Page 37 - The Mechatronics Handbook

A general procedure for theoretical modeling of lumped parameter processes can be sketched as follows
[19].
1. Definition of flows
• energy flow (electrical, mechanical, thermal conductance)
• energy and material flow (fluidic, thermal transfer, thermodynamic, chemical)
2. Definition of process elements: flow diagrams
• sources, sinks (dissipative)
• storages, transformers, converters
3. Graphical representation of the process model
• multi-port diagrams (terminals, flows, and potentials, or across and through variables)
• block diagrams for signal flow
• bond graphs for energy flow
4. Statement of equations for all process elements
(i) Balance equations for storage (mass, energy, momentum)
(ii)Constitutive equations for process elements (sources, transformers, converters)
(iii)Phenomenological laws for irreversible processes (dissipative systems: sinks)
5. Interconnection equations for the process elements
• continuity equations for parallel connections (node law)
• compatibility equations for serial connections (closed circuit law)
6. Overall process model calculation
• establishment of input and output variables
• state space representation
• input/output models (differential equations, transfer functions)
An example of steps 1–3 is shown in Fig. 2.7 for a drive-by-wire vehicle. A unified approach for processes
with energy flow is known for electrical, mechanical, and hydraulic processes with incompressible fluids.
Table 2.4 defines generalized through and across variables.
In these cases, the product of the through and across variable is power. This unification enabled the
formulation of the standard bond graph modeling [39]. Also, for hydraulic processes with compressible
fluids and thermal processes, these variables can be defined to result in powers, as seen in Table 2.4.
However, using mass flows and heat flows is not engineering practice. If these variables are used, so-
called pseudo bond graphs with special laws result, leaving the simplicity of standard bond graphs. Bond
graphs lead to a high-level abstraction, have less flexibility, and need additional effort to generate
simulation algorithms. Therefore, they are not the ideal tool for mechatronic systems [35]. Also, the
tedious work needed to establish block diagrams with an early definition of causal input/output blocks
is not suitable.
Development towards object-oriented modeling is on the way, where objects with terminals (cuts) are
defined without assuming a causality in this basic state. Then, object diagrams are graphically represented,
retaining an intuitive understanding of the original physical components [43,44]. Hence, theoretical
modeling of mechatronic systems with a unified, transparent, and flexible procedure (from the basic
components of different domains to simulation) are a challenge for further development. Many compo-
nents show nonlinear behavior and nonlinearities (friction and backlash). For more complex process
parts, multidimensional mappings (e.g., combustion engines, tire behavior) must be integrated.
For verification of theoretical models, several well-known identification methods can be used, such as
correlation analysis and frequency response measurement, or Fourier- and spectral analysis. Since some
parameters are unknown or changed with time, parameter estimation methods can be applied, both, for
models with continuous time or discrete time (especially if the models are linear in the parameters)
[42,45,46]. For the identification and approximation of nonlinear, multi-dimensional characteristics,

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