Position Error Correction Using Power Functions for Fast Startup
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Solution Overview
Problem
Conventional position detection error correcting methods face delays in startup due to lengthy trigonometric function operations and limited storage capacity, especially when rapid changes in errors occur, making high-accuracy corrections difficult.
Innovation Solution
A position detection error correcting method that uses a series of periodic functions approximated by power functions to calculate correction values using four simple arithmetic operations, allowing for efficient startup and high-accuracy corrections with limited storage capacity by storing correction parameters in nonvolatile memory and calculating error correction values at startup.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If trigonometric function operations are performed multiple times for inverse Fourier transform at startup, then position detection error correction is achieved, but processing time becomes extremely long causing startup delay
Solution Approach 1:
The invention changes the mathematical parameter representation from trigonometric functions to power functions. By expressing the periodic function as G(θ) = θ^n instead of using sine/cosine series, the correction values can be calculated using simple arithmetic operations (multiplication and addition) rather than complex trigonometric computations, dramatically reducing processing time while maintaining correction accuracy
Solution Approach 2:
The invention substitutes complex computational mechanics (trigonometric function operations requiring multiple cycles) with simpler arithmetic mechanics (power function calculations). This replacement eliminates the need for iterative trigonometric computations while preserving the essential function of generating correction values for position detection errors
2Productivity
If trigonometric function operations are approximated using a table stored in random access memory, then work load is reduced, but the capacity of the random access memory decreases by a corresponding amount
Solution Approach 1:
The invention changes the computational parameter from requiring large lookup tables to requiring minimal storage. Power function calculations can be performed algorithmically with very small memory footprint, eliminating the need to store extensive trigonometric tables in random access memory while maintaining fast computation capability
Solution Approach 2:
The invention extracts only the essential correction parameters needed for power function calculation, removing the bulk data (trigonometric tables) that would consume random access memory capacity. This selective extraction allows fast processing without sacrificing memory resources
3Measurement precision
If ranges of detected positions to be corrected are uniformly distributed throughout the entire position detection range, then coverage is complete, but high-accuracy corrections are difficult in areas where rapid changes in error occur
Solution Approach 1:
The invention applies local quality by allowing the power function exponent n to vary based on the characteristics of error changes in different regions. In areas where rapid error changes occur, higher values of n can be used to capture the sharp variations, while in regions with gradual changes, lower values suffice, thereby optimizing correction accuracy locally rather than using a uniform approach
Data Source
AI summary
A position detection error correcting method that corrects position detection errors using a limited storage capacity, by calculating position detection error correction values by four simple arithmetic operations at startup to reduce a startup time delay and consumption of a storage capacity even when a portion containing steep error variations exists. Detection error correction values of a position detector are expressed by a correction function using a periodic function, and correction parameters of the correction values are stored in advance in a non-volatile memory. At startup, these correction parameters are read out, and a position detection error correction value corresponding to each detected position is calculated and stored in a random access memory. The output position detection error correction value detector corresponding to each detected position is read out from the random access memory and a corrected detected position value corrected for the detected position value error is calculated.