Recursive modular modelling methodology for lumped-parameter dynamic systems.

Area of Science:

• Systems Engineering
• Mathematical Modeling
• Control Theory

Background:

• Lumped-parameter dynamic systems often exhibit multilevel modularity.
• Existing modeling techniques can be complex and difficult to reconcile.
• A unified approach is needed to handle hierarchical system structures.

Purpose of the Study:

• To propose a novel recursive modeling methodology for lumped-parameter dynamic systems.
• To develop a general algorithm based on a fundamental theorem for recursive projection operator computation.
• To apply this methodology to create a recursive algorithm for state estimation.

Main Methods:

• Representing systems by hierarchies of mathematical models with increasing complexity.
• Developing a general recursive modeling algorithm based on a theorem for computing projection operators.
• Utilizing orthonormalization, orthogonal complements, and generalized inverses for computations.
• Applying the methodology to the Udwadia-Kalaba equation for recursive algorithm development.

Main Results:

• A general recursive modeling methodology is proposed, integrating existing techniques.
• A fundamental theorem provides conditions for recursive projection operator computation.
• The novel methodology yields a recursive algorithm identical to a Kalman filter for static process state estimation with noiseless measurements.

Conclusions:

• The proposed hierarchical modeling approach offers a flexible and powerful method for dynamic systems.
• Recursive computation of projection operators is feasible and simplifies complex modeling.
• The developed algorithm provides an efficient way to estimate system states under constraint satisfaction.