Non-linear Model Calculation via State Variable Coefficients
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Solution Overview
Problem
Existing methods for calculating non-linear characteristics of non-linear devices are limited by the need to estimate non-linear elements and structures, which restricts accuracy and is dependent on prior knowledge of the system.
Innovation Solution
A non-linear characteristic calculating method that uses a non-linear model formed by changing constant coefficients in a linear state space representation into functions of one state variable, allowing for the representation of a wide range of non-linearities without estimating the non-linear elements and structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If structure estimation method is used to estimate non-linear elements and structure, then the non-linear system can be identified, but the estimation accuracy is limited by the range of non-linear elements and structure assumed in advance
Solution Approach 1:
The patent transforms the non-linear characteristic calculation from a discrete structure estimation approach to a continuous parameter transformation approach. By changing constant coefficients in a linear state space representation into functions of one state variable, the method continuously adjusts model parameters to match non-linear behavior, achieving high accuracy without limiting the range of applicable non-linear elements and structures.
2Ease of manufacture
If structure estimation method is used, then non-linear elements can be estimated, but prior knowledge and insight into the system are required to construct an effective database
Solution Approach 1:
The patent enables the non-linear model to self-adapt by transforming linear state space coefficients into functions of state variables. The model automatically captures non-linear characteristics through parameter transformation without requiring external expertise or preconstructed databases, making the system self-sufficient and eliminating the need for prior knowledge.
Solution Approach 2:
The transformed non-linear model serves multiple functions: it can represent various types of non-linear devices (amplifiers, mixers, etc.) with different non-linear characteristics using the same mathematical framework. This universal approach eliminates the need for device-specific databases or expert knowledge for each particular system.
3Reliability
If Volterra series is used for non-linear characteristic calculation, then weak non-linearities can be represented, but the method is limited to limited-order series expansions
Solution Approach 1:
The patent introduces dynamic parameter transformation where constant coefficients become functions of state variables. This dynamic approach allows the model to adapt to both weak and strong non-linearities by continuously adjusting parameters based on the current state, overcoming the static limitation of fixed-order Volterra series expansions.
Solution Approach 2:
By transforming coefficients from constant to state-variable-dependent functions, the method extends the applicable range from weak to strong non-linearities. The parameter transformation naturally handles different orders of non-linearity without requiring separate models or truncation, providing both accuracy for weak non-linearities and versatility for strong non-linearities.
Data Source
AI summary
In this non-linear characteristic calculating method, a non-linear characteristic of a non-linear device is calculated using a non-linear model consisting of non-linear equations obtained by changing constant coefficients of a linear state space representation that are also coefficients of a transfer function into functions of one state variable.