Stepping Motor Control Using Iterative Root-Finding
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Solution Overview
Problem
Existing speed control methods for stepping motors either increase circuit size and processing time due to precise calculations based on physical theory or compromise on accuracy with approximate calculations, leading to potential vibrations and memory capacity issues, making them unsuitable for applications like medical robot hands.
Innovation Solution
A motor control apparatus using a calculation unit that applies an iterative root-finding procedure, specifically Newton's method in two stages, to determine step times based on a theoretical formula, reducing the need for complex calculations like cubic root calculations and minimizing circuit size and processing time while maintaining high accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If speed control is performed according to calculation based on physical theory, then control precision is improved, but circuit size and processing time increase
Solution Approach 1:
The patent replaces complex physical theory calculations (involving square root and cubic root calculations) with an iterative root-finding procedure using Newton's method. This substitution transforms the mechanical/computational system from direct complex calculation to iterative approximation, reducing circuit complexity while maintaining control precision for stepping motor speed control.
Solution Approach 2:
The patent changes the calculation approach by introducing an iterative parameter-based method. Instead of directly computing complex roots, the system uses Newton's method to iteratively converge on the solution by updating parameters (step time, acceleration rate) based on the derivative of the position function, thereby simplifying the computational requirements.
2Device complexity
If approximate calculation is used for speed control, then circuit size and processing time are reduced, but control accuracy decreases causing vibrations and memory capacity issues
Solution Approach 1:
The patent replaces approximate calculation methods with an iterative root-finding procedure that converges to the accurate solution. Newton's method is used to iteratively compute the step time by finding the root of the position function, providing high accuracy without requiring complex direct calculation circuits or large memory capacity for pre-stored tables.
3Measurement precision
If data such as acceleration and deceleration pattern data are stored in memory, then speed control accuracy is improved, but memory capacity increases with enhancement of micro-step drive accuracy
Solution Approach 1:
The patent extracts the need for large memory storage by implementing real-time iterative calculation. Instead of storing pre-computed acceleration and deceleration pattern data in memory, the system calculates the required values on-demand using Newton's method, extracting only the essential calculation logic and removing the memory burden while maintaining micro-step drive accuracy.
Data Source
AI summary
A motor control apparatus that controls a stepping motor includes a calculation unit configured to determine a time with respect to a distance based on a theoretical formula expressing a parameter in an acceleration period or deceleration period of the stepping motor. The calculation unit includes a first calculation unit and a second calculation unit. The first calculation unit is configured to apply an iterative root-finding procedure to a distance which is a function of a time included in the theoretical formula to determine the time with respect to the distance of the n-th step expressed using a reciprocal of a derivative of the function. The second calculation unit is configured to apply the iterative root-finding procedure to the reciprocal of the derivative to determine the reciprocal of the derivative at a time when the first calculation unit determines the time with respect to the distance of the n-th step.