Physical modeling

The term physical modeling ( PM for short ) comes from systems engineering and generally describes the procedure for using basic physical functions and modules to formulate the behavior of complex systems in mathematical functions and to make them calculable. In contrast to abstract mathematical modeling, there is a natural relationship between model and reality. Physical influences from outside can thus flow into calculations carried out with such models simply and directly as a variation.

Applications

simulation

The PM is z. B. used in the development of mechanical or electronic systems. By forming the model of an electric motor with all mechanical effects such as damping and detent, z. B. the effect of an electronic control can be examined without building and testing it.

In particular, deficits and artifacts of systems such as non-linearity, discontinuity and sporadic effects and defects can be easily reproduced and taken into account when designing control functions. Examples would be the effect of dirty and bent shafts in mechanical drives, the saturation behavior of magnetic materials in electromechanical motors, the partial oscillations of pistons and cylinders in mechanical motors, the distortion effect of oscillating mirrors in laser technology.

emulation

Physical models can also be used within the framework of estimation theory to estimate the behavior of a system in real time by calculating its reaction to external influences on the basis of the physical formulas and comparing it with measurement results. The inversion of the formulas allows conclusions to be drawn about internal states in the system without being able to measure them directly. Examples would be the behavior of the heat flow in a solid body, where measuring points can only be attached to the outside of the edge, or the behavior of the electronics and mechanics of an aircraft turbine.

The results of the calculations can be used permanently to observe the system, to check its function and to ensure that it is still working correctly within its operating limits. Furthermore, the electronic control of such systems can be influenced permanently and favorably.

generation

By simulating physical objects and their behavior, complex system responses can also be generated and used directly outside of theoretical investigations, such as the digital generation of vibrations in SDR and DDS . By mapping acoustic vibrations in musical instruments, the sound-forming and sound-changing behavior of vocal cords, tubes, whistles and resonance bodies can be calculated, as is the case with digital organs, digital violins or, in general, virtual sound generation with synthesizers .

reconstruction

By simulating and varying the physical behavior of sensors, reflectors and absorbers, conclusions can be drawn retrospectively about the internal structure from measurement data and primary data or primary structures can be recalculated. Examples are 3-dimensional astronomical imaging by varying light diffraction and absorption, 2-dimensional reconstruction of a laser image by varying lens effects and the recovery of 3-dimensional body structures by varying tissue absorption in 3D X-rays .

Tools

Simulators

Simulators are used during the development of a model to model and test the behavior. Examples:

PSpice : A simulator for electronic circuits that can process your own models in C. With this, on the one hand, electronic circuits are generated and designed by modeling the surrounding physics with which the circuit is to interact. On the other hand, electronic components can be used to generate an electronic substitute model of physics with which the simulator can also process non-electronic processes

Spice-AMS: A simulator for mixed analog-digital systems in VHDL-AMS, which works similarly to pSPICE, but provides explicit support especially for mechanical components.

Simulink: A simulator for the MATLAB environment, for function-logic and abstract mathematical models with which electrical and mechanical system models can be built.

ModelSIM: A simulator for digital circuits in VHDL and Verilog , with which the behavior of digital logic circuits is examined. Analog functions such as oscillators and PLLs are simulated for the virtual connection of analog components via ADCs . Influences of temperature and voltage changes on the switching times can thus be calculated.

Platforms

Different hardware platforms are used to calculate models in real time, depending on the application and complexity. Examples:

Computer network

For the calculation and forecast of the weather, several mainframe units (clusters) are interconnected, which in turn calculate a partial section of a 4D space (a spatial section for a specific period of time). It is based on physical models that take pressure, temperature, humidity, currents and other weather-relevant parameters into account. Several approaches with different boundary conditions and initial parameters are counted against each other several times.

Single pc

With MATLAB and Simulink, which are mainly used offline, slow processes such as water currents can be recorded directly in real time, flood behavior can be estimated on the basis of the recorded flow profiles and specifications can be made for setting flood barriers. PC-based platforms are used in the field of radar surveillance to calculate dangerous objects in the flight path. In air traffic control one wants to use it to detect collisions - in the military sector it is used to warn soldiers.

Digital signal processors

With the help of DSPs , the oscillation of drive shafts in the vehicle is continuously calculated and the optimal coupling time is determined. Electronic motors and servos are controlled in the best possible way so that they work quietly and quickly, as well as safely when they age. DSPs are also used for acoustic modeling in electronic music devices. In large-capacity aircraft, DSPs constantly calculate the possible flight paths and automatically warn of possible collisions, in addition to external monitoring.

FPGA

FPGAs are of great importance in real-time modeling . Due to their structures, they are ideally suited to simulating and calculating several physical processes in parallel. FPGAs are z. They are used, for example, to compensate for the vibrations of optical lenses and reflectors in cameras and seeker heads by calculating a number of possible subsequent images in real time and comparing them with the real subsequent image in order to track the vibrations and provide optimal exposure times and valid image sections for object recognition to find. Thus, the flight path of fast objects in the image can be measured very precisely. In addition, for 3-dimensional objects, the 2D projection in the image can be estimated and their movement determined.