# Modeling Procedure For Mechatronic Systems

**Modeling Procedure**

Mathematical process models for static and dynamic behavior are required for various steps in the design of mechatronic systems, such as simulation, control design, and reconstruction of variables. Two ways to obtain these models are theoretical modeling based on first (physical) principles and experimental modeling (identification) with measured input and output variables.

A basic problem of theoretical\ modeling of mechatronic systems is that the components originate from different domains. There exists a well-developed domain specific knowledge for the modeling of electrical circuits, multibody mechanical systems, or hydraulic systems, and corresponding software packages. However, a computer-assisted general methodology for the modeling and simulation of components from different domains is still missing.

The basic principles of theoretical modeling for system with energy flow are known and can be unified for components from different domains as electrical, mechanical, and thermal.

The modeling methodology becomes more involved if material flows are incorporated as for fluidics, thermodynamics, and chemical processes

A general procedure for theoretical modeling of lumped parameter processes can be sketched as follows:

**1.**Definition of flows

**a) **Energy flow (electrical, mechanical, thermal conductance)

**b) **Energy and material flow (fluidic, thermal transfer, thermodynamic, chemical)

**2.**Definition of process elements: flow diagrams

**a) **Sources, sinks (dissipative)

**b) **Storages, transformers, converters

**3.**Graphical representation of the process model

**a) **Multi-port diagrams (terminals, flows, and potentials, or across and through variables)

**b) **block diagrams for signal flow

**c) **bond graphs for energy flow

**4.**Statement of equations for all process elements

**a) **Balance equations for storage (mass, energy, momentum)

**b) **Constitutive equations for process elements (sources, transformers, converters)

**c) **Phenomenological laws for irreversible processes (dissipative systems: sinks)

**5.**Interconnection equations for the process elements

**a) **continuity equations for parallel connections (node law)

**b) **compatibility equations for serial connections (closed circuit law)

**6.**Overall process model calculation

**a) **establishment of input and output variables

**b) **state space representation

**c) **input/output models (differential equations, transfer functions)

**Generalized Through and Across Variables for Processes with Energy Flow**