1.1 INTRODUCTION 3 of mechatronics and micromechatronics.Chapter 4 supplies the most important constructs of digital and analogue hardware description languages.Chapters 5 and 6 deal comprehensively with the methods for the consideration of software and mechanics in hardware description languages.This creates a compendium of basic methods that can be combined at will according to the system under consideration. This is illustrated in Chapters 7 and 8 on the basis of six demonstrators for mecha tronics and micromechatronics.The ninth chapter hnally summarises the work and highlights its most important conclusions.At the end of the book there is a bibli- ography,the appendix containing lists of symbols,trademarks,and abbreviations used,plus the index
1.1 INTRODUCTION 3 of mechatronics and micromechatronics. Chapter 4 supplies the most important constructs of digital and analogue hardware description languages. Chapters 5 and 6 deal comprehensively with the methods for the consideration of software and mechanics in hardware description languages. This creates a compendium of basic methods that can be combined at will according to the system under consideration. This is illustrated in Chapters 7 and 8 on the basis of six demonstrators for mechatronics and micromechatronics. The ninth chapter finally summarises the work and highlights its most important conclusions. At the end of the book there is a bibliography, the appendix containing lists of symbols, trademarks, and abbreviations used, plus the index
2 Principles of Modelling and Simulation 2.1 Introduction The introduction of Information Technology in the last fifty years has allowed modelling and simulation to penetrate the majority of engineering disciplines and natural and social sciences.Regardless of whether the matter under debate is the design of wheel suspension for a car,the metabolism of a bacteria,or the intro- duction of a new interest formula,models of these real systems are always drawn upon to gain an understanding of the inner relationships of the system and to make predictions about its behaviour.The simulation is often also used as a substitute for experiments on an existing system,which is associated with a range of benefits: In comparison to real experiments,virtual experiments often require a sig- nificantly lower outlay in financial terms and in terms of time,because it is generally considerably cheaper to model virtual prototypes than it is to build real prototypes. Some system states cannot be brought about in the real system,or at least not in a non-destructive manner. Normally all aspects of virtual experiments are repeatable,something that either cannot be guaranteed for the real system or would involve considerable cost. Simulated models are generally completely controllable.So all input variables and parameters of the system can be predetermined.This is normally not the case for a real system. Simulated models are generally fully monitorable.All output variables and interal states are available,whereas in the real system every variable to be monitored involves at least a significant measurement cost.In addition,each measurement taken influences the behaviour of the system. 8aa冬m世s0nwnm
2 Principles of Modelling and Simulation 2.1 Introduction The introduction of Information Technology in the last fifty years has allowed modelling and simulation to penetrate the majority of engineering disciplines and natural and social sciences. Regardless of whether the matter under debate is the design of wheel suspension for a car, the metabolism of a bacteria, or the introduction of a new interest formula, models of these real systems are always drawn upon to gain an understanding of the inner relationships of the system and to make predictions about its behaviour. The simulation is often also used as a substitute for experiments on an existing system, which is associated with a range of benefits: • In comparison to real experiments, virtual experiments often require a significantly lower outlay in financial terms and in terms of time, because it is generally considerably cheaper to model virtual prototypes than it is to build real prototypes. • Some system states cannot be brought about in the real system, or at least not in a non-destructive manner. • Normally all aspects of virtual experiments are repeatable, something that either cannot be guaranteed for the real system or would involve considerable cost. • Simulated models are generally completely controllable. So all input variables and parameters of the system can be predetermined. This is normally not the case for a real system. • Simulated models are generally fully monitorable. All output variables and internal states are available, whereas in the real system every variable to be monitored involves at least a significant measurement cost. In addition, each measurement taken influences the behaviour of the system. Mechatronic Systems Georg Pelz 2003 John Wiley & Sons, Ltd ISBN: 0-470-84979-7
6 2 PRINCIPLES OF MODELLING AND SIMULATION In some cases the 'time constants'of the experiment and observer are incompatible,such as the investigation of elementary particles or galaxies. In some cases an experiment is ruled out for moral reasons,for example exper- iments on humans in the field of medical technology. However,these benefits are countered by some disadvantages: .Each virtual experiment requires a complete,validated and verified modelling of the system. The accuracy with which details are reproduced and the simulation speed of the models is limited by the power of the computer used for the simulation. In many cases the benefits outweigh the disadvantages and virtual experiments can be used advantageously.The repeatability guaranteed by the computer is partic- ularly beneficial if the virtual experiment is systematically planned and performed as part of an optimisation. In what follows we will define a range of terms relating to modelling and simulation.This will allow us to move from a general consider investigaled in ths work.thus providinga od strcture te following representation relates to the work of the SCS Technical Committee on Model Credibility,see 362] Realiry is initially an entity,situation or system to be investigated by simulation. Its modelling can be viewed as a two-stage process,as shown in Figure 2.1.In the first stage,reality is analysed and modelled using verbal descriptions,equations relationships or laws of nature,which initially establishes a conceptual model.A field of application then has to be defined for this conceptual model.within which the model should provide an acceptable representation of reality.Furtherm the degree of correspondence between conceptual model and reality that should be achieved for the secfield of application,hasto be defined.Acoceptual