多变量模糊逻辑控制系统的设计及其应用
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摘要
在实际工业过程中,很多系统是多入多出系统,例如多连杆机器人和探针扫描显微镜的探针运动等。此外,分布参数系统的状态和控制既与时间有关,又与空间有关,也叫时空耦合系统,例如扫描探针显微镜的微悬臂和催化反应棒等。分布参数系统本质上是无穷维系统,对于这类系统的控制,通常运用一些有限维近似建模方法,将分布参数系统就转换为多入多出系统,同时带来较大的建模误差。此外,这些系统中通常都含有未知非线性和扰动等不确定性因素,因而建立系统的精确数学模型非常困难,这样传统的PID控制器等用于控制这些系统很难达到理想的效果。近年来发展起来的智能控制方法,比如模糊控制器就能减少对数学模型的依赖。然而直接运用多个模糊逻辑控制器来控制这些子系统需要根据专家的经验设计多个隶属函数和多个规则库,这样的设计方法相对比较复杂。针对以上问题,本文的主要工作集中在以下几个方面：
(1)建立了多变量模糊逻辑控制系统
针对所有的子系统仅采用一个隶属函数,通过比例因子来调整其它子系统的隶属函数,并且引入模糊矩阵理论来设计多变量模糊逻辑控制系统。该控制系统的设计不需要按照专家的经验根据每个子系统来设计隶属函数,同时,该设计方法也只采用一个规则库。在设计上可以看成是传统的模糊逻辑控制系统扩展成为多变量模糊逻辑控制系统,并且设计方法比较简单。
(2)设计了多变量模糊逻辑控制器,并推导出解析模型
引用一个推理机制来推导出多变量模糊逻辑控制器的解析模型,建立了多变量模糊逻辑控制和传统PID控制参数之间的关系,从而PID控制器的参数整定方法可用来设计多变量模糊逻辑控制器的比例因子(参数),此外解析模型可以用来研究控制系统的稳定性。
(3)提出了多变量模糊逻辑控制器基于PID的参数整定方法
针对稳定系统采用内模控制的参数设计方法来整定参数。针对不稳定系统,采用增益裕度和相位裕度来整定参数。针对多入多出系统,先将系统解耦,转化为多个单入单出系统,多变量模糊逻辑控制器用于控制解耦后的系统,PID控制器的参数用于设计多变量模糊逻辑控制器的参数。针对分布参数系统,本文先将其时空变量分离,运用Galerkin方法得到分布参数系统的有限维近似模型,然后根据近似模型设计多变量模糊逻辑控制器,再根据空间基函数合成时空控制器来控制分布参数系统,该方法考虑了系统足够的空间信息。通过仿真表明这些设计方法都是非常有效的。
(4)研究了多变量模糊逻辑控制器的智能参数调节方法
运用神经网络来辨识多入多出系统中的未知量,采用梯度下降来自适应调节多变量模糊逻辑控制器的比例因子,通过仿真可以看到该方法行之有效。针对分布参数系统,运用粒子群优化算法设计了多变量模糊逻辑控制器的参数,取得了理想的控制效果。此外,根据多变量模糊逻辑控制器的数学模型,将其应用于分布参数系统控制的稳定性进行了分析,给出了多变量模糊逻辑控制器控制分布参数系统的稳定条件。
(5)扫描探针显微镜的探针在空间运动是一个多入多出系统,运用多变量模糊逻辑控制器对探针运动进行控制,取得了比传统PID控制器更好的控制效果,从而验证了多变量模糊逻辑控制器设计的有效性。
In practical industrial processes, there are many multi-inputs multi-outputs (MIMO) systems, such as multi-link robot and probe movement of scanning probe microscopy (SPM), etc. Morever, states and controls of many distributed parameter systems (DPS) are related with time and space. These systems are called or spatio-temporal systems, such as micro-cantilever in SPM and catalytic reaction rod, etc. DPS are inherent infinite-dimensional, and they are usually converted to MIMO systems with some low-order approximation modeling methods in convenient for controlling them, and will deduce large modeling error. Those systems have uncertainties, such as unknown nonlinearities, disturbances etc., therefore, it is difficult to get their precise models. Traditional controllers, such as PID, cannot get a sound performance. In contract, intelligent methods which are developing these years, such as fuzzy control, can reduce dependence on the mathematical model. However, it needs to design many membership functions (MF) and rule bases on expert experience when many fuzzy logic controllers are used to control them. This design method is complex relatively. In order to solve those problems, the major work of the paper focuses on the following aspects:
(1) Multi-variable fuzzy logic system is built.
On account of only one MF being adopted for all subsystems, MFs for other subsystems are adjusted by scaling factors. A multi-variable fuzzy logic control system is designed following the fuzzy matrix theory. At the same time, the control system adopts only one traditional rule base, and there is no need to design MFs for all subsystems according to expert experience. The control system can be considered as an extension of traditional fuzzy system, and the design method is very simple.
(2) A multi-variable fuzzy logic controller is designed, and a mathematical model is deduced.
Mathematical model of the multi-variable fuzzy logic controller (FLC) is deduced following an inference engine. Relationships between multi-variable FLC and PID controller are built. Therefore, scaling factors (parameters) of multi-variable FLC can be tuned through tuning method of PID controller, and the design method is simple.
