分数阶系统的分数阶PID控制器设计

对于一些复杂的实际系统,用分数阶微积分方程建模要比整数阶模型更简洁准确.分数阶微积分也为描述动态过程提供了一个很好的工具.对于分数阶模型需要提出相应的分数阶控制器来提高控制效果.本文针对分数阶受控对象,提出了一种分数阶PID控制器的设计方法.并用具体实例演示了对于分数阶系统模型,采用分数阶控制器比采用古典的PID控制器取得更好的效果.     

Diagnosability of delay-deadline failures in fair real time discrete event models

In this article a method for failure diagnosis of real time discrete event systems (RTDES) with ‘fairness of traces’ has been developed. Discrete event system (DES) modelling framework with provision for associating timing information with the transitions are required for handling real time systems. RTDES models and timed DES (TDES) models are examples of such modelling frameworks. Failure diagnosis in untimed DES models enables only the study of diagnosability of failures resulting in a change in the logical behaviour of the failed system. In addition to logical failures, failure diagnosis in RTDES and TDES models also enables diagnosability of failures that change the timing behaviour of the system but maintain the logical behaviour. Many systems exhibit fairness of traces with respect to transitions in the sense that any trace that visits a state infinitely often has infinitely many occurrences of all the transitions that emanate from that state. The abstraction employed in obtaining their (timed) DES models often obliterates this property. The RTDES and TDES diagnosability conditions, proposed in the literature and which do not consider fairness, are shown to be inadequate in this article. A new diagnosability condition is achieved by taking into account this fairness property in the RTDES models and shown to be necessary and sufficient for such systems. An analysis of time complexity for analysing the diagnosability of systems with fairness of traces is presented.     

Differential Dynamic Logic for Hybrid Systems

Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce a dynamic logic for hybrid programs, which is a program notation for hybrid systems. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid programs to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. In a case study with cooperating traffic agents of the European Train Control System, we further show that our calculus is well-suited for verifying realistic hybrid systems with parametric system dynamics.     

State-based Components Made Generic

Genericity is a topic which is not sufficiently developed in state-based systems modelling, mainly due to a myriad of approaches and behaviour models which lack unification. This paper adopts coalgebra theory to propose a generic notion of a state-based software component, and an associated calculus, by quantifying over behavioural models specified as strong monads. This leads to the pointfree, calculational reasoning style which is typical of the so-called Bird-Meertens school.     

A monotone framework for CCS

The calculus of communicating systems, CCS, was introduced by Robin Milner as a calculus for modelling concurrent systems. Subsequently several techniques have been developed for analysing such models in order to get further insight into their dynamic behaviour.In this paper we present a static analysis for approximating the control structure embedded within the models. We formulate the analysis as an instance of a monotone framework and thus draw on techniques that often are associated with the efficient implementation of classical imperative programming languages.We show how to construct a finite automaton that faithfully captures the control structure of a CCS model. Each state in the automaton records a multiset of the enabled actions and appropriate transfer functions are developed for transforming one state into another. A classical worklist algorithm governs the overall construction of the automaton and its termination is ensured using techniques from abstract interpretation.     

Prototyping and analysing ubiquitous computing environments using multiple layers

If ubiquitous computing (ubicomp) is to enhance physical environments then early and accurate assessment of alternative solutions will be necessary to avoid costly deployment of systems that fail to meet requirements. This paper presents APEX, a prototyping framework that combines a 3D Application Server with a behaviour modeling tool. The contribution of this framework is that it allows exhaustive analysis of the behaviour models that drive the prototype while at the same time enabling immersive exploration of a virtual environment simulating the proposed system. The development of prototypes is supported through three layers: a simulation layer (using OpenSimulator); a modelling layer (using CPN Tools) and a physical layer (using external devices and real users). APEX allows movement between these layers to analyse different features, from user experience to user behaviour. The multi layer approach makes it possible to express user behaviour in the modelling layer, provides a way to reduce the number of real users needed by adding simulated avatars, and supports user testing of hybrids of virtual and real components as well as exhaustive analysis. This paper demonstrates the approach by means of an example, placing particular emphasis on the simulation of virtual environments, low cost prototyping and the formal analysis capabilities.     

