具有时空耦合特征的模糊逻辑控制系统及其应用
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摘要
绝大多数工业生产过程为时空耦合系统,或分布参数系统,其明显的特征是系统的状态、控制、输出及参数等不仅随时间变化,而且还随空间变化。针对时空耦合系统,传统的基于被控对象精确数学模型的控制方法,需要复杂的控制理论,但实际系统往往存在参数不确定性、复杂非线性等情况,精确的数学模型难以获得,即使获得也很难实施有效控制。而智能模糊控制最大的优点是不依赖被控对象的精确数学模型并能达到令人满意的鲁棒控制效果。由于传统的模糊控制没有将空间信息考虑在内,所以它在本质上不具有处理时空耦合系统的能力。基于此,本文提出了具有时空耦合特征的模糊逻辑控制系统,它最主要的特色是在不增加传统模糊控制复杂度的情况下,只需增加数个传感器用于获得物理场的时空信息就可以实现时空处理机能,从而降低控制器的设计成本和工业生产的运行成本。最后的仿真和实验结果证明了本文提出的方法是有效的。
主要创新点包括以下几个方面：
1)建立了时空模糊逻辑系统
针对时空耦合系统的特点,结合type-2模糊系统,提出了时空模糊集、时空模糊关系及其运算法则,建立了较完善的时空模糊逻辑系统理论。将type-2模糊集的第二隶属度表征空间信息,定义了时空模糊集；时空模糊集可以由时间(第一)隶属函数和空间(第二)隶属函数来描述。跟三维模糊集相类似,时空模糊集具有三个坐标分别用于时间变量的论域、隶属度及表征空间信息。与三维模糊集最大的差别是时空模糊集定义了空间隶属函数来描述空间的信息。由于时空模糊集有明确的空间物理意义,时空模糊集的定义及其运算法则与type-2模糊系统有所差异,在Type-2中的降维运算在时空模糊逻辑系统中变成了空间降维运算。
2)设计了时空模糊逻辑控制器,并推导出其解析模型
针对时空耦合系统,首先归纳了时空模糊控制器存在的相关设计问题,并设计了一个时空模糊逻辑控制器。随后,给出了详细的时空模糊控制器解析模型的推导过程。再根据推导出的解析模型,基于Lyapunov稳定性理论,提出了时空模糊控制器的稳定性参数设计方法。最后,将时空模糊控制器应用在化工过程的反应棒上,仿真结果表明时空模糊逻辑控制器的控制性能优于传统的模糊逻辑控制器。
3)揭示了模糊PID控制器的饱和特性,提出了模糊PID控制器的整定方法
在实际应用模糊控制过程中,模糊规则的数量总是有限的,基于此,揭示了模糊PID控制器内在的饱和特性。然后根据内模控制原理,提出了一种模糊PID控制器的参数整定方法。仿真和实验结果验证了该饱和特性及其整定方法的有效性。
4)提出了时空模糊PID控制器的整定方法
首先基于传统模糊PID控制器的结构,设计了时空模糊PID控制器的结构,再根据传统的一阶加纯滞后模型,提出了融合空间特征的一阶加纯滞后模型。然后,基于奈奎斯特图的原理,提出了基于空间拓展的奈奎斯特图用于时空模糊PID控制器的整定方法,仿真和实验结果验证了时空模糊PID控制器及其整定方法的有效性。
A variety of industrial processes are inherently spatio-temporal systems or distributed parameter systems (DPS) where their states, controls, outputs and process parameters may vary temporally and spatially, such as many thermal, fluid flow and chemical reactor processes. The distributed parameter process is traditionally controlled with model-based methods, within which a precise mathematical model of the process is required. However, a precise mathematical model can not be obtained due to unknown uncertainty, nonlinearity and disturbances. When there are strong unknown uncertainties in the process, the performance will deteriorate. As an intelligent method, the fuzzy logic controller (FLC) is widely used in industrial processes due to its inherent robustness under unknown environment. Though some studies have been presented about application of type-1 FLCs to DPS control, however, these type-1 fuzzy approaches are not inherently designed for the spatially distributed dynamic process because of their two-dimensional (2D) nature. Thus, a new spatio-temporal fuzzy logic system (FLS) is proposed to control DPS. Without additional complexity, the spatio-temporal FLS can process spatial information by adding some sensors for measurement, which may reduce cost.
