【作者】 陈刚；

【导师】 陈立平； 杨卫东；

【作者基本信息】 合肥工业大学 ， 控制工程（专业学位）， 2019， 硕士

【摘要】 分数阶微积分是整数阶微积分的广义形式,随着分数阶微积分理论的完善,分数阶微积分理论在控制领域中的应用逐渐成为研究热点。分数阶PID控制器是分数阶微积分理论应用的重要成果,具有五个控制参数,控制参数的整定较为困难。目前,分数阶PID控制器已得到广泛应用,但对一些复杂系统而言分数阶PID控制器仍然难以取得令人满意的控制效果。针对上述问题,本文主要做了以下研究工作:基于传统量子粒子群优化算法的分数阶PID控制参数优化过程易陷入局部最优解。本文在寻优过程中加入粒子更新处理和粒子扩散处理两种方式,得到一种改进的量子粒子群优化算法,对比仿真验证了改进量子粒子群优化算法在参数寻优上的先进性。低阶整数阶传递函数近似分数阶PID控制器易实现,但精度较低。本文采用改进的量子粒子群优化算法,提出了一种改进的分数阶微积分算子低阶近似方法,有效地提高了分数阶微积分算子低阶近似精度,仿真对比实验验证了该方法的有效性。为提高永磁同步电机控制中分数阶PI控制器的控制性能,在分析分数阶PI控制器作用的基础上,提出了一种积分限幅的分数阶PI控制器。为进一步改进积分限幅的分数阶PI控制器的控制性能,利用离散的负载转矩观测器对分数阶积分器的输出限幅,提出了一种积分限幅追踪的分数阶PI控制器,仿真分析表明了积分限幅追踪的分数阶PI控制器具有更好的控制性能。进行了永磁同步电机转速控制实验,验证了该算法的有效性。提出了一种改进的时域近似法离散格式,解决了具有记忆长度的分数阶PID控制器容易导致受控系统振荡的问题。将改进的时域近似法离散格式与两种Z域近似法进行了对比分析,结果表明改进的离散格式具有更好的控制性能。在改进的离散格式基础上,提出了单步控制参数最优的分数阶PID控制器和变阶次的分数阶PI控制器,通过仿真分析了两种控制器的控制性能,并将其分别应用于SEPIC电路的输出电压控制和永磁同步电机的转速控制,实验结果验证了两种控制器的有效性。更多还原

【Abstract】 Fractional calculus is a generalization of integer calculus.With the improvement of fractional calculus theory,the applications of fractional calculus theory in control field haves gradually become a research hotspot.Fractional order PID controller is an important achievement in the application of fractional order calculus theory.It has five control parameters,so it is difficult to tune the control parameters.At present,fractional order PID controller has been widely used,but for some complex systems,fractional order PID controller is still difficult to achieve satisfactory control results.In view of the above problems,this paper mainly does the following research works:The optimization process of fractional order PID control parameters based on traditional quantum particle swarm optimization algorithm is easy to fall into local optimal solution.In this paper,an improved quantum particle swarm optimization(IQPSO)algorithm is proposed by adding particle update and particle diffusion to the optimization process.The simulation results show that the IQPSO algorithm is advanced in parameter optimization.The fractional order PID controller approximated by low-order integer transfer function is easy to implement,but its accuracy is low.In this paper,an improved low-order approximation method of fractional calculus operator is proposed by using IQPSO algorithm,which effectively improves the low-order approximation accuracy of fractional calculus operator.The effectiveness of this method is verified by simulation.In order to improve the control performance of fractional order PI controller in permanent magnet synchronous motor control,a fractional order PI controller with integral limit is proposed based on the analysis of the function of fractional order PI controller.To further improve the control performance of fractional order PI controller with integral limit,a fractional order PI controller with integral limit tracking is proposed by using discrete load torque observer to limit the output of fractional order integrator.The simulation results show that the fractional order PI controller with integral limit tracking has better control performance.Experiments on speed control of permanent magnet synchronous motor(PMSM)are carried out to verify the effectiveness of the algorithm.An improved discrete scheme of time-domain approximation method is proposed to solve the problem that fractional order PID controller with memory length can easily lead to oscillation of controlled system.The improved discrete scheme of time-domain approximation method is compared with two Z-domain approximation methods.The results show that the improved discrete scheme has better control performance.On the basis of the improved discrete format,the fractional order PID controller with optimal single-step control parameters and the fractional order PI controller with variable order are proposed.The control performances of the two controllers are simulated and analyzed.The two controllers are applied to the output voltage control of SEPIC circuit and the speed control of PMSM respectively.The experimental results verify the effectiveness of the two controllers.更多还原