nature, is proportional to magnitude of discontinuous control. A possible
scenario is that the solution trajectories may successively enter and exit as
well as slide on switching mani-folds of different dimensions. Naturally, this
arises in dynamical systems and control applications whenever there are
multiple discontinuous control variables. The main contribution of this paper
is to provide a robust computational framework for the most general way to
extend a flow map on the intersection of p intersected (n--1)-dimensional
switching manifolds in at least p dimensions. We explore a new formulation to
which we can define unique solutions for such particular behavior in hybrid
systems and investigate its efficient computation/simulation. We illustrate the
concepts with examples throughout the paper.Comment: The 56th Conference on Simulation and Modelling (SIMS 56), Oct 2015,
Link\"oping, Sweden. 2015, Link\"oping University Pres
On the Regularization of Chattering Executions in Real Time Simulation of Hybrid Systems
International audienceIn this paper we present a new method to perform the higher order sliding modes analysis of trajectories of hybrid systems with chattering behavior. This method improves our previous work [AC15] as it modifies numerical simulation algorithms to make them compute the higher order terms of the normal unit vectors of the systems dynamics whenever the first order sliding mode theory cannot be applied. Such modification does not affect the generality of our previous contribution in [AC15]. Our algorithm is general enough to handle both chattering on a single (nâ1) switching manifold (i.e. chattering between two dynamics) as well as chattering on the intersection of finitely many intersected (nâ1) switching manifolds. In this last case, we show by a special hierarchical application of convex combinations, that unique solutions can be found in general cases when the switching function takes the form of finitely many intersecting manifolds so that an efficient numerical treatment of the sliding motion constrained on the entire discontinuity region (including the switching intersection) is guaranteed. Illustrations of the techniques developed in this article are given on representative examples
Microgrid energy management system for smart home using multi-agent system
This paper proposes a multi-agent system for energy management in a microgrid for smart home applications, the microgrid comprises a photovoltaic source, battery energy storage, electrical loads, and an energy management system (EMS) based on smart agents. The microgrid can be connected to the grid or operating in island mode. All distributed sources are implemented using MATLAB/Simulink to simulate a dynamic model of each electrical component. The agent proposed can interact with each other to find the best strategy for energy management using the java agent development framework (JADE) simulator. Furthermore, the proposed agent framework is also validated through a different case study, the efficiency of the proposed approach to schedule local resources and energy management for microgrid is analyzed. The simulation results verify the efficacy of the proposed approach using Simulink/JADE co-simulation
Fuzzy logic-based controller of the bidirectional direct current to direct current converter in microgrid
Microgrids are small-scale power networks that include renewable energy sources, load, energy storage systems, and energy management systems (EMS). Lithium-ion batteries are the most used battery for energy storage in microgrids due to their advantages over other types of batteries. However, to protect the battery from the explosion and to manage to charge and discharge based on state-of-charge (SoC) value, this type of battery requires the use of an energy management system. The main objective of this paper is to propose an intelligent control strategy for energy management in the microgrid to control the charge and discharge of Li-ion batteries to stabilize the system and reduce the cost of electricity due to the high cost of grid electricity. The proposed technique is based on a fuzzy logic controller (FLC) for voltage control. The FLC is based on the measured voltage of the direct current (DC) bus and the fixed reference voltage to generate buck/boost converter signal control. The proposed technique has been simulated and tested using MATLAB/Simulink software which illustrates the tracking of desired power and DC bus voltage regulation. The simulation results confirm that the proposed systems can diminish the deviations of the system's voltage
Microgrid energy management and monitoring systems: A comprehensive review
Microgrid (MG) technologies offer users attractive characteristics such as enhanced power quality, stability, sustainability, and environmentally friendly energy through a control and Energy Management System (EMS). Microgrids are enabled by integrating such distributed energy sources into the utility grid. The microgrid concept is proposed to create a self-contained system composed of distributed energy resources capable of operating in an isolated mode during grid disruptions. With the Internet of Things (IoT) daily technological advancements and updates, intelligent microgrids, the critical components of the future smart grid, are integrating an increasing number of IoT architectures and technologies for applications aimed at developing, controlling, monitoring, and protecting microgrids. Microgrids are composed of various distributed generators (DG), which may include renewable and non-renewable energy sources. As a result, a proper control strategy and monitoring system must guarantee that MG power is transferred efficiently to sensitive loads and the primary grid. This paper evaluates MG control strategies in detail and classifies them according to their level of protection, energy conversion, integration, benefits, and drawbacks. This paper also shows the role of the IoT and monitoring systems for energy management and data analysis in the microgrid. Additionally, this analysis highlights numerous elements, obstacles, and issues regarding the long-term development of MG control technologies in next-generation intelligent grid applications. This paper can be used as a reference for all new microgrid energy management and monitoring research
Simulation AccĂ©lĂ©rĂ©e des SystĂšmes Hybrides : mĂ©thode combinant analyse statique et analyse Ă lâexĂ©cution.
