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针对分数阶PI~λD~μ控制器参数整定研究,回顾了分数阶微积分的数学描述,采用基于改进差分进化算法的分数阶PI~λD~μ控制器参数整定方法,并利用Oustaloup,Euler,Tustin,Al-Alaoui方法实现了分数阶微分算子。仿真结果表明,该算法计算精度高,收敛快,基于Euler,Al-Alaoui方法分数阶微分算子所设计的控制器能满足顸设的性能指标,但Oustaloup,Tustin分数阶微分算子由于引入了额外的极点,影响了主导极点,不能满足预设的性能指标。
Aiming at the parameter tuning of fractional PI ~ λD ~ μ controller, the mathematical description of fractional calculus is reviewed. The parameter tuning method of fractional PI ~ λD ~ μ controller based on improved differential evolution algorithm is adopted. Oustaloup, Euler, Tustin, Al-Alaoui method to achieve fractional differential operator. The simulation results show that the proposed algorithm has the advantages of high precision and fast convergence. The controller designed by Euler and Al-Alaoui fractional differential operators can meet the performance requirements. However, due to the introduction of the fractional differential operators of Oustaloup and Tustin, The extra pole, affecting the dominant pole, can not meet the preset performance indicators.