Peter C. Breedveld

Modelling of physical systems for the design and control of mechatronic systems

Abstract Mechatronic design requires that a mechanical system and its control system be designed as an integrated system. This contribution covers the background and tools for modelling and simulation of physical systems and their controllers, with parameters that are directly related to the real-world system. The theory will be illustrated with examples of typical mechatronic systems such as servo systems and a mobile robot. Hands-on experience is realised by means of exercises with the 20-sim software package (a demo version is freely available on the Internet). In mechatronics, where a controlled system has to be designed as a whole, it is advantageous that model structure and parameters are directly related to physical components. In addition, it is desired that (sub-)models be reusable. Common block-diagram- or equation-based simulation packages hardly support these features. The energy-based approach towards modelling of physical systems allows the construction of reusable and easily extendible models. This contribution starts with an overview of mechatronic design problems and the various ways to solve such problems. A few examples will be discussed that show the use of such a tool in various stages of the design. The examples include a typical mechatronic system with a flexible transmission and a mobile robot. The energy-based approach towards modelling is treated in some detail. This will give the reader sufficient insight in order to exercise it with the aid of modelling and simulation software (20-sim). Such a tool allows high level input of models in the form of iconic diagrams, equations, block diagrams or bond graphs and supports efficient symbolic and numerical analysis as well as simulation and visualisation. Components in various physical domains (e.g. mechanical or electrical) can easily be selected from a library and combined into a process that can be controlled by block-diagram-based (digital) controllers. This contribution is based on object-oriented modelling: each object is determined by constitutive relations at the one hand and its interface, the power and signal ports to and from the outside world, at the other hand. Other realizations of an object may contain different or more detailed descriptions, but as long as the interface (number and type of ports) is identical, they can be exchanged in a straightforward manner. This allows top–down modelling as well as bottom–up modelling. Straightforward interconnection of (empty) submodels supports the actual decision process of modelling, not just model input and output manipulation. Empty submodel types may be filled with specific descriptions with various degrees of complexity (models can be polymorphic) to support evolutionary and iterative modelling and design approaches. Additionally, submodels may be constructed from other submodels in hierarchical structures. An introduction to the design of controllers based on these models is also given. Modelling and controller design as well as the use of 20-sim may be exercised in hands-on experience assignments, available at the Internet ( http://www.ce.utwente.nl/IFACBrief/ ). A demonstration copy of 20-sim that allows the reader to use the ideas presented in this contribution may be downloaded from the Internet ( http://www.20sim.com ).

Structured modeling for processes: A thermodynamical network theory

We review the use of bond graphs for modeling of physico-chemical processes. We recall that bond graphs define a circuit-type language which root on a thermodynamical consistent definition of its network elements. We present the bond graph basic elements in the light of lumped models arising from chemical engineering. We first illustrate it on the historical example of the diffusion process through a membrane. The examples of a Continuous Stirred Tank Reactor and an adsorption process illustrate how the network structure and the choice of variables ease the reusability of submodels and localize the changes in models to some network elements.

An Alternative Model for Static and Dynamic Friction in Dynamic System Simulation

Abstract A benchmark problem is defined to test potential solutions for re-usable submodels representing static (‘stick’) and dynamic dry (‘Coulomb’) friction in dynamic system simulation that are based on relevant physical port behavior. Next an alternative submodel is proposed with several advantages over other possible implementations. It is shown that dynamic causality and dynamic model structure can always be prevented and that some solutions for numerical computation can be completely embedded in a one-port resistor, if necessary externally modulated by the normal force between the contact surfaces. This makes these solutions highly re-usable, although they create a trade-off between accuracy and numerical stiffness. The key issue is that the generic expression for the contact force derived originally to solve the case with dynamic structure, results in a numerically robust and efficient submodel with static port causality and static model structure that does not create this numerical stiffness.

Port-based modelling of multidomain physical systems in terms of bond graphs

This chapter discusses how a port-based approach to multiphysics modeling provides a systematic and efficient way to enhance insight in both the physical and the computational structure of the model, thus allowing optimal preparation for numerical simulation. In particular systems containing mechanisms are addressed.

Stability of rigid body rotation from a bond graph perspective

This paper describes the history of the bond graph description of rigid body rotation dynamics and resolves a paradox that resulted from the common Euler Junction Structure (EJS) description of the exterior product in the Newton–Euler equation describing rigid body rotation [D.C. Karnopp, R.C. Rosenberg, Analysis and Simulation of Multiport Systems – The Bond Graph Approach to Physical Systems Dynamics, MIT Press, Boston, 1968; D.C. Karnopp, The energetic structure of multibody dynamic systems, J. Franklin Inst. 306 (2) (1978) 165–181]. The proposed alternative representation that resolves this paradox allows direct insight into the stability of rotations around the principal axes of a rigid body. It eliminates the bond loop and it is shown to be a canonical decomposition of the corresponding nonlinear 3-port gyrator, whereas the EJS is not canonical. The consequences of these differences are demonstrated, in particular the increased expressive power of this notation, which is particularly important in education.

Port-Based Modeling of Dynamic Systems

Many engineering activities, in particular mechatronic design, require that a multi-domain or ‘multi-physics’ system and its control system be designed as an integrated system. This chapter discusses the background and concepts of a portbased approach to integrated modeling and simulation of physical systems and their controllers, with parameters that are directly related to the real-world system, thus improving insight and direct feedback on modeling decisions. It serves as the conceptual motivation from a physical point of view that is elaborated mathematically and applied to particular cases in the remaining chapters.

Decomposition of Multiports

Decomposition of multiports is used to show that the nine basic elements of bond graphs are based on the two basic principles of physics, viz., the energy conservation principle and the positive entropy production principle, and the fact that each model has to be separated from its environment that can still influence its behavior. These three concepts have to be conceptually interconnected which leads to the concept of a power continuous junction structure. This junction structure can be decomposed itself, which finally leads to nine basic concepts.

Bond Graph Representation of Linear Time-Varying Systems

The bond graph representation is applied to Linear Time-Varying (LTV) systems.The state-space repre-sentation and an equivalence transformation are pre-sented. From the state space description of a LTV sys-tem, a bond graph model using a prede.ned junction structure can be built. The proposed methodologies are applied to some examples.

Canonical Decomposition of Multiports Revisited: Properties and Relations to Fundamental Principles of Physics

Abstract Properties of decompositions of multiport models are discussed. In particular, it is shown that the congruent canonical decomposition of multiport storage elements or multiport resistors that is based on Choleski factorization of their Jacobians can be causally inverted without generating algebraic loops and that an arbitrary number of ports of such a multiport may be dualized without generating essential gyrators in its decomposition. As a result, it is argued that the congruent canonical decomposition is a preferred decomposition, in particular from a computational point of view.