基于等价输入干扰补偿的几类典型系统扰动抑制设计
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摘要
摘要：在电力系统、机械系统等工业过程控制中,外界扰动普遍存在。这些扰动不仅使系统的工作点发生漂移,还会使系统的动态和稳态性能变差。为了抑制扰动对系统的影响,获得良好的鲁棒稳定性和控制性能,许多学者进行了大量的理论和应用研究。然而,现有扰动抑制方法仍存在一定的局限性,例如,控制性能与鲁棒稳定性的折中选择会限制扰动抑制效果；被控对象逆模型的使用易导致不稳定零极点的对消；系统内部耦合参数设计复杂,使控制方法难以实现等。因此,设计更为简便、有效、实用的扰动抑制方法,具有重要的理论和实际意义。
本文针对几类典型系统,基于等价输入干扰(EID)补偿的思想,综合运用极点配置、多参数优化和Lyapunov二次稳定等方法,对控制系统的扰动抑制设计进行深入的分析和研究,主要研究成果和创新点如下：
(1)适合非最小相位系统的极点配置扰动抑制方法
通过分析非最小相位系统的特性,提出一种基于极点配置的扰动抑制方法。建立包含扰动估计器、一般状态观测器(GSO)、状态反馈和内模的控制系统结构。采用GSO估计EID,对观测器与状态反馈增益进行分离设计,应用小增益定理得到系统稳定性条件,进而给出基于极点配置的控制器设计算法。实例仿真表明,该方法对最小相位和非最小相位系统都能获得良好的扰动抑制性能。
(2)具有时变结构不确定性系统的鲁棒扰动抑制
在基于EID的控制系统结构中,为了解决不确定性造成控制器参数耦合的问题,针对一类带时变结构不确定性的系统,提出基于EID的鲁棒扰动抑制方法。通过矩阵变换,建立闭环系统的状态空间模型。应用Lyapunov二次稳定方法,以线性矩阵不等式的形式给出系统的鲁棒稳定条件,并进一步得到多参数耦合的控制器设计算法。通过与滑模控制等方法的对比仿真以及电机转速实验,证实该方法在处理不确定性的同时,有效地抑制匹配及不匹配扰动。
(3)基于参数优化的状态时滞系统扰动抑制方法
针对一类含有状态时滞的对象,提出基于参数优化的扰动抑制方法。采用时滞观测器重构时滞对象的状态并估计扰动。推导出状态时滞系统稳定化问题的标准模型,进而利用已知的稳定性准则给出系统稳定性条件及多参数优化控制器设计算法。通过与已有方法的仿真对比,显示出所提方法能够处理时滞并有效地抑制任意形式的外界扰动。
(4)不确定重复控制系统的非周期鲁棒扰动抑制
重复控制系统常会受到周期及非周期扰动同时作用的影响。针对带时变不确定性的严真对象,提出重复控制系统非周期鲁棒扰动抑制方法。将基于EID的扰动估计器引入重复控制系统,建立改进型重复控制系统结构及状态空间模型,应用Lyapunov二次稳定方法推导出系统鲁棒稳定条件及多参数耦合控制器设计方法。该方法通过重复控制器跟踪周期参考输入,利用扰动估计器抑制未知的周期及非周期扰动。通过与现有方法的对比仿真验证方法优良的特性。
(5)基于扰动补偿的多变量系统解耦控制方法
针对带未知扰动的多变量系统,提出一种基于扰动补偿的解耦控制方法。将系统每个回路中不必要的耦合部分以及外部扰动均看作加在该回路的“扰动”,再利用基于EID的方法对这些扰动进行主动补偿。给出等效单回路的稳定性条件及控制器设计方法,使得各回路的参数可以分别独立设计。通过实例仿真验证方法良好的解耦控制效果及扰动抑制性能。
Abstract:External disturbances are often encountered in industrial process control, such as electric power systems and mechanical systems. These disturbances cause not only the movement of the working point, but also bad dynamic and steady-state performance of the system. In order to reject the disturbances and to achieve good control performance, researchers have made a great effort on the study of theories and applications. However, there are still some drawbacks in the existing methods. For example, the trade-off between the control performance and the robust stability restricts the disturbance rejection effect; the inverse model of the plant may cause cancelation of unstable zeros and poles; some methods are difficult to realize due to the complexity of the coupling parameters design in the system. So, it is significant to find a simple, effective and practical disturbance rejection method.
This paper focuses on the disturbance rejection problem for some typical systems based on the idea of the equivalent-input-disturbance (EID). Some methods are applied in this study, such as the pole placement method, multi-parameter optimization and Lyapunov quadratic stability (LQS) method. The main results and the contributions are listed as follows.
