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

Abstract

<jats:p>&lt;span lang="EN-US"&gt;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. &lt;/span&gt;</jats:p>

Phase Loss Detection Using Current Signals: A Review

“…A similar method, which uses root mean square (RMS) values instead of averaging, was proposed in [86,87]. Calculation of square roots is a high load for the microcontroller even when using acceleration techniques [88,89], so it is desired to avoid it if possible. Since there is no big difference between the averaging and RMS-based methods, the latter will not be discussed separately.…”

Fast Square Root Calculation without Division for High Performance Control Systems of Power Electronics

“…where the authors suggested to use two variables method. This method was considered in detail in [38], which reported poorer performance, compared to other algorithms. An interesting approach was proposed in [39], where the authors suggested to use sixteen intervals of approximation for 16-bit numbers.…”

“…The most perspective algorithms for the calculation of square roots were implemented in code, analyzed and compared in [38], which reported that the Newton-Raphson algorithm was one of the fastest, despite usage of divisions. Therefore, we included the Newton-Raphson algorithm in our research as the main competitive technique.…”

Novel seed generation and quadrature-based square rooting algorithms

“…Computing the square root is highly useful in a variety of science and engineering areas. In particular, it is an essential operation in Digital Signal Processing (DSP) and many applications in control systems 1 , 2 . Indeed, the IEEE 754 standard, revised in 2019, classifies the square root operation as one of the five basic arithmetic operations besides addition, subtraction, multiplication, and division 3 .…”

“…Subtractive methods (a.k.a digit-recurrence or digit-by-digit methods) compute the square root directly one digit at a time, starting from the most significant digit. The main advantages of such methods are the absence of division operation and the generation of accurate results 1 . On the other hand, the downside of this type of algorithm is its slow convergence resulting in increased computational time 1 .…”