基于分数阶控制器的永磁同步电动机速度控制研究
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摘要
PID控制作为线性最佳控制在工业过程控制中得到了广泛的应用。PID控制器依据对象模型进行设计，方法规范成熟，简单实用，是其得以广泛应用的根本原因。然而，控制对象的现有模型往往是忽略许多时变、非线性等因素而简化得到的。对于高性能的控制系统，上述因简化被忽略的因素将直接影响系统的性能。本文尝试利用分数阶微积分理论来设计PID控制器——分数阶PIλDμ控制器，旨在继承和发扬传统PID控制器的优点和弥补其不足，满足高性能的速度控制需求。研究围绕分数阶典型环节特性研究、分数阶速度控制系统性能研究和分数阶速度控制系统实验研究三个方面展开。
一、论文通过频率特性和阶跃响应系统深入地分析了分数阶积分环节、分数阶微分环节、分数阶比例积分环节、分数阶比例微分环节和分数阶比例积分微分环节等典型环节的特性。分数阶典型环节不同于整数阶典型环节的特性，有可能为在高性能系统中设计期望的频率特性拓展空间。
二、在传统的速度控制系统中，用分数阶控制器代替整数阶控制器，利用理论分析和仿真实验深入研究了分数阶速度控制系统的性能，包括稳定性、快速性和鲁棒性。证明了采用分数阶控制器的速度控制系统的稳定性。采用仿真实验研究的方法分别对采用分数阶控制器和整数阶控制器的速度控制系统的阶跃响应进行了比较研究并得出了采用分数阶控制器的速度控制系统快速性要优于采用整数阶控制器速度控制系统的结论。并给出了采用分数阶控制器的速度控制系统满足系统鲁棒性的条件。
三、在理论研究的基础上，分别研究了分数阶比例积分（FO-PI）控制器、分数阶比例微分（FO-PD）控制器和分数阶比例[微分]（FO-[PD]）控制器，并将其应用于交流永磁同步电动机的速度控制。在相同的条件下，对采用按照最优化方法设计的整数阶比例积分（IO-PI）控制器的系统与采用本文提出的分数阶比例积分（FO-PI）控制器、分数阶比例微分（FO-PD）控制器和分数阶比例[微分]（FO-[PD]）控制器的系统，分别进行了仿真和实验研究。仿真和实验结果表明采用提出的分数阶速度控制器的系统响应速度、跟随性能、抗扰性能、超低速控制效果和鲁棒性均优于采用整数阶速度控制器的系统，并且具有很好的节能效果。上述实验研究结果与理论研究结论接近。分数阶控制器能够提高PMSM速度控制系统的控制性能，增强系统的抗干扰能力，减少能量消耗，适合于对控制性能要求更高或对降低能耗有一定要求的速度控制系统。研究结果为分数阶控制器在PMSM速度控制系统中的应用提供了理论基础和实际应用依据。
As a linear optimal control, PID control has been widely used in industrial processcontrol. PID controller based on object model design, method standard mature, simple andpractical, it is the root cause can be widely applied. However, the existing models of thecontrol object is often to ignore the time-varying, nonlinear factors and simplified to get. Forhigh-performance control system, these neglected factors will directly affect the systemperformance. Looking forward to developing the merit of the classic PID controllers andovercoming the flaw of the classic PID controllers to meet the high performance speed controlneeds. This paper attempts to use the fractional calculus theory to design a PIDcontroller-fractional PIλDμcontroller. Research focus on three aspects of the fractional ordertypical links features, fractional order speed control system performances and the fractionalorder speed control system experimental study.
1. In-depth analysis of these typical aspects of the fractional integrator, the fractionaldifferential link, the fractional proportional integral link, the fractional proportion differentiallinks and fractional order proportional integral derivative link by frequency characteristics andstep responses. The characteristics of fractional order typical links are different from integerorder typical links, may expand the space for the desired frequency characteristics in thehigh-performance system design.
2. Replaced the integral order controller by fractional order controller in traditional speedcontrol system, in-depth study of the properties of fractional order speed control system bytheoretical analysis and simulation, which include stabilization, rapidity and robustness.Proved the stabilization of fractional order speed control system. Simulation research hasbeen used to compare the step response performance of fractional order controller and integralorder controller in speed control system, and obtain the conclusion of the rapidity of fractionalorder speed control system is better than integral order speed control system. Also gives theconditions of the fractional order speed control system to meet the robustness.
3. Proposed a fractional order proportional integral controller, fractional orderproportional derivative controller and fractional order [proportional derivative] controller onthe basis of theoretical studies, and applied to a permanent magnet synchronous motor(PMSM) speed control. In the same conditions, the simulation and experimental study areimplemented to validate the effectiveness and advantages of the designed fractional ordercontrollers by comparing with the optimized integer order controller in the real-time PMSMservo system. Simulation and experimental show that the designed fractional order controllers outperform the traditional optimal integer order controller in transient response, trackingperformance, load disturbance rejection, robustness to the loop gain variations and theultra-low speed tracking performance with severe nonlinear effects, and also have a goodenergy-saving effect, suitable for the speed control system demanding higher performancerequirements or lower the energy consumption. The above experimental results andtheoretical conclusions close. Fractional order controllers can improve the controlperformance of the PMSM speed control system, enhanced load disturbance rejectioncapability of the system, reduce energy consumption. Suitable for speed control system indemand of higher control performance and decreasing energy consume. Research resultprovide a theoretical basis and practical application basis for application of fractional ordercontroller in PMSM speed control system.
