# Parameter Tuning of PI Control for Speed Regulation of a PMSM Using Bio-Inspired Algorithms
## 1 Introduction
Thanks to this research, the behaviors of some biological species have been emulated, such as birds, fish, ants, fireflies, whales, bats, gray wolves, termites, among others. These search algorithms are based on a randomly generated population that moves continuously around a search space using variation operators. In [25] the cuckoo search algorithm (CSA) is modeled on the aggressive way of reproduction of the cuckoo bird and the characteristic flight patterns of other types of birds. In reference [26] the so-called bat algorithm (BA) is proposed that mimics the phenomenon of echolocation of small bats to reach their prey. [PERSON] et al [27] proposed an algorithm based on the behavior of the African buffalo that has the ability to organize itself through two basic sounds for finding solutions. Another algorithm based on swarm intelligence is the Artificial Bee Colony (ABC), in which the honeybee's food search is imitated to solve problems of numerical optimization, both the ABC and the improved algorithms that derive from it have been applied in the training of neural networks [28; 29]. There are also meta-heuristics that do not necessarily have a real inspiration, where simple mathematical functions can also be used to design optimization algorithms in this field. One of these is the sine cosine algorithm (SCA), which uses the sine and cosine functions to explore and exploit the space between two solutions in the search space in order to find better solutions. Several bioinspired algorithms have been used for the calculation of conventional controller gains are detailed in different works. In reference [30], the BA is used to optimize a PID robust controller that takes care of maintaining a constant voltage level at the load of a DC-DC converter. Similarly, in reference [31] a BA searches for the gains of a PI controller to calculate the maximum power point of a photovoltaic system that supplies the current and voltage for a switchable reluctance motor. In the same way, in reference [32] the performance of the frequency control strategy of a hybrid power system based on the CSA is investigated. The system's generator units are used in hybrid vehicles. Here CSA-optimized PI/PID controllers are used for control of wind turbine generators, a diesel engine generator, and a battery power storage system to adjust total active power generation according to load demand. Also, in reference [33] we have found the use of the CSA for finding optimal tuning parameters for the I-PD and PI-PD controllers, which are applied for speed control of DC motors in the presence of load disturbances. In reference [34], FPA is used for the calculation of the gains of a PI controller of two degrees of freedom, to control of the heat flow experiment. Also, in reference [35], it is used for the optimization of a PI-PD controller in cascade within a multi-area power system. The BBO algorithm is also found in reference [36] where the comparison is made between the use of BBO for the optimization of PI and PID controllers, for handling of a thermal hybrid system composed of a Dish-Stirling solar thermal and a wind turbine. This type of strategy is also present in the control of electrical devices as in reference [37], where a PI controller is optimized for the control of the voltage of a three-phase rectifier. In reference [38] SCA is used along with a PI controller for the optimal control of a capacitive energy storage system, just as in reference [39] a hybrid system is used that consists of the calculation of optimal gains of a PID controller through the use of SCA and fuzzy logic for frequency control in an autonomous power system. The purpose of this paper is to compare five different nature inspired algorithms to adjust the parameters of the PI controllers in order to determine which provides better performance when applied to the speed control of a PMSM. Algorithms inspired by the nature of BA, BBO, CSA, FPA and SCA are tested and the result is compared to show which one is more useful for speed regulation tasks.