Multi-Mode DAE Models - Challenges, Theory and Implementation

2012

ABSTRACT Cyber-Physical Systems (CPS) are composed of computational and physical components, which includes various types of physical phenomena such as electrical and mechanical domains. Many modeling paradigms exist to model the static properties and dynamic behavior of such components. However, there is no unified modeling framework to compose components that use different paradigms and/or tools.

Fourth Workshop on Model-Based Development of Computer-Based Systems and Third International Workshop on Model-Based Methodologies for Pervasive and Embedded Software (MBD-MOMPES'06)

This paper presents a component oriented modeling environment for building hybrid dynamic models of physical system. The modeling environment is created using the Generic Modeling Environment (GME), a metaprogrammable visual modeling application developed at the Institute for Software Integrated Systems (ISIS). The core of the modeling language itself is a hybrid extension of the bond graph modeling language. The advantages of an object-oriented approach to physical system modeling combined with the advanced features of GME for managing model complexity are illustrated by building a library of hydraulic system components. A simulation model can be automatically generated from the physical system model using a model translator. As an example application we use the component library to build the model of a coupled multi-tank system with controlled and autonomous hybrid behaviors, and illustrate this with a simulation example.

ArXiv, 2021

Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAEs), i.e., constraints of the form f(x′, x, u) = 0. This drastically facilitates modeling from first principles of the physics, as well as model reuse. In recent works [2, 3], we presented the mathematical theory needed to establish the development of compilers and tools for DAE-based physical modeling languages on solid mathematical grounds. At the core of this analysis sits the so-called structural analysis, whose purpose, at compile time, is to either identify underand overspecified subsystems (if any), or to rewrite the model in a form amenable of existing DAE solvers, including the handling of mode change events. The notion of “structure” collects, for each mode and mode change event, the variables and equations involved, as well as the latent equations (additional equations redundant with the system), needed to prepare the code submitted to...

Information Technology for Dynamical Systems, 2004

Complex control systems integrate a variety of functions and capabilities, which will in general rely on different computational mechanisms. The plant model may be represented as a set of ordinary differential equations, the mode switching logic may be expressed as a finite state machine, and dataflow models may be used to capture the architecture of a sensor processing subsystem, for example. Design tools are needed that can support these heterogeneous models of computation-and their integration within a single control system. This chapter describes Ptolemy II, a component-based design environment that allows different models of computation to be hierarchically composed. Individual components are called actors; these can include simple operators such as an AND gate and, through compositionality in the form of arbitrarily nested actor hierarchies, complex functions such as a Kalman filter. Different models of computation can then be realized by imposing a (possibly partial) execution order and a communication mechanism on the actors that comprise a composite actor. Ptolemy II can be particularly useful for the design of hybrid dynamical systems-systems that combine discrete event mode logic and continuous time dynamics within each mode. By using

SIMULATION, 2002

This article presents the design and implementation of a robust simulation methodology for hybrid models of physical systems that encompasses behavior patterns that undergo discrete transitions between modes of continuous behavior evolution. This methodology is based on a mathematical framework that captures time scale and parameter abstractions in modeling complex physical phenomena. The formal semantics for characterizing hybrid behaviors is defined in terms of three distinct modes of system operation: (1) continuous, (2) pinnacles, and (3) mythical. A key link is established between the switching transitions and the a priori and a posteriori state vector values, which defines the recursive mode switching functions that govern the interactions between the continuous and discrete components of the system models. The effectiveness of the approach is demonstrated by examples of physical system models that are presented along with a simulator to handle these.

The modelling and simulation of sophisticated technical systems is a demanding task. On the one hand, the physical part consists of a large number of subsystems which exhibit predominantly continuous dynamics, sometimes with (infrequent) discontinuities. On the other hand, the distributed computerised control systems constitute complex discrete-time and discrete-event systems that require completely different modelling and simulation methods. For an evaluation of the behaviour and the performance of the overall systems, both types of models have to be combined and simulated efficiently. This contribution presents the requirements for a modelling environment for such systems and discusses an approach that consists of object-oriented modelling and efficient simulation of the physical part using the physical systems modelling language MODELICA, a software environment for the definition of discrete-event models using various formalisms, and the integration of both parts of the system vi...

Artificial Intelligence, 2000

This paper describes a comprehensive and systematic framework for building mixed continuous/discrete, i.e., hybrid physical system models. Hybrid models are a natural representation for embedded systems (physical systems with digital controllers) and for complex physical systems whose behavior is simplified by introducing discrete transitions to replace fast, often nonlinear dynamics. In this paper we focus on two classes of abstraction mechanisms, viz., time scale and parameter abstractions, discuss their impact on building hybrid models, and then derive the transition semantics required to ensure that the derived models are consistent with physical system principles. The transition semantics are incorporated into a formal model representation language, which is used to derive a computational architecture for hybrid systems based on hybrid automata. This architecture forms the basis for a variety of hybrid simulation, analysis, and verification algorithms. A complex example of a colliding rod system demonstrates the application of our modeling framework. The divergence of time and behavior analysis principles are applied to ensure that physical principles are not violated in the definition of the discrete transition model. The overall goal is to use this framework as a basis for developing systematic compositional modeling and analysis schemes for hybrid modeling of physical systems. Preliminary attempts in this area are discussed, with thoughts on how to develop this into a more general methodology.

Electronics

Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In this article, we propose several contributions to this multifaceted issue, namely: an efficient and scalable multimode extension of the structural analysis of Modelica models; a systematic way of rewriting a multimode Modelica model, based on this analysis, so that the rewritten model is guaranteed to be correctly compiled by state-of-the-art Modelica tools; a proposal for the handling of the consistent initialization of multimode models; multimode structural analysis algorithms that handle both multiple modes and mode change events in a unified framework, coupled with a compile-time algorithm for identifying and quantifying impulsive behaviors at mode changes. Our approach is illu...

HAL (Le Centre pour la Communication Scientifique Directe), 2022

Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In this report, we illustrate this behavior on several small-sized examples, shedding light on the shortcomings of the approximate structural analysis implemented in current Modelica tools. To address part of these issues, we propose a systematic transformation process for multimode Modelica models, based on the results of an already implemented multimode structural analysis, that guarantees that the output Modelica model is correctly compiled by state-of-the-art Modelica tools. Still, this transformation is limited to models that do not exhibit impulsive behaviors at mode changes: the remaining issues illustrated by our introductory examples can only be solved by a structural analysis of mode changes, coupled with a specific handling of impulsive variables. We address these points in this report by proposing, first, a structural analysis method able to handle modes and mode changes in a unified framework, and second, a compile-time identification and characterization of impulsive variables. Implementations of both methods, based on efficient symbolic representations and algorithms, are in the works.