Interval type-2 fuzzy logic controller (IT2FLC) owns good performance under uncertainty and nonlinearity environments while its optimization is hard and complicated. In this work, we propose an optimization method based on differential evolution with better and nearest option (NbDE) for interval type-2 fuzzy logic PID controller (IT2FL-PID-C) in order to control the position of hydraulic serial elastic actuator (SEA). Firstly, a simplified IT2FL-PID-C structure with fewer parameters is proposed to reduce the difficulty of the optimization of IT2FL-PID-C. To balance its frequency and step performance, an objective function with weighted integral time absolute error and integral square error is given. Secondly, to investigate the performance of NbDE based IT2FL-PID-C, three experiments are conducted. A set of experiments is taken to determine the weight for fitness function. Then we compare NbDE with other algorithms. In addition, NbDE-IT2FL-PID-C is also compared with other optimization methods. At last, NbDE-IT2FL-PID-C is applied to hydraulic SEA and compared with PID. And a range for the weight of fitness function is given. The results have shown the superiority of NbDE with proposed fitness function to optimize IT2FL-PID-C and the superiority of NbDE-IT2FL-PID-C to control the position of hydraulic SEA.

中文翻译：

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基于微分进化的区间2型模糊逻辑PID控制器，具有更好和最近的液压串联弹性执行器选项

区间2型模糊逻辑控制器(IT2FLC)在不确定性和非线性环境下具有良好的性能，但其优化困难且复杂。在这项工作中，我们提出了一种基于差分进化的优化方法，具有更好和最近选项（NbDE）的区间 2 型模糊逻辑 PID 控制器（IT2FL-PID-C），以控制液压串联弹性执行器（SEA）的位置）。首先，提出了一种参数较少的简化IT2FL-PID-C结构，以降低IT2FL-PID-C的优化难度。为了平衡其频率和阶跃性能，给出了加权积分时间绝对误差和积分平方误差的目标函数。其次，为了研究基于 NbDE 的 IT2FL-PID-C 的性能，进行了三个实验。进行一组实验来确定适应度函数的权重。然后我们将 NbDE 与其他算法进行比较。此外，NbDE-IT2FL-PID-C 还与其他优化方法进行了比较。最后将NbDE-IT2FL-PID-C应用于水力SEA并与PID进行比较。并给出了适应度函数权重的范围。结果表明，NbDE 具有优化 IT2FL-PID-C 的适应度函数的优越性和 NbDE-IT2FL-PID-C 控制液压 SEA 位置的优越性。