(1) A disturbance rejection method for non-minimum-phase plants based on the pole placement
A disturbance rejection method is presented based on the pole placement by analyzing the characteristics of a non-minimum-phase plant. The configuration of the system contains a disturbance estimator, a generalized state observer (GSO), a state feedback and an internal model. The GSO is employed to estimate the EID. The gains of the state feedback and the observer are designed separately. The stability condition is derived using the small-gain theorem and a controller design algorithm is further developed based on the pole placement method. Simulation results demonstrate that the presented method achieves good disturbance rejection performance for both minimum-and non-minimum-phase plants.
(2) Robust disturbance rejection for a system with time-varying structured uncertainties
To solve the problem of parameters coupling in the configuration of the control system, an EID-based robust disturbance rejection method is presented for a system with time-varying structured uncertainties. A state-space model of the closed-loop system is derived using matrix transformation. The robust stability condition is presented in the form of an LMI using the LQS method. A parameter coupling design algorithm is further given for the controller design. Simulations and an experiment of a rotational-speed control system demonstrate that the method handles modeling uncertainties and rejects both matched and unmatched disturbances effectively.
(3) Disturbance rejection for state time-delay systems based on the parameter optimization
A disturbance rejection method is presented for a state time-delay plant based on the parameter optimization. The time-delay observer is employed to reconstruct the state of the plant and to actively estimate the disturbances. A standard model for the stability problem of the time-delay system is derived. Then a stability condition and a parameter optimal design algorithm are given using a known stability criterion. Comparison simulations to the sliding-mode method demonstrate that the method handles time-delay and rejects any external disturbance effectively.
(4) Aperiodic robust disturbance rejection for uncertain repetitive control systems
A repetitive control system (RCS) is often affected by both periodic and aperiodic disturbances. For an RCS that contains a strictly proper plant with time-varying uncertainties, an aperiodic robust disturbance rejection method is presented. An EID-based estimator is introduced into the RCS to yield a modified RCS. A robust stability condition for the system and a parameter coupling design for the controller are presented using the LQS method. In this system, the repetitive controller ensures tracking of a periodic reference input, and the disturbance estimator enables rejection of both unknown periodic and aperiodic disturbances. Simulation results demonstrate good performance of the method.
(5) Decoupling control for multivariable systems based on the disturbance compensation
A decoupling control method is presented for multivariable systems with disturbances based on the disturbance compensation. In this method, the undesirable coupling part in one loop is treated as the "disturbance" imposed on this loop. Then the "disturbance" and external disturbances are actively compensated for using the EID approach. The stability condition and controller design are given for each equivalent single loop. The control parameters in each loop can be designed independently. A practical example demonstrates good performance for both the decoupling control and the disturbance rejection.
本文针对几类典型系统,基于等价输入干扰(EID)补偿的思想,综合运用极点配置、多参数优化和Lyapunov二次稳定等方法,对控制系统的扰动抑制设计进行深入的分析和研究,主要研究成果和创新点如下：
(1)适合非最小相位系统的极点配置扰动抑制方法
通过分析非最小相位系统的特性,提出一种基于极点配置的扰动抑制方法。建立包含扰动估计器、一般状态观测器(GSO)、状态反馈和内模的控制系统结构。采用GSO估计EID,对观测器与状态反馈增益进行分离设计,应用小增益定理得到系统稳定性条件,进而给出基于极点配置的控制器设计算法。实例仿真表明,该方法对最小相位和非最小相位系统都能获得良好的扰动抑制性能。
(2)具有时变结构不确定性系统的鲁棒扰动抑制
在基于EID的控制系统结构中,为了解决不确定性造成控制器参数耦合的问题,针对一类带时变结构不确定性的系统,提出基于EID的鲁棒扰动抑制方法。通过矩阵变换,建立闭环系统的状态空间模型。应用Lyapunov二次稳定方法,以线性矩阵不等式的形式给出系统的鲁棒稳定条件,并进一步得到多参数耦合的控制器设计算法。通过与滑模控制等方法的对比仿真以及电机转速实验,证实该方法在处理不确定性的同时,有效地抑制匹配及不匹配扰动。
(3)基于参数优化的状态时滞系统扰动抑制方法
针对一类含有状态时滞的对象,提出基于参数优化的扰动抑制方法。采用时滞观测器重构时滞对象的状态并估计扰动。推导出状态时滞系统稳定化问题的标准模型,进而利用已知的稳定性准则给出系统稳定性条件及多参数优化控制器设计算法。通过与已有方法的仿真对比,显示出所提方法能够处理时滞并有效地抑制任意形式的外界扰动。
(4)不确定重复控制系统的非周期鲁棒扰动抑制
重复控制系统常会受到周期及非周期扰动同时作用的影响。针对带时变不确定性的严真对象,提出重复控制系统非周期鲁棒扰动抑制方法。将基于EID的扰动估计器引入重复控制系统,建立改进型重复控制系统结构及状态空间模型,应用Lyapunov二次稳定方法推导出系统鲁棒稳定条件及多参数耦合控制器设计方法。该方法通过重复控制器跟踪周期参考输入,利用扰动估计器抑制未知的周期及非周期扰动。通过与现有方法的对比仿真验证方法优良的特性。
(5)基于扰动补偿的多变量系统解耦控制方法
针对带未知扰动的多变量系统,提出一种基于扰动补偿的解耦控制方法。将系统每个回路中不必要的耦合部分以及外部扰动均看作加在该回路的“扰动”,再利用基于EID的方法对这些扰动进行主动补偿。给出等效单回路的稳定性条件及控制器设计方法,使得各回路的参数可以分别独立设计。通过实例仿真验证方法良好的解耦控制效果及扰动抑制性能。
