# Stable Rules Definition for Fuzzy TS Speed Controller Implemented for BLDC Motor
## 1 Introduction  
The application of artificial intelligence (AI) elements has become the most common trend in modern electric drives. This is mainly due to the requirements of Industry 5.0, which often promotes the autonomous, robust, and adaptive operation of machines and robots. This machinery should be able to reproduce the desired dynamics without the intervention of a dedicated operator. The machinery's operation in various conditions is the most important and inextricable requirement. Different ideas have provided solutions to this issue, each having advantages and disadvantages. Neural network controllers [1, 2, 3] are commonly described in the literature; however, the most notable disadvantage is the necessity for the parallel computing of the neurons in a single layer. This leads to more powerful hardware and, therefore, cost increases. On the other hand, there are standard PI controllers or state controllers enhanced by tunable parameters. This adaptation can be achieved with different algorithms, leading to varied complexity and efficiency. A common problem of such controllers is the stability issue [4, 5, 6]. Modern industry is a meaningful concept whose main role is to ensure the sustainable development of the economy and the dynamic growth of the quality of people's lives. In almost every single factory there are plenty of essential devices that use electric drives. Coal mines, heavy elevators, HVAC control systems, small tools, printers, and CNC machines all use electric drives. A strong desire to generate high-quality products has forced factories tobecome more productive. The key to ensuring a reasonable production rate is to minimize the risk of breakdowns or outages caused by electric drive systems. One of the biggest weaknesses of conventional brushed DC motors is their maintenance. Because of the friction caused by brushes, classic DC motors require the periodic exchange of certain components [7; 8]. Comparing both constructions, it is unquestionable that the brushless DC (BLDC) motor has a simplified internal structure. Furthermore, the lower number of internal elements in the BLDC motor allows manufacturers to design a motor with a smaller chassis than its conventional equivalent with the same power. This has a huge influence on decreasing the electromagnetic noise generated by the motor. From another point of view, the construction of the BLDC motor is a critical feature that ensures much better dynamics and a higher efficiency compared to brushed motors, with improvements of up to 95%. Because of this, it is obvious that BLDC motors provide the user with an opportunity to control their speed and position at a precise level. This makes these machines a perfect choice as the main drive in popular applications (e.g., CNC machines or robots) [9; 10]. The biggest and most noticeable disadvantage of brushless motors is the necessity of using a dedicated controller to ensure correct operation. Nowadays, brushless electric motors can be distinguished as one of the most important parts of electric drives and can be divided into permanent-magnet synchronous motors (PMSMs) and BLDC motors. In spite of their similar mechanical constructions (stator windings and permanent magnets placed on the rotor), a huge difference between them can be noticed while developing a proper control system. Due to the fact that the BLDC motor works with a direct current, the shape of the back electromotive force is trapezoidal. Because of this, a different technique of control is required. The most essential element of a typical drive with a three-phase BLDC motor is a power electronic controller--a three-branch inverter module, with two switches in each branch [11; 12]. The internal structure of a typical drive with a BLDC motor is shown in Figure 1.  
The goal is to make the BLDC motor rotate properly in both directions. For this purpose, a particular inverter is used. It is a substitute for the mechanical commutator used in brushed DC motors.