When do aquatic systems models provide useful predictions,what is changing,and what is next?

This article considers how aquatic systems modelling has changed since 1995 and how it must change in future if we are to continue to advance. A distinction is made between mechanistic and statistical models, and the relative merits of each are considered. The question of “when do aquatic systems models provide accurate and useful predictions?” is addressed, implying some guidelines for model development. It is proposed that, in general, ecological models only provide management-relevant predictions of the behaviour of real systems when there are strong physical (as opposed to chemical or ecological) drivers. Developments over the past 15 years have included changes in technology, changes in the modelling community and changes in the context in which modelling is conducted: the implications of each are briefly discussed. Current trends include increased uptake of best practice guidelines, increasing integration of models, operationalisation, data assimilation, development of improved tools for skill assessment, and application of models to new management questions and in new social contexts. Deeper merging of statistical and mechanistic modelling approaches through such techniques as Bayesian Melding, Bayesian Hierarchical Modelling and surrogate modelling is identified as a key emerging area. Finally, it is suggested that there is a need to systematically identify areas in which our current models are inadequate. We do not yet know for which categories of problems well-implemented aquatic systems models can (or cannot) be expected to accurately predict observational data and system behaviour. This can be addressed through better modelling and publishing practices.     

无刷直流电机的分数阶建模方法

传统的基于机理的整数阶无刷直流电机仿真模型和实际物理样机有较大差距.论文通过分析无刷直流电机的数学模型,在基于机理建模整数阶模型基础上引入分数阶微积分,将机理建模和数字建模相结合,提出一种新的无刷直流电机建模方法.首先根据物理样机建立基于机理的无刷直流电机仿真模型,然后采用基于输出误差的最小二乘法辨识出分数阶模型的参数...     

The stream-based service-centred calculus: a foundation for service-oriented programming

We give a formal account of stream-based, service-centered calculus (SSCC), a calculus for modelling service-based systems, suitable to describe both service composition (orchestration) and the protocols that services follow when invoked (conversation). The calculus includes primitives for defining and invoking services, for isolating conversations (called sessions) among clients and servers, and for orchestrating services. The calculus is equipped with a reduction and a labelled transition semantics related by an equivalence result. SSCC provides a good trade-off between expressive power for modelling and simplicity for analysis. We assess the expressive power by modelling van der Aalst workflow patterns and an automotive case study from the European project Sensoria. For analysis, we present a simple type system ensuring compatibility of client and service protocols. We also study the behavioural theory of the calculus, highlighting some axioms that capture the behaviour of the different primitives. As a final application of the theory, we define and prove correct some program transformations. These allow to start modelling a system from a typical UML Sequence Diagram, and then transform the specification to match the service-oriented programming style, thus simplifying its implementation using web services technology.     

Specifying active databases as non-Markovian theories of actions

Over the last 15 years, database management systems (DBMSs) have been enhanced by the addition of rule-based programming to obtain active DBMSs. One of the greatest challenges in this area is to formally account for all the aspects of active behavior using a uniform formalism. In this paper, we formalize active relational databases within the framework of the situation calculus by uniformly accounting for them using theories embodying non-Markovian control in the situation calculus. We call these theories active relational theories and use them to capture the dynamics of active databases. Transaction processing and rule execution is modelled as a theorem proving task using active relational theories as background axioms. We show that the major components of an ADBMS, namely the rule sets and the execution models, may be given a clear semantics using active relational theories. More precisely: we represent the rule set as a program written in a suitable version of the situation calculus based language ConGolog; then we extend an existing situation calculus based framework for modelling advanced transaction models to one for modelling the execution models of active behaviors.