Abstract:External disturbances are often encountered in industrial process control, such as electric power systems and mechanical systems. These disturbances cause not only the movement of the working point, but also bad dynamic and steady-state performance of the system. In order to reject the disturbances and to achieve good control performance, researchers have made a great effort on the study of theories and applications. However, there are still some drawbacks in the existing methods. For example, the trade-off between the control performance and the robust stability restricts the disturbance rejection effect; the inverse model of the plant may cause cancelation of unstable zeros and poles; some methods are difficult to realize due to the complexity of the coupling parameters design in the system. So, it is significant to find a simple, effective and practical disturbance rejection method.
This paper focuses on the disturbance rejection problem for some typical systems based on the idea of the equivalent-input-disturbance (EID). Some methods are applied in this study, such as the pole placement method, multi-parameter optimization and Lyapunov quadratic stability (LQS) method. The main results and the contributions are listed as follows.
(1) A disturbance rejection method for non-minimum-phase plants based on the pole placement
A disturbance rejection method is presented based on the pole placement by analyzing the characteristics of a non-minimum-phase plant. The configuration of the system contains a disturbance estimator, a generalized state observer (GSO), a state feedback and an internal model. The GSO is employed to estimate the EID. The gains of the state feedback and the observer are designed separately. The stability condition is derived using the small-gain theorem and a controller design algorithm is further developed based on the pole placement method. Simulation results demonstrate that the presented method achieves good disturbance rejection performance for both minimum-and non-minimum-phase plants.
(2) Robust disturbance rejection for a system with time-varying structured uncertainties
To solve the problem of parameters coupling in the configuration of the control system, an EID-based robust disturbance rejection method is presented for a system with time-varying structured uncertainties. A state-space model of the closed-loop system is derived using matrix transformation. The robust stability condition is presented in the form of an LMI using the LQS method. A parameter coupling design algorithm is further given for the controller design. Simulations and an experiment of a rotational-speed control system demonstrate that the method handles modeling uncertainties and rejects both matched and unmatched disturbances effectively.
(3) Disturbance rejection for state time-delay systems based on the parameter optimization
A disturbance rejection method is presented for a state time-delay plant based on the parameter optimization. The time-delay observer is employed to reconstruct the state of the plant and to actively estimate the disturbances. A standard model for the stability problem of the time-delay system is derived. Then a stability condition and a parameter optimal design algorithm are given using a known stability criterion. Comparison simulations to the sliding-mode method demonstrate that the method handles time-delay and rejects any external disturbance effectively.
(4) Aperiodic robust disturbance rejection for uncertain repetitive control systems
A repetitive control system (RCS) is often affected by both periodic and aperiodic disturbances. For an RCS that contains a strictly proper plant with time-varying uncertainties, an aperiodic robust disturbance rejection method is presented. An EID-based estimator is introduced into the RCS to yield a modified RCS. A robust stability condition for the system and a parameter coupling design for the controller are presented using the LQS method. In this system, the repetitive controller ensures tracking of a periodic reference input, and the disturbance estimator enables rejection of both unknown periodic and aperiodic disturbances. Simulation results demonstrate good performance of the method.
(5) Decoupling control for multivariable systems based on the disturbance compensation
A decoupling control method is presented for multivariable systems with disturbances based on the disturbance compensation. In this method, the undesirable coupling part in one loop is treated as the "disturbance" imposed on this loop. Then the "disturbance" and external disturbances are actively compensated for using the EID approach. The stability condition and controller design are given for each equivalent single loop. The control parameters in each loop can be designed independently. A practical example demonstrates good performance for both the decoupling control and the disturbance rejection.
引文
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