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TUTORIAL. Efficient Modeling and Simulation of Multidisciplinary Systems across the Internet. Heřman Mann Computing and Information Centre Czech Technical University in Prague. Tutorial objectives. After attending this tutorial you should be able to:

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## Efficient Modeling and Simulation of Multidisciplinary Systems across the Internet

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**TUTORIAL**Efficient Modeling and Simulation of Multidisciplinary Systemsacross the Internet Heřman Mann Computing and Information Centre Czech Technical University in Prague**Tutorial objectives**After attending this tutorial you should be able to: • understand the difference between various approaches to modeling and their suitability to different tasks • be able to apply the concepts of multipole modeling in different physical domains • be motivated to try the simulation software system DYNAST freely accessible across the Internet • be aware of the importance of physical-level simulation for reliable control design • be prepared to introduce a unified approach to engineering dynamics at you school (if you are a teacher) • interested in visiting the DynLAB web-based course on modeling and simulation (to be fully completed soon)**Kernel engineering tools**Modeling = procedure to simplify investigation of their dynamic behavior Simulation = imitation of dynamic behavior of real systems Analysis = relating system behavior to a changing variable or parameter Diagnostics = indicating the reason for a system failure Why engineers need these tools? • to better understand behavior of existing dynamic systems • to predict, verify and optimize behavior of designed systems • to detect, localize and diagnose faults in engineering products**Multidisciplinary approach**Contemporary engineering crosses borders between traditional disciplines: • different physical domains • electrical, magnetic, mechanical, fluid, thermal, ... • different levels of modeling abstraction • conceptual, functional, physical, virtual prototyping, (digital) control, diagnossis, ... • different levels of modeling idealization • (non)linear, time (in)variable, parameter (in)dependent, … • different model descriptions • equations, transfer functions, block diagrams, multipoles, ...**Efficiency of simulation**In the past: • efficiency of simulation was evaluated with regard to its demand of computer time only Nowadays: • the computer time is so inexpensive that the cost of simulation is dominated by the cost of personnel qualified to be able • to prepare the input data • to supervise the computation • to interpret the results Therefore: • efficient simulation software should provide • automated equation formulation • robust computational algorithms • user-friendly interface**Design procedure**• Design proceeds through several levels of abstraction • conceptual • functional (e.g., control design) • physical (e.g., real or virtual prototyping) • technological • Different system descriptions are used • geometric (blue • topological (geometric dimensions of subsystems are not shown, only their interactions) • behavioral (internal interactions of subsystems are not shown, only their external behavior) • Design proceeds through several levels of granularity (perpendicular to the design-space diagram)**Design space**design space trajectory of ideal design procedure (real one in many loops) blocks multipoles**Modeling & simulation procedure**• System definition • system separation from its surroundings • system decomposition into subsystems • identification of subsystem energy interactions • Model development • subsystem abstraction and idealization • identification of subsystem parameters • Formulation of • equations for subsystems • equations for subsystem interactions • combined and reduced equations • Equation solution • Interpretation of the solution**Simulation using Simulink**• System definition • system separation from its surroundings • system decomposition into subsystems • Model development • subsystem abstraction and idealization • parameter identification • Formulation of • equations for subsystems • equations for subsystem interactions • combined and reduced equations • Composition of a block diagram • Block-diagram analysis • Interpretation of the solution**Block diagram applications**Graphical representation of • causes-effects relations • inputs: causes • outputs: effects • explicit equations • inputs: independent variables • outputs: dependent variables • control structures • inputs: excitations, disturbances • outputs: desired variables**Copying lathe (1)**Geometric description**Copying lathe (2)**force exerted by cylinder master-shape waveform workpiece-shape waveform Behavioral description (block diagram for control design)**Copying lathe (3)**source of master- shape waveform r source of pressure cylinder mass F model of workpiece resistance slide-bed friction Topological description (multipole diagram for physical design)**Multipole diagrams**• can be set up based on mere inspection of the modeled real systems without any equation formulation or block-diagram construction • equations underlying the system models can be not only solved, but also formed automatically by the computer • they project geometric configuration of real dynamic systems onto their topological configuration • they portray graphically energy interactions between subsystems in the systems • they can be combined with block diagrams, which represent a special case of multipole diagrams)**Multipole modeling**• Principles of multipole modeling • Concept of across and through variables • Postulates of continuity and compatibility • Advantages of multipole modeling**Investigation of dynamic behavior**Dynamic behavior of a dynamic system is governed • by the flow of energy and matter between subsystems of the system and between the subsystems and the surroundings • by storing energy in the subsystems or releasing it later as well as by changes from one form to another. Therefore, before starting any dynamic investigation of a system we should clearly • separate the system from its surroundings • decompose the system into its disjoint subsystems**Multipole models**Multipole model approximates subsystem mutual energy interactions assuming that • the interactions take place just in a limited number of interaction sites formed by adjacent energy entries into the subsystems • the energy flow through each such entry can be expressed by a product of two complementary power variables**Multidisciplinary system (2)**Subsystems are separated by energy boundaries, sites of energy interactions are denoted by small circles**Multidisciplinary system (3)**Energy interactions between subsystems are characterized exclusively by energy flows through the sites of interactions at the energy boundaries**Multidisciplinary system (4)**The energy boundaries are detached and the energy interactions are interconnected with the energy entries of subsystems by ideal links**Multipole constitutive relation**5 - pole across variables through variables • Each multipole can be characterized by a constitutive relation between its across and through variables expressed by means of a combination of • physical elements • blocks • equations • look-up tables**Measurement of variables**Direct measurement of through variables requires including the measuring instrument between disconnected adjacent energy entries Across variables are measured between distant energy entries without disconnecting them**a**b Through variables a, b, c : a + b + c = 0 c Postulate of Continuity**b**a c Postulate of Compatibility Across variables a, b, c : a + b + c = 0**Reference across-variables**Measurement of reference across variables**Additional advantages**• multipole models can be developed once for the individual subsystems and stored to be used any time later • this job can be done for different types of subsystems by specialists in the field • submodels can be represented by different descriptions suiting best to the related engineering discipline or application • submodel refinement or subsystem replacement can be taken into account without interfering with the rest of the system model • mixed-level modeling is allowed**Mechanical systems**• Translational systems • Rotational systems • Coupled mechanical systems • Rotary-to-rotary couplings • Rotary-to-linear couplings • Linear-to-linear couplings • Planar systems**Motor on vibration isolator**stop characteristic**Rotary-to-rotary coupling**Coupling ratio: Power consumption: Pure transformer**Coupling ratio:**Power consumption: Coupled gears Pure transformer**Model**Gear trains (part 1)

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