The theme of this dissertation is to deal with Zeno behaviour of hybrid systems from a simulation perspective.Hybrid systems can be defined as dynamical systems in which continuous and discrete dynamics interact with each other. Such systems exist in a large number of technological systems where the physical continuous evolution of the system is combined with embedded control actions. The mathematical models of hybrid systems consist typically of continuous time dynamics usually described by differential equations describing the continuous behaviour of the system, and discrete event dynamics such as finite state machines (synchronous or data-flow programs) that describe the discrete behaviour of the system.However, due to the complex interaction between the continuous and discrete dynamics, designers should pay special attention when modelling hybrid systems. In fact, realistic models of hybrid systems almost always necessitate part of the hybrid systemâs physical behaviour to be abstracted by means of âideal equationsâ such as reset and conditional constraints that typically lead to discontinuities in physical signals. The term modelling abstraction is thus designated to any mechanism that enables concrete physical behaviour to be âhiddenâ by considering idealized models. Intuitively, because of such abstraction, the model jumps over instants corresponding to the violation of abstraction mechanisms. Such modelling abstraction mechanism may result in hybrid models that exhibit Zeno behaviour. Formally, we define Zeno behaviour as an infinite sequence of discrete events occurring in a finite amount of time. Basically, the presence of Zeno behaviour indicates that the hybrid systemâs model incompletely describes the real physical behaviour of the system being modelled. If we consider the standard semantics of executions of hybrid systems models, the problem can best be described as follows: the physical system keeps evolving continuously beyond a certain point, but the modelâs continuous evolution is undefined beyond that point, because of the infinity of the discrete transitions or mode switchings. Such inherent limitation of the hybrid system model makes the solution of the system reaches a (Zeno limit) point in time at which the model is no longer valid. This is due the fact that the modelling abstraction mechanism incompletely describes the complex interaction between the continuous and discrete dynamics of the hybrid system being modelled. That is, Zeno behaviour can be seen as a modelling artifact that can never occur in reality.Analytically, we distinguish between two different types of Zeno behaviour in hybrid systems: i) chattering-Zeno, and ii) genuinely-Zeno. In models that exhibit chattering- Zeno, the system infinitely moves back and forth between modes in a discrete fashion with infinitesimal time spent between the successive mode switchings. Any Zeno behaviour that is not chattering-Zeno can be classified as genuinely-Zeno. In this dissertation we focus on both chattering-Zeno and a particular type of genuinely-Zeno which we call geometric-Zeno. In models that exhibit geometric-Zeno, an accumulation of an infinite number of mode switchings occurs in finite time. Geometric-Zeno behaviour leads the solution of the system to converge to a Zeno limit point according to a geometric series. Roughly speaking, in geometric-Zeno models discrete events occur at an increasingly smaller distance in time, converging against a limit point.Zeno behaviour is highly challenging from a simulation perspective. In fact, although chattering-Zeno and geometric-Zeno are analytically different, the effect of these two types of Zeno during the numerical simulation is similar: the simulation process effectively stalls, halts and terminates with an error message, or