# Parameter Tuning of PI Control for Speed Regulation of a PMSM Using Bio-Inspired Algorithms
## 1 Introduction  
Recently, the permanent magnet synchronous motor (PMSM) has achieved notoriety in industrial applications (e.g., electric vehicles [1], computer numerical control machines [2], industrial robots [3]). Among its most relevant features are a fast dynamic response, compact size, high power density, high torque capacity and low losses due to heat dissipation, which make it highly efficient. The performance of the PMSM can be affected during operation by the non-linearity of the dynamic system, some parametric variations and bounded perturbations of the load torque, which the controller must be able to overcome in real-time operation by always considering the physical constraints of the machine [4; 5; 6]. In the literature, several speed-control schemes have been proposed for PMSM, where a proper performance in tasks of regulating the speed of the rotor is achieved [7; 8; 9; 10; 11; 12]. Some controllers use adaptive schemes [8; 13; 14; 15], artificial neural networks (ANNs) [5; 11; 12; 16], sliding mode control (SMC) based techniques [17; 18; 19; 20], and fuzzy logic [5; 10], to name a few methods. Sliding-modes based control provides a high disturbance rejection and a low sensitivity to parametric variations. However, the well-known phenomenon of chattering is also presented, which leads to low precision, warm-up in electrical power devices and wear in motor's mechanical parts. With the use of fuzzy logic a good performance is presented but it has the problem that the fuzzification rules, the inference mechanism, and the defuzzification operations are not clear and, in addition, they demand high computational processing capacity. Where using ANNs, a large amount of data and various operating scenarios of the plant are required for offline training. Also, it's necessary to have a device with a high processing capacity to manipulate all of the data, resulting in greater cost and system complexity. The conventional integral proportional controller (PI) is the dominant choice in most industrial applications due to its easy implementation. However, PI controllers are unable to offer effective solutions against different external disturbances and parametric variations. In this paper, we propose the use of stochastic optimization algorithms based on evolutionary and particle intelligence techniques, as well as mathematical functions for calculation of the controller gains, in order to improve and optimize the closed-loop system performance under different operating conditions. Nature inspired algorithms, stochastic algorithms, and algorithms based on population behavior are inspired by two principles: (1) nature; (2) the environment. The first aspect is [PERSON]'s evolutionary theory, where only the strongest individuals or those who adapt to the environment around them survive [21]. This feature is the basis for the development or inspiration of evolutionary algorithms, where the best solutions generated by mutation and crossover operators are used to transfer the best genes to the next generation in an evolutionary simulation process, an example of which is the biogeography-based optimization (BBO) algorithm developed by [PERSON] [22], which takes up the work \"The Theory of Island Biogeography\" by [PERSON] and [PERSON] (1960), this algorithm is based on the behavior of the species within a habitat, taking into account the phenomena of emigration, immigration and mutation. Another clear example is the flower pollination algorithm (FPA) proposed by [PERSON] (2012) [23], in which flower reproduction is imitated by taking into account all the factors and processes necessary for pollination, and where the reproduction of the most suitable floral species predominates. The second aspect of inspiration are the algorithms developed or created from observing different kinds of particle swarms [24]. In 1995 [PERSON] and [PERSON] developed a particle swarm optimization algorithm based on groups of social relationships between individuals.