Linear fractional order controllers; A survey in the frequency domain

Today, there is a great tendency toward using fractional calculus to solve engineering problems. The control is one of the fields in which fractional calculus has attracted a lot of attention. On the one hand, fractional order dynamic models simulate characteristics of real dynamic systems better than integer order models. On the other hand, Fractional Order (FO) controllers outperform Integer Order (IO) controllers in many cases. FO-controllers have been studied in both time an frequency domain. The latter one is the fundamental tool for industry to design FO-controllers. The scope of this paper is to review research which has been carried out on FO-controllers in the frequency domain. In this review paper, the concept of fractional calculus and their applications in the control problems are introduced. In addition, basic definitions of the fractional order differentiation and integration are presented. Then, four common types of FO-controllers are briefly presented and after that their representative tuning methods are introduced. Furthermore, some useful continuous and discrete approximation methods of FO-controllers and their digital and analogue implementation methods are elaborated. Then, some Matlab toolboxes which facilitate utilizing FO calculus in the control field are presented. Finally, advantages and disadvantages of using FO calculus in the control area are discussed. To wrap up, this paper helps beginners to get started rapidly and learn how to select, tune, approximate, discretize, and implement FO-controllers in the frequency domain.     

Modelling pollution dispersion,the ecosystem and water quality in coastal waters: a review

This review is intended as a comprehensive but concise summary of present capabilities in coastal pollutant, ecosystem and water quality modelling. It reflects the recent rapid developments in multidisciplinary modelling in shelf seas.The behaviour of conservative pollutants that act as passive tracers is contrasted with those that have more complex behaviours, including oil spills. The importance of sediment modelling is emphasised, since contaminants commonly exist in both a dissolved and a particulate state, or adhere to sediments.Recently developed ecological models can have great complexity, reflecting the complexity of the real ecosystem. These models are now being linked to physical models of coastal waters and run with the same resolution. This has become possible only recently because of increases in computer power, particularly the availability of parallel systems at reasonable cost.The main advances in physical modelling are likely to come through greater understanding of turbulence and other sub-grid-scale processes as well as increased resolution.In the coastal seas there is often a lack of oceanographic data, which is even greater for the many biological and chemical variables than it is for physical variables. This is probably the single most important factor limiting the progress of operational water quality models.     

Agent-Based Simulation of Animal Behaviour

In the biological literature on animal behaviour, in addition to real experiments and field studies, also simulation experiments are a useful source of progress. Often specific mathematical modelling techniques are adopted and directly implemented in a programming language. Modelling more complex agent behaviours is less adequate using the usually adopted mathematical modelling techniques. The literature on AI and Agent Technology offers more specific methods to design and implement (also more complex) intelligent agents and agent societies on a conceptual level. One of these methods is the compositional multi-agent system design method DESIRE. In this paper it is shown how (depending on the complexity of the required behaviour) a simulation model for animal behaviour can be designed at a conceptual level in an agent-based manner. Different models are shown for different types of behaviour, varying from purely reactive behaviour to pro-active, social and adaptive behaviour. The compositional design method for multi-agent systems DESIRE and its software environment supports the conceptual and detailed design, and execution of these models. A number of experiments reported in the literature on animal behaviour have been simulated for different agent models.     

分数阶系统频域辨识算法

分数阶微积分提供了一个很好的工具来描述一些复杂的实际系统,比整数阶模型更简洁准确.针对分数阶系统建模问题,阐述了一种同元次分数阶系统频域辨识的极大似然算法.为此首先简要地介绍了同元次分数阶系统的传递函数表达形式,然后在此基础上推导了分数阶系统频域极大似然算法,利用拉格朗日法证明了似然函数和代价函数的等价性,从而将辨识问题归结为一等价的优化问题,并进一步对采用Gauss-Newton优化计算方法进行了讨论.最后通过仿真实例验证了其有效性.     