model is adequately qualified for a predetermined field of application if it produces the required degree of correspondence with reality.In the second stage of modelling the conceptual model is transformed into an executable,i.e.simulatable,model as part of implementation.This primarily consists of a set of instructions that describe the system's response to external stimuli.The instructions can be processed manually or using a computer.The latter is called simulation and permits the processing of significantly greater data quantities,and thus the consideration of significantly more complex problems. The development of models for simulation is a difficult process,and thus prone to errors.On the other hand,the reliability of a simulation is crucially dependent upon the quality of the model.So methods and tools are required that are capable of validating and verifying the models.Let us now define these two terms,valida- tion and verification,more closely,see Figure 2.1.Model verification investigates whether the executable model reflects the conceptual model within the specified limits of accuracy.Verification transfers the conceptual model's field of application
6 2 PRINCIPLES OF MODELLING AND SIMULATION • In some cases the ‘time constants’ of the experiment and observer are incompatible, such as the investigation of elementary particles or galaxies. • In some cases an experiment is ruled out for moral reasons, for example experiments on humans in the field of medical technology. However, these benefits are countered by some disadvantages: • Each virtual experiment requires a complete, validated and verified modelling of the system. • The accuracy with which details are reproduced and the simulation speed of the models is limited by the power of the computer used for the simulation. In many cases the benefits outweigh the disadvantages and virtual experiments can be used advantageously. The repeatability guaranteed by the computer is particularly beneficial if the virtual experiment is systematically planned and performed as part of an optimisation. In what follows we will define a range of terms relating to modelling and simulation. This will allow us to move from a general consideration to the systems investigated in this work, thus providing a good structure to the discussion. The following representation relates to the work of the SCS Technical Committee on Model Credibility, see [362]. Reality is initially an entity, situation or system to be investigated by simulation. Its modelling can be viewed as a two-stage process, as shown in Figure 2.1. In the first stage, reality is analysed and modelled using verbal descriptions, equations, relationships or laws of nature, which initially establishes a conceptual model. A field of application then has to be defined for this conceptual model, within which the model should provide an acceptable representation of reality. Furthermore, the degree of correspondence between conceptual model and reality that should be achieved for the selected field of application, has to be defined. A conceptual model is adequately qualified for a predetermined field of application if it produces the required degree of correspondence with reality. In the second stage of modelling the conceptual model is transformed into an executable, i.e. simulatable, model as part of implementation. This primarily consists of a set of instructions that describe the system’s response to external stimuli. The instructions can be processed manually or using a computer. The latter is called simulation and permits the processing of significantly greater data quantities, and thus the consideration of significantly more complex problems. The development of models for simulation is a difficult process, and thus prone to errors. On the other hand, the reliability of a simulation is crucially dependent upon the quality of the model. So methods and tools are required that are capable of validating and verifying the models. Let us now define these two terms, validation and verification, more closely, see Figure 2.1. Model verification investigates whether the executable model reflects the conceptual model within the specified limits of accuracy. Verification transfers the conceptual model’s field of application
2.1 INTRODUCTION Verification Analysis Simulation Validation Reality Figure 2.1 Model generation,simulation,validation and verification in context to the executable model.Model validation,on the other hand,should tell us whether the executable model is suitable for fulfilling the envisaged task within its field of application.In other words:Verification ensures the system is modelled right, whereas validation is all about modelling the right system.Various degrees of validity can be defined for a model: Replicative validity A model is replicatively valid if it moves along tracks that have already been marked out by measurements upon the real system.This is the lowest level of validity.Such models may,for example,be used in the field of training to teach people to use a real system by means of virtual experiments Predictive validity A model is predictively valid if it 'predicts'data that are not extracted from the system until later.So,for example,simulations supply important information on the functionality of a circuit even before it has been constructed in the form of a chip or board.It is also perfectly possible to mix predictively valid component models with replicatively valid models if measurement data is available for the modelling of some components but not for others.A predictively valid model is also replicatively valid. Structural validity A model is structurally valid if it not only describes the outward behaviour of a real system accurately enough,but also imitates the internal processes for the
2.1 INTRODUCTION 7 Conceptual model Reality Executable model Analysis Simulation Qualification Validation Verification Implementation Figure 2.1 Model generation, simulation, validation and verification in context to the executable model. Model validation, on the other hand, should tell us whether the executable model is suitable for fulfilling the envisaged task within its field of application. In other words: Verification ensures the system is modelled right, whereas validation is all about modelling the right system. Various degrees of validity can be defined for a model: Replicative validity A model is replicatively valid if it moves along tracks that have already been marked out by measurements upon the real system. This is the lowest level of validity. Such models may, for example, be used in the field of training to teach people to use a real system by means of virtual experiments. Predictive validity A model is predictively valid if it ‘predicts’ data that are not extracted from the system until later. So, for example, simulations supply important information on the functionality of a circuit even before it has been constructed in the form of a chip or board. It is also perfectly possible to mix predictively valid component models with replicatively valid models if measurement data is available for the modelling of some components but not for others. A predictively valid model is also replicatively valid. Structural validity A model is structurally valid if it not only describes the outward behaviour of a real system accurately enough, but also imitates the internal processes for the