becomes numerically incorrect and produces faulty results, as infinitely many discrete transitions would need to be simulated.This dissertation takes the perspective that models of hybrid systems are executable programs written in programming languages having a hybrid system semantics. Basically, defining a proper hybrid semantic model is the first step of developing a simulation framework for hybrid systems. This step is mandatory even before designing the language or the simulator. The development of a hybrid simulation framework typically include the following steps:1. Properly define a hybrid semantic model that can account for the expected properties of the hybrid systems under simulation.2. Design and develop a simulator that could approximate the model dynamics conforming to the defined hybrid semantic model.3. Design a language capable of expressing all models elements and components conforming to the hybrid semantic model. Type-checking must be included in this step to prove statically the semantic validity of the simulated models.4. Design a compiler for the language. The compiler should be capable of performing static checks of models and also rejecting models that are invalid.Many modelling and simulation tools for hybrid systems have been developed in the past years. They can be classified into two categories: those who put special attention on defining models rigorously, such as for instance SpaceEx, Ptolemy (based on the super-dense time semantics in), and ZeÌlus (based on the non-standard semantics); and those who use informal approach for model definition such as Simulink, Modelica language and its associated tools. All these modelling and simulation tools share the same approach of hybrid model execution alternating between continuous evolution and sequences of discrete switchings as defined by the notion of hybrid automata. For all of these tools, the operational semantics of continuous dynamics (differential equations) is not included in the core semantic model: numerical solvers execute the continuous behaviour by advancing time and computing the values of physical continuous variables. None of the above tools have a Zeno-free semantic model. They all rely on analyzing the solver output at each integration time step, with the solver behaviour at the Zeno-limit point being usually unspecified.In this dissertation we focus on the first two steps above. In particular, we focus on proposing a rigorous Zeno-free computational framework for hybrid semantic model design, and how this Zeno-free computational framework can be implemented in the design of hybrid systems simulators.The first part of our contribution is to propose non-standard semantics for Zeno executions of hybrid systems models. This is based on interpreting Zeno executions in a non-standard densely ordered hybrid time domain. The advantages of using non- standard semantics in the analysis of Zeno behaviour is that it allows for solutions of Zeno hybrid models to be well-defined beyond the Zeno limit points, as well as representing the complex interaction between continuous and discrete dynamics in a concrete way:1. The continuous dynamics of the hybrid system is reduced to the recurrence equation that represents the infinite iteration of infinitesimal discrete changes with infinitesimal duration. Therefore, we can handle the hybrid dynamics based only on fully discrete paradigm.2. The representation of dynamics based on non-standard analysis is complete and the exact limit point of discrete change, like chattering-Zeno and geometric-Zeno limit points, can be handled.The second part of our contribution is to propose a rigorous Zeno-free computational framework for hybrid semantic model design and implementation. The key idea in our proposed computational framework is