Mathematical and computational (digital twin) models of physical systems: motivation, practical use

This introductory video for novices presents the concepts of models of physical systems in continuous time and their main applications as a motivation for further detailed study of them (in other materials).
Apart from reduced "physical" models (prototypes), engineering uses mathematical models in the form of differential equations, and computational models (sometimes named as 'digital twin', in today's lexicon 'full of hype wording' for a 70-year old concept) are also used as tools to get things to work as intended, prescribed in some technical specifications in an engineering project.
Specifically, the models can be used in the project phase to design the system and perform computer simulations of its behavior before its construction.
Once the system has been built, a computational model can be executed to check the effect of certain maneuvers before performing them on the real physical system at the cost of materials, energy, or risk to people or goods. It can also be used to simulate the signal evolution in time for signals for which actual physical sensors are unavailable (this application is called an {observer} in control theory).
Lastly, it can be used to adjust constant parameter values so that the simulation looks as close to the experiment as possible. If those values are abnormal, then a fault has been detected.
Finally, the video describes the basic ideas of control system design based on these models.
Obviously, the details of all the above concepts and use cases constitute the core of bachelor's and master's courses in Systems Engineering, Control, Robotics, etc., which this video gives a glimpse of.
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#controlengineering #industrialengineering #simulation
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Antonio Sala
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