Discretizing Continuous Models Using System Inputs and Feedback Loops

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Solution Overview

Problem

Existing discretization techniques for continuous models fail to accurately represent system behavior due to neglecting connected systems, feedback loops, and rate conversions, leading to increased discretization error.

Innovation Solution

A technical computing environment (TCE) is used to discretize models by considering system inputs and outputs, including feedback loops and rate conversions, to generate discrete linear representations with reduced distance to continuous frequency responses, thereby improving accuracy.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If traditional discretization techniques are used, then the model can be executed on processors, but discretization error increases due to neglecting connected systems, feedback loops, and rate conversions

Engineering Contradiction:

Improveaccuracy of system behavior representationVSAvoiddiscretization error

Core Design Contradiction:

ReliabilityVSManufacturing precision

Solution Approach 1:

The patent applies feedback by incorporating feedback loops into the discretization process. The method identifies feedback connections in the continuous model and preserves them in the discrete model, ensuring that the discretized model accurately represents the original system's feedback mechanisms. This resolves the contradiction by maintaining reliability through feedback preservation while reducing discretization error.

Inventive Principle:

Principle #23Feedback

Solution Approach 2:

The patent segments the discretization process into distinct steps: identifying connected systems, identifying feedback loops, identifying rate conversions, and applying appropriate discretization methods to each segment. This segmentation allows the method to handle complex interactions systematically, improving accuracy while maintaining computational feasibility for processor execution.

Inventive Principle:

Principle #1Segmentation

Solution Approach 3:

The patent changes parameters by adjusting discretization methods based on the specific characteristics of connected systems, feedback loops, and rate conversions. Different discretization parameters and methods are applied to different parts of the model depending on their properties, thereby reducing overall discretization error while maintaining executability on processors.

Inventive Principle:

Principle #35Parameter changes

2Device complexity

If discretization is performed without considering connected systems and feedback loops, then computational complexity is reduced, but the accuracy of frequency response approximation deteriorates

Engineering Contradiction:

Improvediscretization process complexityVSAvoidfrequency response accuracy

Core Design Contradiction:

Device complexityVSMeasurement precision

Solution Approach 1:

The patent systematically identifies and preserves feedback loops in the discretization process. By detecting feedback connections in the continuous model and implementing appropriate discretization strategies for these feedback paths, the method maintains frequency response accuracy without excessively increasing computational complexity.

Inventive Principle:

Principle #23Feedback

Solution Approach 2:

The patent applies local quality by using different discretization methods for different parts of the model based on their specific characteristics. Connected systems, feedback loops, and rate conversions each receive tailored discretization treatment, optimizing the balance between computational complexity and frequency response accuracy for each local region of the model.

Inventive Principle:

Principle #3Local quality

3Productivity

If simple discretization methods are used, then processing speed is improved, but the ability to represent rate conversions and feedback loops accurately is lost

Engineering Contradiction:

Improvemodel execution speedVSAvoidsystem behavior simulation accuracy

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The patent segments the model into distinct components (connected systems, feedback loops, rate conversions) and applies efficient discretization methods to each segment. This segmentation enables the use of optimized algorithms that maintain both processing speed and simulation accuracy, resolving the contradiction between productivity and reliability.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent changes discretization parameters based on the specific requirements of different model components. For rate conversions and feedback loops, appropriate parameters are selected to maintain accuracy, while other parts of the model use more computationally efficient parameters, thereby balancing execution speed with simulation fidelity.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS10817629B2Discretization of a model of a system or a portion of the model using system inputs and outputs

Publication Date: 2020.10.27 MATHWORKS INC

AI summary

According to some possible implementations, a method may include determining one or more inputs to a model of a system and one or more outputs from the model. The method may include identifying a continuous portion of the model to be discretized. The method may include discretizing the continuous portion of the model, using at least one of a continuous linear representation for the model or a frequency response associated with the continuous linear representation, to generate a discrete linear representation for the continuous portion of the model. The method may include outputting information associated with the discrete linear representation to permit the continuous portion of the model to be implemented on one or more processors.