一、论文通过频率特性和阶跃响应系统深入地分析了分数阶积分环节、分数阶微分环节、分数阶比例积分环节、分数阶比例微分环节和分数阶比例积分微分环节等典型环节的特性。分数阶典型环节不同于整数阶典型环节的特性，有可能为在高性能系统中设计期望的频率特性拓展空间。
二、在传统的速度控制系统中，用分数阶控制器代替整数阶控制器，利用理论分析和仿真实验深入研究了分数阶速度控制系统的性能，包括稳定性、快速性和鲁棒性。证明了采用分数阶控制器的速度控制系统的稳定性。采用仿真实验研究的方法分别对采用分数阶控制器和整数阶控制器的速度控制系统的阶跃响应进行了比较研究并得出了采用分数阶控制器的速度控制系统快速性要优于采用整数阶控制器速度控制系统的结论。并给出了采用分数阶控制器的速度控制系统满足系统鲁棒性的条件。
三、在理论研究的基础上，分别研究了分数阶比例积分（FO-PI）控制器、分数阶比例微分（FO-PD）控制器和分数阶比例[微分]（FO-[PD]）控制器，并将其应用于交流永磁同步电动机的速度控制。在相同的条件下，对采用按照最优化方法设计的整数阶比例积分（IO-PI）控制器的系统与采用本文提出的分数阶比例积分（FO-PI）控制器、分数阶比例微分（FO-PD）控制器和分数阶比例[微分]（FO-[PD]）控制器的系统，分别进行了仿真和实验研究。仿真和实验结果表明采用提出的分数阶速度控制器的系统响应速度、跟随性能、抗扰性能、超低速控制效果和鲁棒性均优于采用整数阶速度控制器的系统，并且具有很好的节能效果。上述实验研究结果与理论研究结论接近。分数阶控制器能够提高PMSM速度控制系统的控制性能，增强系统的抗干扰能力，减少能量消耗，适合于对控制性能要求更高或对降低能耗有一定要求的速度控制系统。研究结果为分数阶控制器在PMSM速度控制系统中的应用提供了理论基础和实际应用依据。
As a linear optimal control, PID control has been widely used in industrial processcontrol. PID controller based on object model design, method standard mature, simple andpractical, it is the root cause can be widely applied. However, the existing models of thecontrol object is often to ignore the time-varying, nonlinear factors and simplified to get. Forhigh-performance control system, these neglected factors will directly affect the systemperformance. Looking forward to developing the merit of the classic PID controllers andovercoming the flaw of the classic PID controllers to meet the high performance speed controlneeds. This paper attempts to use the fractional calculus theory to design a PIDcontroller-fractional PIλDμcontroller. Research focus on three aspects of the fractional ordertypical links features, fractional order speed control system performances and the fractionalorder speed control system experimental study.
1. In-depth analysis of these typical aspects of the fractional integrator, the fractionaldifferential link, the fractional proportional integral link, the fractional proportion differentiallinks and fractional order proportional integral derivative link by frequency characteristics andstep responses. The characteristics of fractional order typical links are different from integerorder typical links, may expand the space for the desired frequency characteristics in thehigh-performance system design.
2. Replaced the integral order controller by fractional order controller in traditional speedcontrol system, in-depth study of the properties of fractional order speed control system bytheoretical analysis and simulation, which include stabilization, rapidity and robustness.Proved the stabilization of fractional order speed control system. Simulation research hasbeen used to compare the step response performance of fractional order controller and integralorder controller in speed control system, and obtain the conclusion of the rapidity of fractionalorder speed control system is better than integral order speed control system. Also gives theconditions of the fractional order speed control system to meet the robustness.
3. Proposed a fractional order proportional integral controller, fractional orderproportional derivative controller and fractional order [proportional derivative] controller onthe basis of theoretical studies, and applied to a permanent magnet synchronous motor(PMSM) speed control. In the same conditions, the simulation and experimental study areimplemented to validate the effectiveness and advantages of the designed fractional ordercontrollers by comparing with the optimized integer order controller in the real-time PMSMservo system. Simulation and experimental show that the designed fractional order controllers outperform the traditional optimal integer order controller in transient response, trackingperformance, load disturbance rejection, robustness to the loop gain variations and theultra-low speed tracking performance with severe nonlinear effects, and also have a goodenergy-saving effect, suitable for the speed control system demanding higher performancerequirements or lower the energy consumption. The above experimental results andtheoretical conclusions close. Fractional order controllers can improve the controlperformance of the PMSM speed control system, enhanced load disturbance rejectioncapability of the system, reduce energy consumption. Suitable for speed control system indemand of higher control performance and decreasing energy consume. Research resultprovide a theoretical basis and practical application basis for application of fractional ordercontroller in PMSM speed control system.
引文
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