to perform Zeno detection and avoidance by using behavioral analysis of the system, instead of only considering zero-crossings in a hybrid time domain. The behavioral analysis technique we propose for treating Zeno is based on analyzing both types of Zeno systematically. We provide formal conditions on when the simulated models of hybrid systems display chattering-Zeno and geometric-Zeno executions. We also provide methods for carrying solutions beyond Zeno. The issue of existence and uniqueness of solution beyond Zeno is also studied in this dissertation. Our Zeno-free computational framework allows sacrificing the notion of Zeno-freeness as: i) the decision on whether or not the Zeno limiting state is chattering-Zeno or geometric-Zeno is based on formal conditions explicitly defined and provided to the hybrid simulatorâs solver, and ii) the correct notion of solution beyond Zeno is well defined and established in our framework.Our approach also supports mixing compile-time transformations of hybrid programs (i.e. generating what is necessary for Zeno detection and avoidance), the decision, in run-time, for the urgent transition from pre-Zeno to post-Zeno state (based on formal conditions for the existence of Zeno), and the computation, in run-time, of the system dynamics beyond Zeno.Examples of hybrid systems with domains, guard sets, vector fields, and reset maps, illustrating the use of the methods proposed in this dissertation, are also provided.Cette thĂšse de doctorat porte sur la modĂ©lisation et la simulation de systĂšmes hybridescomportant des phĂ©nomĂšnes ZĂ©non.Les systĂšmes hybrides peuvent ĂȘtre dĂ©finis comme des systĂšmes dynamiques danslesquels les dynamiques en temps continu et les dynamiques en temps discret inter-agissent les unes avec les autres. De tels systĂšmes existent dans un grand nombredâapplications technologiques oĂč lâĂ©volution de la partie physique du systĂšme, le plussouvent modĂ©lisĂ©e par un systĂšme dynamique en temps continu, est combinĂ©e avec desactions de contrĂŽle intĂ©grĂ©es, modĂ©lisĂ©e par un systĂšme dynamique en temps discret. LesmodĂšles mathĂ©matiques des systĂšmes hybrides consistent gĂ©nĂ©ralement en dynamiquesde temps continu habituellement dĂ©crites par des Ă©quations diffĂ©rentielles qui dĂ©criventle comportement continu du systĂšme, et des dynamiques dâĂ©vĂ©nements discrets telles queles machines Ă Ă©tats finis, qui dĂ©crivent le comportement discret du systĂšme.Cependant, en raison de lâinteraction complexe entre les dynamiques continues etles dynamiques discrĂštes des systĂšmes hybrides, les concepteurs des systĂšmes complexestechnologiques devraient accorder une attention particuliĂšre lors de la modĂ©lisation dessystĂšmes hybrides. En fait, les modĂšles rĂ©alistes de systĂšmes hybrides nĂ©cessitent presquetoujours lâabstraction dâune partie du comportement physique du systĂšme modĂ©lisĂ©.Cette abstraction se fait au moyen dâĂ©quations idĂ©ales telles que la rĂ©-initialisation et lescontraintes conditionnelles qui conduisent gĂ©nĂ©ralement Ă des discontinuitĂ©s dans les sig-naux physiques du modĂšle. Le termeabstraction de modĂ©lisationest donc dĂ©signĂ© pourtout mĂ©canisme qui permet de âcacherâ un comportement physique concret en consid-Ă©rant des modĂšles idĂ©alisĂ©s. Les modĂšles ainsi produits peuvent prĂ©senter des comporte-ments ZĂ©non, câest Ă dire une sĂ©quence infinie dâĂ©vĂ©nements discrets se produisant dansun intervalle de temps fini. Fondamentalement, la prĂ©sence du comportement ZĂ©nonindique que le modĂšle dĂ©crive de maniĂšre incomplĂšte le comportement physique rĂ©el dusystĂšme hybride. Ce comportement peut ĂȘtre considĂ©rĂ© donc comme un problĂšme demodĂ©lisation.Nous distinguons deux types de comportement ZĂ©non dans les systĂšmes hybrides:1) chattering-ZĂ©non, et 