Fuzzy inductive reasoning for variable selection analysis and modelling of biological systems

Fuzzy inductive reasoning (FIR) is a qualitative inductive modelling and simulation methodology for dealing with dynamical systems. It has proven to be a powerful tool for qualitative model identification and prediction of future behaviour of various kinds of dynamical systems, especially from the soft sciences, such as biology, biomedicine and ecology. This paper focuses on modelling aspects of the FIR methodology. It is shown that the FIR variable selection analysis is a useful tool not only for FIR but also for other classical quantitative methodologies such as nonlinear autoregressive moving average modelling with external inputs (NARMAX). The tool allows us to obtain models that interpret a system under study in optimal ways, in the sense that these models are well suited for predicting the future behaviour of the system they represent. The FIR variable selection analysis turns out to work well even in those applications where standard statistical variable selection analysis does not provide any useful information. In this paper, the FIR variable selection analysis is applied to a real system stemming from biology, namely, shrimp farming. The main goal is the identification of a growth model for occidental white shrimp (Penaeus vannamei), which allows farmers to plan the dates for seeding and harvesting the ponds in order to maximise their profits. FIR and NARMAX shrimp growth models are identified, and their prediction capabilities are compared to each other.     

A novel self-organizing fuzzy rule-based system for modelling traffic flow behaviour

The study and development of transportation systems have been a focus of attention in recent years, with many research efforts directed in particular at modelling traffic behaviour from both macroscopic and microscopic points of views. Although many statistical regression models of road traffic relationships have been formulated, they have proven to be unsuitable due to multiple and ill-defined traffic characteristics. Alternative methods such as neural networks have thus been sought but, despite some promising results, their design remains problematic and implementation is equally difficult. Another salient issue is that the opaqueness of trained networks prevents understanding the underlying models. Hybrid neuro-fuzzy rule-based systems, which combine the complementary capabilities of both neural networks and fuzzy logic, constitute a more promising technique for modelling traffic flow. This paper describes the application of a specific class of neuro-fuzzy system known as the Pseudo Outer-Product Fuzzy-Neural Network using Truth-Value-Restriction method (POPFNN-TVR) for modelling traffic behaviour. This approach has been shown to perform better on such problems than similar architectures. The results obtained highlight the capability of POPFNN-TVR in fuzzy knowledge extraction for modelling inter-lane relationships in a highway traffic stream, as well as in generalizing from sample data, as compared to traditional feed-forward neural networks using back-propagation learning. The model thus obtained automatically can be understood, analysed, and readily applied for transportation planning.     

Towards true linguistic modelling through optimal numerical solutions

This paper is concerned with both the problems of quantitative and qualitative modelling of complex systems by using fuzzy techniques. A unified approach for the identification and subsequent extraction of linguistic knowledge of systems using fuzzy relational models is addressed. This approach deals with the identification problem by means of optimal numerical solutions based on weighted least squares and quadratic programming formulations. The linguistic knowledge is extracted in the form of consistent fuzzy rules that describe linguistically the behaviour of the identified system. A new methodology for the simplification of the extracted rules is derived by using a pruning criterion based on the representability matrix concept introduced in previous work. Several numerical aspects concerning the proposed optimization schemes and a covering discussion about the linguistic interpretation of the resulting models are also included together with illustrative examples in the contexts of pattern classification and dynamic systems identification. The paper also provides an overview of fuzzy modelling techniques that intends to situate the relational models among other fuzzy model architectures typically adopted in the literature, highlighting their main advantages and drawbacks.     

Behavioural equivalence in simulation modelling

Discrete event simulation has grown up as a practical technique for estimating the quantitative behaviour of systems, where direct measurement is undesirable or impractical. It is also used to understand the detailed functional behaviour of such systems. Its theory is largely that of experimental science, centering on statistical approaches to validation, rather than on the verification of detailed behaviour. On the other hand, much work has been done on understanding and proving functional properties of systems, using techniques of formal specification and concurrency modelling. This article presents an approach to understanding equivalence of behaviour of discrete event simulation models, using a technique from the concurrency world, Milner’s Calculus of Communicating Systems (CCS). This yields a significant advance over the main previous work, Schruben and Yücesan’s simulation graphs. CCS allows for the use of observational equivalence, which can capture a more flexible, behavioural notion of equivalence than the structural equivalence defined there.A common framework based on the process view of models is constructed, using a hierarchical graphical modelling language (Extended Activity Diagrams). This language is shown to map onto both the major constructs of the DEMOS discrete event simulation language and the corresponding CCS models. A graphically driven tool based on such a framework is presented, which generates both types of models. Using the CCS model, behavioural equivalences and differences in simulation models are demonstrated.