INTRODUCTIONGoal of the subjectMethods for mathematical modeling of engineering systemsComputational approaches are ubiquitous in engineeringThey all depend upon a mathematical representationFormulation of an appropriate mathematical model is essential—the critical link between analysis and engineering reality Focus of this courseThe modeling process—a systematic approach to formulating practical mathematical models of physical systems MULTI-DOMAIN MODELINGEngineering systems are becoming progressively more integratedThey involve interactions between phenomena in different engineering domainsThey depend on strong coupling between electronicsmechanicsfluid flowthermal processeschemical processesetc. Requires a multi-disciplinary approach covering each of these domains Integrated models of multi-domain behavior require special care —modeling assumptions that appear reasonable in one domain can be problematical in others ENERGY-BASED APPROACHThe central theme of this course: a multi-disciplinary, integrated approach to modeling physical system behavior in different engineering domains The course will present an energy-based approachWe will make extensive use of bond graph notationSIMPLIFIED MODELSDeveloping models is the goal of much of engineering and most of scienceWe’re not (quite) that ambitious Our aim: Simplified models of physical system dynamic behavior Simplicity vs. competenceCompetence: how faithfully a model represents important physical system behavior"Important behavior" is defined by contextWe will use control system design and implementation for contextThe methods are relevant to many other engineering applicationsWhy control systems? This application provides a natural incentive for model simplicity Design, implementation and operation of control systems leans heavily on mathematical modelsDesign (e.g., LQG, pole-placement)Measurement (e.g., Kalman filter)Control (e.g., adaptive)Diagnosis (e.g., fault identification)Model complexity directly affects cost and performanceNETWORK MODELSContinuing advances in computer technology permit mathematical models of increasingly finer detail—but this is not without cost Fine-grained models may improve numerical predictive accuracybut fine-grained models may obscure insightInsight is the main goal of modelingOur goal will be a state-determined representationthe point of departure for modern control system design analysis and implementationfinite number of state variablesTherefore we will use networks of elementsa generalization of familiar circuit modelsCOURSE OUTLINEIntroductory review of network modelscollections of the familiar “lumped-parameter” elements: mass, spring, damper, inductor, capacitor, resistor, etc.Model representation using block diagrams and bond graphsExtension to multi-variable net work componentsModel representation using multi-port elementsMulti-port elements represent more complex behavior while retaining the clarity and properties of network models Applications of multi-variable network modelsMulti-port and nonlinear elements will be ap plied todifferent kinds of energy transductionelectrical to mechanicalmechanical to fluidetc.thermal processesnonlinear mechanical systemsconvection and matter transport processeschemical processesApplicationsExamples will emphasize mechanical, electrical and fluid systems and may includeelectrical machinesfluid power control systemsroboticspower electronicsthermal systemscompressible gas processespolymeric actuatorsetc.TheorySome fundamental theoretical aspects of multi-variable network models will be exploredHow physical system structure affects control-relevant behaviorzero dynamicsrelative degreecontrollabilityobservabilityetc.Massachusetts Institute of Technology Department of Mechanical Engineering 2.141 Modeling and Simulation of Dynamic Systems INTRODUCTION GOAL OF THE SUBJECT Methods for mathematical modeling of engineering systems Computational approaches are ubiquitous in engineering They all depend upon a mathematical representation Formulation of an appropriate mathematical model is essential —the critical link between analysis and engineering reality FOCUS OF THIS COURSE The modeling process —a systematic approach to formulating practical mathematical models of physical systems Modeling and Simulation of Dynamic Systems Introduction page 1MULTI-DOMAIN MODELING ENGINEERING SYSTEMS ARE BECOMING PROGRESSIVELY MORE INTEGRATED They involve interactions between phenomena in different engineering domains They depend on strong coupling between electronics mechanics fluid flow thermal processes chemical processes etc. Requires a multi-disciplinary approach covering each of these domains INTEGRATED MODELS OF MULTI-DOMAIN BEHAVIOR REQUIRE SPECIAL CARE —modeling assumptions that appear reasonable in one domain can be problematical in others Modeling and Simulation of Dynamic Systems Introduction page 2ENERGY-BASED APPROACH THE CENTRAL THEME OF THIS COURSE: a multi-disciplinary, integrated approach to modeling physical system behavior in different engineering domains The course will present an energy-based approach We will make extensive use of bond graph notation Modeling and Simulation of Dynamic Systems Introduction page 3SIMPLIFIED MODELS Developing models is the goal of much of engineering and most of science We’re not (quite) that ambitious OUR AIM: Simplified models of physical system dynamic behavior SIMPLICITY VS. COMPETENCE Competence: how faithfully a model represents important physical system behavior "Important behavior" is defined by context We will use control system design and implementation for context The methods are relevant to many other engineering applications Modeling and Simulation of Dynamic Systems Introduction page 4WHY CONTROL SYSTEMS? This application provides a natural incentive for model simplicity Design, implementation and operation of control systems leans heavily on mathematical models Design (e.g., LQG, pole-placement) Measurement (e.g., Kalman filter) Control (e.g., adaptive) Diagnosis (e.g., fault identification) Model complexity directly affects cost and performance Modeling and Simulation of Dynamic Systems Introduction page 5NETWORK MODELS Continuing advances in computer technology permit mathematical models of increasingly finer detail —but this is not without cost Fine-grained models may improve numerical predictive accuracy but fine-grained models may obscure insight INSIGHT