2) genuinely-ZĂ©non. Dans les modĂšles qui prĂ©sentent de com-portement chattering-ZĂ©non, le systĂšme Ă©volue de façon infinie entre ses Ă©tats discrets,selon un alternance de transitions de modes et de dynamiques continues diffĂ©rentes Ă une frĂ©quence infinie. Tout comportement ZĂ©non qui nâest pas chattering-ZĂ©non peutĂȘtre classifiĂ© comme un comportement genuinely-ZĂ©non. Dans cette thĂšse nous Ă©tudions,dâune maniĂšre systĂ©matique et analytique, le comportement chattering-ZĂ©non et aussi untype particulier de comportement genuinely-ZĂ©non appelĂ© genuinely-ZĂ©non gĂ©omĂ©trique.Dans les modĂšles qui prĂ©sentent de comportement genuinely-ZĂ©non gĂ©omĂ©trique, une ac-cumulation dâun nombre infini de commutations entre les Ă©tats discrets â du systĂšmehybride â se produit en temps fini. Le comportement genuinely-ZĂ©non gĂ©omĂ©triqueamĂšne la solution du systĂšme Ă converger vers un point limite ZĂ©non selon une sĂ©riegĂ©omĂ©trique, câest Ă dire, dans les modĂšles qui prĂ©sentent de comportement genuinely-ZĂ©non gĂ©omĂ©trique, les Ă©vĂ©nements discrets se produisent Ă une pĂ©riode de plus en plusfaible, convergeant vers une date limite.La simulation des comportements ZĂ©non â des systĂšmes hybrides â pose une dif-ficultĂ© majeure: la simulation devient numĂ©riquement incorrect; le simulateur devientincapable dâavancer la simulation au delĂ du point limite ZĂ©non, Ă cause de lâinfinitĂ© descommutations discrĂštes en temps fini.Dans cette thĂšse, nous considĂ©rons les modĂšles de systĂšmes hybrides comme des pro-grammes exĂ©cutables Ă©crits par des langages de programmation ayant des sĂ©mantiqueshybrides. Fondamentalement, la dĂ©finition dâun modĂšle sĂ©mantique hybride appropriĂ©est la premiĂšre Ă©tape vers un dĂ©veloppement dâun environnement propre de simulationpour les systĂšmes hybrides. Le dĂ©veloppement dâun environnement de simulation hybrideconsiste gĂ©nĂ©ralement Ă suivre les Ă©tapes suivantes:1. DĂ©finir correctement un modĂšle sĂ©mantique hybride, qui peut considĂ©rer les pro-priĂ©tĂ©s de comportement continue/discret des systĂšmes hybrides.2. Concevoir et dĂ©velopper un simulateur capable Ă calculer les dynamiques et lessolutions des modĂšles des systĂšmes hybrides conformĂ©ment au modĂšle sĂ©mantiquehybride dĂ©fini.3. Concevoir et dĂ©velopper un langage de programmation capable dâexprimer tous lesĂ©lĂ©ments et composants des modĂšles hybrides conformĂ©ment au modĂšle sĂ©mantiquehybride dĂ©fini. La vĂ©rification de code doit ĂȘtre incluse dans cette Ă©tape pourprouver de maniĂšre statique la validitĂ© sĂ©mantique des modĂšles simulĂ©s.4. Concevoir et dĂ©velopper un compilateur pour le langage de programmation dĂ©veloppĂ©.Le compilateur devrait ĂȘtre capable dâeffectuer une vĂ©rification statique efficace desmodĂšles, et rejeter les modĂšles invalides.De nombreux outils de modĂ©lisation et de simulation pour les systĂšmes hybrides ont Ă©tĂ©dĂ©veloppĂ©s ces derniĂšres annĂ©es. Ils peuvent ĂȘtre classĂ©s en deux catĂ©gories: ceux quiaccordent une attention particuliĂšre Ă une dĂ©finition rigoureuse des modĂšles, comme parexemple SpaceEx [44], Ptolemy [27], et ZĂ©lus [57], et ceux qui utilisent une approcheinformelle pour la dĂ©finition des modĂšles, comme Simulink1, le langage Modelica [55]et ses outils associĂ©s. Tous ces outils partagent la mĂȘme approche de lâexĂ©cution dumodĂšle hybride alternant entre lâĂ©volution continue et les sĂ©quences de commutationsdiscrĂštes similaire Ă lâapproche dĂ©finie par la notion dâautomate hybride [30]. Pour tousces outils, la sĂ©mantique opĂ©rationnelle de la dynamique continue (Ă©quations diffĂ©ren-tielles) nâest pas incluse dans le modĂšle sĂ©mantique: les solveurs numĂ©riques exĂ©cutentle comportement continu en faisant progresser le temps et en calculant les valeurs desvariables continues physiques. Aucun