## 1 Introduction
In this context, different optimization techniques, such as cuckoo search algorithm (CSA) [14], biogeography-based optimization (BBO) [16], firefly algorithm (FA) [17], hybrid FA-pattern search [18], krill herd algorithm [19], flower pollination algorithm (FPA) [12], hybrid flower pollination algorithm (HFPA) [20], grey wolf optimization algorithm (GWO) [21], bacterial foraging algorithm [22], particle swarm optimization (PSO) [23], differential evolution [24], artificial bee colony (ABC) [25], whale optimization algorithm (WOA) [26], moth-flame optimization algorithm (MOA) [27], dragonfly algorithm (DA) [13] have been developed and can be used to compute the optimal PID controller gains of many dynamic systems. However, useful algorithms' performance depends on the adequate search procedure, which implies the correct objective function definition, search limits, the setting the search algorithm control parameters, and the complexity of the analysis system. In [28] a WOA application is presented to optimally design PID controllers in the automatic generation control loops of interconnected power systems, including renewable energy sources. The effectiveness of the proposed controller to deal with the uncertainties in generation systems is an essential feature of this study. An objective function to enhance transient response of terminal voltage in terms of maximum overshoot, rise time, settling time, and steady state error is solved by CSA algorithm [14]. A PID controller is used in automatic voltage regulator scheme. Also, in [10] the automatic control problem of synchronous generator is attended with MOA optimization procedure. In [13] DA, is applied for design and implementation of a PID controller with three degrees of freedom. The control stabilizes the frequency and power fluctuations after some disturbance is presented in a hybrid topology of an electric distribution system. In [29] a meta-heuristic optimization algorithm called chaotic whale optimization algorithm is used to regulate the performance of PMSM when it is affected by load disturbances and changes in system parameters. In [30] a control system for permanent magnet synchronous motors, together with an online self-tuning method is presented. In this work, a meta-heuristic bio-inspired approach has been implemented to find the voltage source converter parameter set which minimizes a specific objective function. In the last three cases, there is not a robustness analysis, sensitivity analysis, or statistical test to affirm robust performance of designed controller, analyze the effectiveness of the controller and verify the significance of the results, respectively. The purpose of this paper is to compare different reactive, nature-inspired algorithms for tuning parameters of the PID controller in order to discover the most suitable algorithm for use in solving this class of problem. The six nature-inspired algorithms such as whale, moth-flame, flower pollination, dragonfly, cuckoo search, and modified flower pollination are compared in order to show which of them are the best to work with the same population sizes and generation numbers. This proposal uses six nature-inspired algorithms to search optimal values of a regulatory scheme for robust tracking tasks of desired velocity profiles of a PMSM [31]. This evolutionary technique is applied on one objective/fitness function to find an optimal solution that minimizes the overall error. In another context, the contributions of a meta-heuristic must be objectively evaluated and reported; however, as described in [32], this is not always the case. This is due to the fact that the meta-heuristic procedures are not described in sufficient detail, the experimental adjustments are very generally described and this results in the impossibility of replicating an experiment exactly and an equitable comparison as mentioned in [33]. Statistical analysis [34] is used for the objective evaluation of the performance of metaheuristic algorithms.