# Stable Rules Definition for Fuzzy TS Speed Controller Implemented for BLDC Motor
## 1 Introduction
The electronic commutator works with no physical connection between the stator and rotor (a lack of brushes). In order to make the motor rotate properly, information about the current rotor position needs to be given to the microcontroller unit. In modern BLDC motor controllers, this is usually realized by receiving information from Hall sensors located inside the motor. More advanced devices are based on the fact that in a specific time period the current flows only through two of three phases. Therefore, it is possible to deduce a current rotor position based on calculating the back electromotive force induced on the unused phase [13; 14]. Having received the rotor position, it is compared by a microcontroller with the implemented switching tables. These are used to define which of the six transistor switches need to be open or closed (based on the current rotor position) in a specific time window to make the motor rotate in the desired direction. There are many types of BLDC motor controllers available on the market. This allows the user to choose an appropriate controller for the project to be performed. No matter what kind of project is being realized, one can find a proper controller for its requirements, e.g., a Radio-Controlled  
Figure 1: The concept of an electric drive with a BLDC motor. (RC) model, electric scooter, automotive industry application, or large control cabinet for a high-power BLDC motor [15; 16; 17; 18; 19]. Moreover, the constant improvement of microcontrollers ensures that a variety of hardware solutions are available on the market. Depending on the designed application and initial requirements of the project, it is possible to choose between both amateur and professional microprocessors. Even a simple programmable device, due to its computational capabilities, can provide enough power to handle the BLDC commutation process [20; 21]. Furthermore, modern Advanced RISC Machine (ARM) processors ensure a perfect combination of computational capabilities while fulfilling the assumption of a low-cost solution. These devices are capable of running even complicated algorithms while handling the BLDC commutation process simultaneously [22; 23]. Due to the constantly increasing interest in ARM processors, manufacturers offer BLDC motor controllers in the form of dedicated shields [24]. Additionally, demanding applications are often handled by modern digital signal processors, which are a convenient way to run a variety of advanced algorithms [25; 26; 27]. The most sophisticated implementations (e.g., BLDC neural speed controllers) are often executed with the use of parallel computing ensured by field-programable gate array (FPGA) modules [28; 29; 30]. However, in terms of testing and developing rapid-prototyping systems, FPGAs are widely used as well [31]. Despite the fact that classic control structures (e.g., PID) are incredibly popular methods in modern industry, it is well known that they are not convenient in the context of nonlinear systems. Moreover, the values of the object parameters can fluctuate over time. Using conventional techniques, the precision of control is difficult to ensure. This is the point at which fuzzy logic becomes a reasonable solution. It is by definition a branch of mathematics that was designed for describing uncertain objects. The main goal while creating fuzzy logic principles is to obtain a tool capable of modeling nonlinear phenomena, which are usually hard to describe with mathematical equations. One of the most important parts of data processing in a fuzzy model is the rule base--defined using the designer's experience and knowledge. Considering the fact that, nowadays, fuzzy logic may be used in many fields, it is also widely implemented in control systems, in the form of a fuzzy logic controller [32; 33; 34; 35]. The main idea of these controllers is to create a dependency between the input signals and the output of the controller using predefined rules.