Review of fast square root calculation methods for fixed point microcontroller-based control systems of power electronics

Abstract

Square root calculation is a widely used task in real-time control systems especially in those, which control power electronics: motors drives, power converters, power factor correctors, etc. At the same time calculation of square roots is a bottle-neck in the optimization of code execution time. Taking into account that for many applications approximate calculation of a square root is enough, calculation time can be decreased with the price of precision of calculation. This paper analyses existing methods for fast square root calculation, which can be implemented for fixed point microcontrollers. It discusses algorithms’ pros and cons, analyses calculation errors and gives some recommendations on their use. The paper also proposes an original method for fast square root calculation, which does not use hardware acceleration and therefore, is suitable for implementation at a variety of modern Digital Signal Processors, which have high-speed hardware multipliers, but do not have effective dividers. The maximum relative error of the proposed method is 3.36% for calculation without division, and can be decreased to 0.055% using one division operation. Finally, the most promising methods are compared and results of their performance comparisons are depicted in tables.