Problem No 2 on Analogous Systems - Mathematical Modelling of Physical Systems - Control Systems

TL;DR

Solving how to determine analogous electrical systems from mechanical systems using force voltage and force current analogies.

Transcript

hello friends in this video we are going to solve a problem on how to determine the analogous system of a mechanical system and this analog system we will derive it or determine it by first finding the mathematical model of the system writing the nodal equations for it and from those nodal equations we will determine the analogous system so let us ... Read More

Key Insights

• 🦾 Mechanical systems can be converted to analogous electrical systems using force voltage and force current analogies.
• ❓ Deriving the mathematical model and nodal equations are crucial steps in determining analogous systems.
• 🦾 Elements in mechanical systems like mass, damping, and stiffness have electrical equivalents in the analogous system.
• ⚾ Force current analogy connects elements based on their relationship to currents in the system.

Questions & Answers

Q: What is the first step in determining an analogous electrical system from a mechanical one?

The first step involves deriving the mathematical model of the system and drawing the nodal diagram to represent the system visually.

Q: What are the two analogies used to determine analogous electrical systems?

The two analogies used are force voltage analogy and force current analogy, which involve replacing mechanical elements with electrical equivalents.

Q: How are mass, damping, and stiffness elements translated in force voltage analogy?

Mass is replaced by inductance, damping by resistance, and stiffness by reciprocal capacitance, while displacements become charges and external forces become voltages.

Q: How is the analogous electrical system represented using force current analogy?

The relationships of capacitance, resistance, and inductance to the two nodes in the system are identified and a circuit is drawn to represent the analogous system using force current analogy.

Summary & Key Takeaways

• Explanation of how to determine analogous systems from mechanical to electrical.

• Process involves deriving mathematical model and writing nodal equations.

• Two analogies utilized: force voltage analogy and force current analogy.