Variable Transport Delay Modeling for Dynamic Systems
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Solution Overview
Problem
Existing models of physical systems that require variable transport delays, such as fluid flow through pipes with varying velocities, are limited by assumptions of constant velocity, which restrict the accurate modeling of dynamic systems.
Innovation Solution
A variable transport delay system is developed, using an input signal and output signal with an instantaneous delay signal, where the delay is calculated through integration and interpolation methods, allowing for non-constant velocity conditions, and can be integrated into graphical block diagram environments like Simulink.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If constant velocity assumption is used in transport delay modeling, then the model is simple to implement, but it cannot accurately model dynamic systems with varying velocities
Solution Approach 1:
The patent transforms the static constant velocity model into a dynamic variable velocity model by introducing time-varying velocity functions v(t) and integrating them over time to compute transport delays. This allows the model to adapt to changing system conditions while maintaining mathematical tractability through numerical integration methods.
Solution Approach 2:
The patent changes the fundamental parameter from constant velocity to variable velocity by introducing time-dependent velocity functions. This parameter transformation enables the model to capture dynamic behavior of physical systems where transport speed varies over time, such as fluid flow through pipes with changing pressure or conveyor systems with variable speeds.
2Reliability
If variable velocity is introduced to model dynamic systems, then modeling accuracy improves, but computational complexity increases
Solution Approach 1:
The patent pre-computes and stores the integral of the velocity function as a position function p(t) = ∫v(t)dt before solving delay equations. This preliminary action transforms the complex variable velocity problem into a simpler root-finding problem, reducing computational burden during real-time simulation while maintaining accuracy.
Solution Approach 2:
The patent introduces an intermediary position function p(t) that mediates between the variable velocity input and the transport delay output. This intermediary transformation simplifies the mathematical relationship, allowing delay calculation through position matching rather than direct integration of variable velocity, thus reducing computational complexity.
3Productivity
If existing constant delay models are used, then computational efficiency is maintained, but the ability to represent real-world dynamic transport phenomena is limited
Solution Approach 1:
The patent creates a universal transport delay model that can handle both constant velocity (reducing to traditional models) and variable velocity cases. This multi-functional approach allows the same mathematical framework to represent diverse physical systems including fluid flow, material transport, and signal propagation, enhancing versatility without sacrificing efficiency for common cases.
Data Source
AI summary
A method, system and apparatus for generating a variable transport delay for use in modeling a dynamic system. The variable transport delay of the present invention may be calculated using a variety of means, including the use of a lookup table generated at a variety of time steps such that an accurate variable transport delay can be calculated by interpolation.