8 2 PRINCIPLES OF MODELLING AND SIMULATION generation of the behaviour at the pins.This is the highest level of validity and this level in particular is required in order to understand the real system.A structurally valid system is also predictively valid. 2.2 Model Categories We can obtain an initial classification of models by considering the range of values of the system variables,see for example Zeigler [435].These may be continuous or discrete.A range of values is continuous if it covers real numbers or an interval of them.For example,a mechanical position has a continuous range of values.In a discrete range of values,on the other hand,the system variable takes on a value from a finite (or at least countable)quantity of values,as is the case for digital, electronic signals.The states of the model take on a discrete,continuous or mixed form depending upon the system variables. Time is explicitly removed from the system variables and investigated in a similar manner with respect to its value range.In the discrete case time proceeds in leaps;valid time points are calculated as the product of awholenumber and a basic time span.This may,for example,be suitable if a gate simulation is run with unit delays.By contrast,we can also consider models in which time is continuous. These can be divided into two categories:models and equation models.In the former case each change of state of the model is triggered by an event,so that the trajectory of system states proceeds in leaps.The events themselves can occur at arbitrary points in time:their number in relation to a predetermined time interval is however finite.By contrast,in models based upon differential equations the trajectory of system states is continuous.Changes are described on the basis of the syste variables and their rate of change A further possibility for differentiating between models is based upon whether the description uses concentrated or distributed parameters.Examples of the for- mer case are elect tronic omponentso the fixed and elastic bodies f the multibody representation of a mechanical system.Distributed parameters should be used in the consideration of a mechanical continuum,for example. Models may furthermore be of a static or dynamic nature.In the former case in electronics for example,when determining the operating point of a circuit it is sufficient to represent capacitors as open circuits and coils as short-circuits.In multibody mechanics stationary systems can be analysed.Dynamic models are required in electronics for transient simulations,i.e.for those over a time range, whereas in mechanics we can differentiate between two application cases:kine- matics and kinetics,see for example Nikravesh [299].Kinematics relates to the investigation of positions,speeds and accelerations without taking into account the forces that cause the movement they describe.Kinetics also considers the acting forces In some cases a model cannot be described in a purely deterministic manner, meaning that at least one random variable must be included.As an example,a
8 2 PRINCIPLES OF MODELLING AND SIMULATION generation of the behaviour at the pins. This is the highest level of validity and this level in particular is required in order to understand the real system. A structurally valid system is also predictively valid. 2.2 Model Categories We can obtain an initial classification of models by considering the range of values of the system variables, see for example Zeigler [435]. These may be continuous or discrete. A range of values is continuous if it covers real numbers or an interval of them. For example, a mechanical position has a continuous range of values. In a discrete range of values, on the other hand, the system variable takes on a value from a finite (or at least countable) quantity of values, as is the case for digital, electronic signals. The states of the model take on a discrete, continuous or mixed form depending upon the system variables. Time is explicitly removed from the system variables and investigated in a similar manner with respect to its value range. In the discrete case time proceeds in leaps; valid time points are calculated as the product of a whole number and a basic time span. This may, for example, be suitable if a gate simulation is run with unit delays. By contrast, we can also consider models in which time is continuous. These can be divided into two categories: event-oriented models and differential equation models. In the former case each change of state of the model is triggered by an event, so that the trajectory of system states proceeds in leaps. The events themselves can occur at arbitrary points in time; their number in relation to a predetermined time interval is however finite. By contrast, in models based upon differential equations the trajectory of system states is continuous. Changes are described on the basis of the system variables and their rate of change. A further possibility for differentiating between models is based upon whether the description uses concentrated or distributed parameters. Examples of the former case are electronic components or the fixed and elastic bodies of the multibody representation of a mechanical system. Distributed parameters should be used in the consideration of a mechanical continuum, for example. Models may furthermore be of a static or dynamic nature. In the former case, in electronics for example, when determining the operating point of a circuit it is sufficient to represent capacitors as open circuits and coils as short-circuits. In multibody mechanics stationary systems can be analysed. Dynamic models are required in electronics for transient simulations, i.e. for those over a time range, whereas in mechanics we can differentiate between two application cases: kinematics and kinetics, see for example Nikravesh [299]. Kinematics relates to the investigation of positions, speeds and accelerations without taking into account the forces that cause the movement they describe. Kinetics also considers the acting forces. In some cases a model cannot be described in a purely deterministic manner, meaning that at least one random variable must be included. As an example, a