The novelty of the spatio-temporal FLS mainly includes the following four parts:
1) A spatio-temporal FLS is built.
A novel application of type-2 FLS is presented by developing a spatio-temporal FLS to control a class of DPS. The key difference to the previous type-2 fuzzy system is that the secondary membership function describes a different physical variable - space domain. A spatio-temporal fuzzy set consists of a temporal (primary) membership function and a spatial (secondary) membership function. Since its secondary membership function is designed for the spatial domain, it has some different definitions and operations from the previous type-2 application. The type-reduction will become the spatial reduction before the traditional defuzzification. This spatio-temporal FLS is successfully applied to a catalytic reaction rod to demonstrate its effectiveness and potential to a wide range of engineering applications on modeling and control of DPS.
2) A spatio-temporal FLC is designed. And its model is derived.
A three domain FLC is proposed based on the spatial fuzzy set for the spatially distributed systems. An analytical mathematical model of the spatio-temporal FLC is derived using an extended graphic analytical method. The model of the spatio-temporal FLC is characteristic of a global sliding mode control techniques. A catalytic reactor is given to demonstrate the effectiveness of the spatio-temporal FLC and the proposed tuning method by comparing with other controller.
3) An inherent saturation of the traditional FLC is revealed. And an efficient tuning method is proposed for fuzzy PID controller.
An inherent saturation of the traditional FLC is revealed due to the finite fuzzy rules used. An equivalent structure and model of the fuzzy rule base is derived to show a saturation property. The bandwidth of the fuzzy PID control system can be adjusted by changing saturation parameter. An internal model control (IMC) based tuning method is proposed to auto-tune the fuzzy PID controller in this paper. The simulation and experiment results demonstrate these amazing effects of the inherent saturation, the proposed tuning method, and its influence to the robustness of fuzzy PID controller.
4) A tuning method is proposed for spatio-temporal fuzzy PID controller.
A spatio-temporal fuzzy PID controller and its tuning method are proposed to control a class of DPS. An analytical mathematical model of the 3D fuzzy PID controller is first obtained after simple derivation. Then, a spatial first-order plus delay time (FOPDT) model is proposed to tune the spatio-temporal fuzzy PID controller. An extension Nyquist principle is used to design parameter of the spatio-temporal fuzzy PID controller based on the FOPDT model. The stability of the fuzzy PID control system is analyzed using the Lyapunov stability theory. Finally, the simulation and experiment results demonstrate the effectiveness of the spatio-temporal fuzzy PID control and the proposed tuning method by comparing with other controller.
主要创新点包括以下几个方面：
1)建立了时空模糊逻辑系统
针对时空耦合系统的特点,结合type-2模糊系统,提出了时空模糊集、时空模糊关系及其运算法则,建立了较完善的时空模糊逻辑系统理论。将type-2模糊集的第二隶属度表征空间信息,定义了时空模糊集；时空模糊集可以由时间(第一)隶属函数和空间(第二)隶属函数来描述。跟三维模糊集相类似,时空模糊集具有三个坐标分别用于时间变量的论域、隶属度及表征空间信息。与三维模糊集最大的差别是时空模糊集定义了空间隶属函数来描述空间的信息。由于时空模糊集有明确的空间物理意义,时空模糊集的定义及其运算法则与type-2模糊系统有所差异,在Type-2中的降维运算在时空模糊逻辑系统中变成了空间降维运算。
2)设计了时空模糊逻辑控制器,并推导出其解析模型
针对时空耦合系统,首先归纳了时空模糊控制器存在的相关设计问题,并设计了一个时空模糊逻辑控制器。随后,给出了详细的时空模糊控制器解析模型的推导过程。再根据推导出的解析模型,基于Lyapunov稳定性理论,提出了时空模糊控制器的稳定性参数设计方法。最后,将时空模糊控制器应用在化工过程的反应棒上,仿真结果表明时空模糊逻辑控制器的控制性能优于传统的模糊逻辑控制器。
3)揭示了模糊PID控制器的饱和特性,提出了模糊PID控制器的整定方法
在实际应用模糊控制过程中,模糊规则的数量总是有限的,基于此,揭示了模糊PID控制器内在的饱和特性。然后根据内模控制原理,提出了一种模糊PID控制器的参数整定方法。仿真和实验结果验证了该饱和特性及其整定方法的有效性。
4)提出了时空模糊PID控制器的整定方法
首先基于传统模糊PID控制器的结构,设计了时空模糊PID控制器的结构,再根据传统的一阶加纯滞后模型,提出了融合空间特征的一阶加纯滞后模型。然后,基于奈奎斯特图的原理,提出了基于空间拓展的奈奎斯特图用于时空模糊PID控制器的整定方法,仿真和实验结果验证了时空模糊PID控制器及其整定方法的有效性。