de ces outils nâa un modĂšle sĂ©mantique qui permetde dĂ©tecter le comportement ZĂ©non et de lâĂ©liminer. Ils comptent tous sur lâanalyse dela sortie du solveur Ă chaque pas dâintĂ©gration numĂ©rique, sans aucun moyen de spĂ©cifierle comportement du solveur au point limite ZĂ©non.Dans cette thĂšse, nous proposons une solution Ă ce problĂšme. En particulier, nousproposons une mĂ©thode combinant un analyse statique et un analyse Ă lâexecution pourdĂ©tecter et Ă©liminer le comportement ZĂ©non lors de la simulation des modĂšles des sys-tĂšmes hybrides. Nous montrons aussi comment notre mĂ©thode peut ĂȘtre utilisĂ©e dans ledĂ©veloppement dâoutils de modĂ©lisation et de simulation qui produisent une simulationcorrecte Ă©liminatoire de comportement ZĂ©non.La premiĂšre partie de notre contribution est destinĂ©e Ă proposer de sĂ©mantiquenon-standard pour les exĂ©cutions ZĂ©non des automates hybrides. Ceci est basĂ© surlâinterprĂ©tation des exĂ©cutions ZĂ©non dans un domaine de temps hybride non-standard.Lâ avantage de lâutilisation de la sĂ©mantique non-standard dans lâanalyse du comporte-ment ZĂ©non câest que lâanalyse non-standard permet aux solutions des modĂšles ayantun comportement ZĂ©non dâĂȘtre bien dĂ©finies au-delĂ des points limites ZĂ©non, ainsi quede reprĂ©senter lâinteraction complexe entre les dynamiques continues et les dynamiquesdiscrĂštes de maniĂšre concrĂšte:1. Les dynamiques continues du systĂšme hybride sont rĂ©duites Ă des Ă©quations rĂ©cur-rentes qui reprĂ©sentent rigoureusement lâitĂ©ration infinie des commutations dis-crĂštes en durĂ©e infinitĂ©simale. Par consĂ©quent, nous pouvons gĂ©rer les dynamiqueshybrides en appuyant seulement sur un paradigme complĂštement discret.2. La reprĂ©sentation non-standard des dynamiques hybrides est complĂšte, qui permetde traiter les points limites ZĂ©non.La deuxiĂšme partie de notre contribution est attribuĂ©e Ă proposer une techniquede calcul Ă©liminatoire de comportement ZĂ©non. LâidĂ©e clĂ© dans notre technique estdâeffectuer la dĂ©tection et lâĂ©limination de comportement ZĂ©non en utilisant lâanalysecomportementale du systĂšme, au lieu de seulement considĂ©rer le nombre des passages Ă zĂ©ro, comme ce qui est le cas dĂ©sormais dans tous les outils de modĂ©lisation et de simu-lation dĂ©veloppĂ©s pour les systĂšmes hybrides. La technique dâanalyse comportementaleque nous proposons pour le traitement de comportement ZĂ©non est basĂ©e sur un anal-yse systĂ©matique des deux types de ZĂ©non. Nous proposons des conditions formellespour bien distinguer si les modĂšles hybrides simulĂ©s prĂ©sentent ou non de comporte-ment ZĂ©non. Nous proposons Ă©galement des mĂ©thodes pour une dĂ©finition correcte dessolutions au delĂ des points limites ZĂ©non. La question de lâexistence et lâunicitĂ© de lasolution au delĂ du point limite ZĂ©non est Ă©galement bien Ă©tudiĂ©e dans cette thĂšse. NosmĂ©thodes proposĂ©es dans cette thĂšse permettent de sacrifier la notion de ZĂ©non-free: 1)la dĂ©cision algorithmique est basĂ© sur des conditions formelles explicitement dĂ©finies etfournies au simulateur hybride, et 2) la notion correcte de solution au delĂ du pointlimite ZĂ©non est bien dĂ©finie et Ă©tablie dans notre technique proposĂ©e.Des exemples de systĂšmes hybrides, illustrant lâutilisation des mĂ©thodes proposĂ©esdans cette thĂšse, sont Ă©galement prĂ©sentĂ©s
Hybrid Modelling and Sliding Mode Control of Semi-Active Suspension Systems for Both Ride Comfort and Road-Holding
