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10 - Tools for modeling, simulation, control, and verification of piecewise affine systems
- from Part II - Tools
- Edited by Jan Lunze, Ruhr-Universität, Bochum, Germany, Françoise Lamnabhi-Lagarrigue, Centre National de la Recherche Scientifique (CNRS), Paris
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- Book:
- Handbook of Hybrid Systems Control
- Published online:
- 21 February 2011
- Print publication:
- 15 October 2009, pp 297-324
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- Chapter
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Summary
Tools for mixed logical dynamical and piecewise affine systems based on the model description language HYSDEL are described. They concern various modeling, identification, analysis, control design, and verification tasks. The data exchange format explained in this chapter facilitates the combination of these tools.
This chapter describes MATLAB/Simulink tools for modeling, identifying, simulating, analyzing, and controlling discrete-time hybrid systems with piecewise affine dynamics, described in mixed logical dynamical (MLD) or piecewise affine (PWA) form. Such tools include:
modeling and identification tools for describing the hybrid model in a high-level user-friendly way, or for identifying hybrid models from data;
simulation tools for open-loop simulation and validation of hybrid models;
analysis tools for characterization of stability and reachability properties of hybrid models;
control design tools for designing hybrid model-predictive controllers, simulating closed-loop performances, and generating real-time control code.
(Section 10.1) describes the modeling language HYSDEL, which ease the process of formulating a hybrid model. Sections 10.2 and 10.3 describe two toolboxes for analysis, simulation, and control of hybrid systems, the Multi-Parametric Toolbox and the Hybrid Toolbox. (Section 10.4) describes two tools for identification of hybrid piecewise-affine models from data, the Hybrid Identification Toolbox and the PieceWise Affine Identification Toolbox. Finally, (Section 10.5) describes an interchange format for transferring models among all the aforementioned tools.
HYSDEL
Modeling aim
HYSDEL (HYbrid System DEscription Language) [632] allows modeling a class of hybrid systems described by interconnections of linear dynamical systems, finitestate automata, IF-THEN-ELSE rules, and propositional logic statements.
15 - Automotive control
- from Part III - Applications
- Edited by Jan Lunze, Ruhr-Universität, Bochum, Germany, Françoise Lamnabhi-Lagarrigue, Centre National de la Recherche Scientifique (CNRS), Paris
-
- Book:
- Handbook of Hybrid Systems Control
- Published online:
- 21 February 2011
- Print publication:
- 15 October 2009, pp 439-470
-
- Chapter
- Export citation
-
Summary
Automotive systems offer a rich opportunity for hybrid models, controls, and tools. Beyond the traditional use of hybrid models for representing the behavior of the composition of discrete controller and continuous plants, automotive mechanical systems exhibit hybrid behavior as demonstrated in this chapter. In addition, hybrid systems can be used to capture system specifications at the highest level of abstraction and to model implementation architectures thus enabling a rich design space exploration.
Introduction
This chapter presents an application of hybrid systems that is of significant industrial interest: power-train modeling and control for automobiles.
Engine control is a challenging problem that involves many functional and non functional requirements. The problem is to develop control algorithms and their implementation with guaranteed properties that can substantially reduce emissions and gas consumption with increased performance.
The introduction of hybrid system modeling and control was motivated by the need for verifying closed-loop systems where the plant to be controlled are continuous-time systems and the controller is a digital system. However, hybrid models are general enough to be useful in other areas of design. In particular, engine control offers a rich set of application of hybrid systems:
The power-train itself can be represented as a hybrid system. In fact, an accurate model of a four-stroke gasoline engine has a “natural” hybrid representation:
Each cylinder in the engine has four discrete modes of operation corresponding to the stroke it is in (hence, its behavior is well represented by a finite state machine (FSM)). […]