Hybrid Square Root Algorithm for Electric Motor Control
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Solution Overview
Problem
Existing square-root extraction algorithms for Field Orientated Control systems in electric motors lack precision and speed, with known methods either being too slow or providing insufficient accuracy for modern control systems.
Innovation Solution
A method that calculates an initial approximate square root value using the Dijkstra algorithm and then corrects it to achieve 32 bits precision, combining the results to overcome the limitations of existing algorithms while maintaining computational speed comparable to Dijkstra's algorithm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Newton's iterative algorithm is used for square root extraction, then precision of 32 bits is achieved, but execution time becomes very slow
Solution Approach 1:
The patent segments the square root calculation into two distinct phases: a first phase using Dijkstra's algorithm to compute an initial approximation with limited precision (16 bits), and a second phase using Newton's iterative algorithm to refine this approximation to full precision (32 bits). This segmentation allows the system to benefit from both algorithms - the speed of Dijkstra's for the initial computation and the precision of Newton's for the final result, thereby resolving the contradiction between execution time and precision.
2Productivity
If Dijkstra's algorithm is used for square root extraction, then computational speed is high, but precision is limited to 16 bits
Solution Approach 1:
The patent applies preliminary action by using Dijkstra's algorithm to compute an initial approximation of the square root before applying the more precise but slower Newton's iterative algorithm. This preliminary computation provides a starting point that is already close to the final result, allowing the refinement phase to converge faster and reducing the overall computational burden while achieving high precision.
3Loss of time
If Turkowski algorithm is used for square root extraction, then execution time is reduced compared to Newton's algorithm, but precision and speed are still insufficient for modern control systems
Solution Approach 1:
The patent merges two different algorithms - Dijkstra's algorithm and Newton's iterative algorithm - into a hybrid approach. By combining the strengths of both algorithms (Dijkstra's speed for initial computation and Newton's precision for refinement), the patent achieves computational speed and precision that exceed what either algorithm can provide alone, thereby resolving the insufficiency of the Turkowski algorithm for modern control systems.
Data Source
AI summary
An embodiment is a method, and related system, to implement the square root extraction operation, which grants a 32 bits precision, which has high execution speed and is able to process a decimal radicand. An embodiment relates to a method for controlling an electric machine, comprising the detection of the value of at least one electrical quantity characterizing the machine operation and processing the detected value of said electrical quantity. The control method controls the machine operation on the basis of this processing. In particular the processing of the detected value of the electrical quantity comprises calculating a square root of a radicand value related to the detected value of electrical quantities. The calculation of the square root includes: calculating an approximated value of the square root, having a first precision, and then calculating a corrective value and combining said approximated value with said corrective value to obtain a square root value having a second precision greater than the first precision.