A variety of industrial processes are inherently spatio-temporal systems or distributed parameter systems (DPS) where their states, controls, outputs and process parameters may vary temporally and spatially, such as many thermal, fluid flow and chemical reactor processes. The distributed parameter process is traditionally controlled with model-based methods, within which a precise mathematical model of the process is required. However, a precise mathematical model can not be obtained due to unknown uncertainty, nonlinearity and disturbances. When there are strong unknown uncertainties in the process, the performance will deteriorate. As an intelligent method, the fuzzy logic controller (FLC) is widely used in industrial processes due to its inherent robustness under unknown environment. Though some studies have been presented about application of type-1 FLCs to DPS control, however, these type-1 fuzzy approaches are not inherently designed for the spatially distributed dynamic process because of their two-dimensional (2D) nature. Thus, a new spatio-temporal fuzzy logic system (FLS) is proposed to control DPS. Without additional complexity, the spatio-temporal FLS can process spatial information by adding some sensors for measurement, which may reduce cost.
The novelty of the spatio-temporal FLS mainly includes the following four parts:
1) A spatio-temporal FLS is built.
A novel application of type-2 FLS is presented by developing a spatio-temporal FLS to control a class of DPS. The key difference to the previous type-2 fuzzy system is that the secondary membership function describes a different physical variable - space domain. A spatio-temporal fuzzy set consists of a temporal (primary) membership function and a spatial (secondary) membership function. Since its secondary membership function is designed for the spatial domain, it has some different definitions and operations from the previous type-2 application. The type-reduction will become the spatial reduction before the traditional defuzzification. This spatio-temporal FLS is successfully applied to a catalytic reaction rod to demonstrate its effectiveness and potential to a wide range of engineering applications on modeling and control of DPS.
2) A spatio-temporal FLC is designed. And its model is derived.
A three domain FLC is proposed based on the spatial fuzzy set for the spatially distributed systems. An analytical mathematical model of the spatio-temporal FLC is derived using an extended graphic analytical method. The model of the spatio-temporal FLC is characteristic of a global sliding mode control techniques. A catalytic reactor is given to demonstrate the effectiveness of the spatio-temporal FLC and the proposed tuning method by comparing with other controller.
3) An inherent saturation of the traditional FLC is revealed. And an efficient tuning method is proposed for fuzzy PID controller.
An inherent saturation of the traditional FLC is revealed due to the finite fuzzy rules used. An equivalent structure and model of the fuzzy rule base is derived to show a saturation property. The bandwidth of the fuzzy PID control system can be adjusted by changing saturation parameter. An internal model control (IMC) based tuning method is proposed to auto-tune the fuzzy PID controller in this paper. The simulation and experiment results demonstrate these amazing effects of the inherent saturation, the proposed tuning method, and its influence to the robustness of fuzzy PID controller.
4) A tuning method is proposed for spatio-temporal fuzzy PID controller.
A spatio-temporal fuzzy PID controller and its tuning method are proposed to control a class of DPS. An analytical mathematical model of the 3D fuzzy PID controller is first obtained after simple derivation. Then, a spatial first-order plus delay time (FOPDT) model is proposed to tune the spatio-temporal fuzzy PID controller. An extension Nyquist principle is used to design parameter of the spatio-temporal fuzzy PID controller based on the FOPDT model. The stability of the fuzzy PID control system is analyzed using the Lyapunov stability theory. Finally, the simulation and experiment results demonstrate the effectiveness of the spatio-temporal fuzzy PID control and the proposed tuning method by comparing with other controller.
引文
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