Rigorous model-based design and control for intelligent vehicle suspension systems play an important role in providing better driving characteristics such as passenger comfort and road-holding capability. This paper investigates a new technique for modelling, simulation and control of semi-active suspension systems supporting both ride comfort and road-holding driving characteristics and implements the technique in accordance with the functional mock-up interface standard FMI 2.0. Firstly, we provide a control-oriented hybrid model of a quarter car semi-active suspension system. The resulting quarter car hybrid model is used to develop a sliding mode controller that supports both ride comfort and road-holding capability. Both the hybrid model and controller are then implemented conforming to the functional mock-up interface standard FMI 2.0. The aim of the FMI-based implementation is to serve as a portable test bench for control applications of vehicle suspension systems. It fully supports the exchange of the suspension system components as functional mock-up units (FMUs) among different modelling and simulation platforms, which allows re-usability and facilitates the interoperation and integration of the suspension system components with embedded software components. The concepts are validated with simulation results throughout the paper
Hybrid Sliding Mode Control of Full-Car Semi-Active Suspension Systems
With the advance in technology in driving vehicles, there is currently more emphasis on developing advanced control systems for better road handling stability and ride comfort. However, one of the challenging problems in the design and implementation of intelligent suspension systems is that there is currently no solution supporting the export of generic suspension models and control components for integration into embedded Electronic Control Units (ECUs). This significantly limits the usage of embedded suspension components in automotive production code software as it requires very high efforts in implementation, manual testing, and fulfilling coding requirements. This paper introduces a new dynamic model of full-car suspension system with semi-active suspension behavior and provides a hybrid sliding mode approach for control of full-car suspension dynamics such that the road handling stability and ride comfort characteristics are ensured. The semi-active suspension model and the hybrid sliding mode controller are implemented as Functional Mock-Up Units (FMUs) conforming to the Functional Mock-Up Interface for embedded systems (eFMI) and are calibrated with a set experimental tests using a 1/5 Soben-car test bench. The methods and prototype implementation proposed in this paper allow both model and controller re-usability and provide a generic way of integrating models and control software into embedded ECUs
Hybrid Modelling and Sliding Mode Control of Semi-Active Suspension Systems for Both Ride Comfort and Road-Holding
Chattering-Free Simulation of Hybrid Dynamical Systems with the Functional Mock-Up Interface 2.0
International audienceThe numerical simulation of non-smooth hybrid systems exhibiting chattering behavior requires high computational costs. In the worst case, the simulation appears to come to a halt, since infinitely many discrete transitions would need to be simulated. In this paper we present an FMI-based framework and prototypical implementation for robust and reliable detection and elimination âOn the Flyâ of chattering behavior in run-time simulation of non-smooth hybrid systems. The main benefit of the developed framework is that it establishes solvability requirements and theorems for simulating hybrid systems while performing the chattering path avoidance internally in the master algorithm of the interface. This increases the efficiency of the chattering-free simulation as no enumeration of modes is required during the chattering detection and elimination process. The developed FMI-based framework can generate a chattering-free simulation for any generic chattering Functional Mockup Unit (FMU) conforming to the FMI standard v2.0 Specification for model exchange