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Efficient Modeling and Simulation of Multidisciplinary Systems across the Internet

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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)