(3) Tuning method of multi-variable FLC is proposed based on PID controller.
Tuning based on internal mode control is proposed for stable processes. Phase margin and gain margin tuning method is proposed for unstable processes. For MIMO systems, parameters of PID are used to design parameters of multi-variable FLC thorough decoupling. For DPS, a finite-dimensional approximate model is obtained through time/space variable separation and Galerkin method. The approximate model is used to design multi-variable FLC,and a spatio-temporal controller is synthesized by spatial basis and multi-variable FLC. Enough spatial information is considered in this method and the design method is effective through simulating.
(4) Intelligent tuning methods of multi-variable FLC are researched.
Scaling factors of multi-variable FLC are adaptively adjusted by gradient descent, and neural network is used to identify unknown variables. The simulations show the usefulness of it. Particle swarm optimization is used to tuning parameters of multi-variable FLC for DPS, and a sound performance is obtained from simulations. Stability of multi-variable FLC controlled DPS is analyzed through the mathematical model. The stability conditions are also given for the controlled system.
(5) Probe movement of SPM in nano-manipulation platform is considered as a DPS. Multi-variable FLC is used to control the movement. Performance of multi-variable FLC is better than PID controller in experiment. Therefore, the design of multi-variable FLC are effective.
(1)建立了多变量模糊逻辑控制系统
针对所有的子系统仅采用一个隶属函数,通过比例因子来调整其它子系统的隶属函数,并且引入模糊矩阵理论来设计多变量模糊逻辑控制系统。该控制系统的设计不需要按照专家的经验根据每个子系统来设计隶属函数,同时,该设计方法也只采用一个规则库。在设计上可以看成是传统的模糊逻辑控制系统扩展成为多变量模糊逻辑控制系统,并且设计方法比较简单。
(2)设计了多变量模糊逻辑控制器,并推导出解析模型
引用一个推理机制来推导出多变量模糊逻辑控制器的解析模型,建立了多变量模糊逻辑控制和传统PID控制参数之间的关系,从而PID控制器的参数整定方法可用来设计多变量模糊逻辑控制器的比例因子(参数),此外解析模型可以用来研究控制系统的稳定性。
(3)提出了多变量模糊逻辑控制器基于PID的参数整定方法
针对稳定系统采用内模控制的参数设计方法来整定参数。针对不稳定系统,采用增益裕度和相位裕度来整定参数。针对多入多出系统,先将系统解耦,转化为多个单入单出系统,多变量模糊逻辑控制器用于控制解耦后的系统,PID控制器的参数用于设计多变量模糊逻辑控制器的参数。针对分布参数系统,本文先将其时空变量分离,运用Galerkin方法得到分布参数系统的有限维近似模型,然后根据近似模型设计多变量模糊逻辑控制器,再根据空间基函数合成时空控制器来控制分布参数系统,该方法考虑了系统足够的空间信息。通过仿真表明这些设计方法都是非常有效的。
(4)研究了多变量模糊逻辑控制器的智能参数调节方法
运用神经网络来辨识多入多出系统中的未知量,采用梯度下降来自适应调节多变量模糊逻辑控制器的比例因子,通过仿真可以看到该方法行之有效。针对分布参数系统,运用粒子群优化算法设计了多变量模糊逻辑控制器的参数,取得了理想的控制效果。此外,根据多变量模糊逻辑控制器的数学模型,将其应用于分布参数系统控制的稳定性进行了分析,给出了多变量模糊逻辑控制器控制分布参数系统的稳定条件。
(5)扫描探针显微镜的探针在空间运动是一个多入多出系统,运用多变量模糊逻辑控制器对探针运动进行控制,取得了比传统PID控制器更好的控制效果,从而验证了多变量模糊逻辑控制器设计的有效性。
In practical industrial processes, there are many multi-inputs multi-outputs (MIMO) systems, such as multi-link robot and probe movement of scanning probe microscopy (SPM), etc. Morever, states and controls of many distributed parameter systems (DPS) are related with time and space. These systems are called or spatio-temporal systems, such as micro-cantilever in SPM and catalytic reaction rod, etc. DPS are inherent infinite-dimensional, and they are usually converted to MIMO systems with some low-order approximation modeling methods in convenient for controlling them, and will deduce large modeling error. Those systems have uncertainties, such as unknown nonlinearities, disturbances etc., therefore, it is difficult to get their precise models. Traditional controllers, such as PID, cannot get a sound performance. In contract, intelligent methods which are developing these years, such as fuzzy control, can reduce dependence on the mathematical model. However, it needs to design many membership functions (MF) and rule bases on expert experience when many fuzzy logic controllers are used to control them. This design method is complex relatively. In order to solve those problems, the major work of the paper focuses on the following aspects:
(1) Multi-variable fuzzy logic system is built.
On account of only one MF being adopted for all subsystems, MFs for other subsystems are adjusted by scaling factors. A multi-variable fuzzy logic control system is designed following the fuzzy matrix theory. At the same time, the control system adopts only one traditional rule base, and there is no need to design MFs for all subsystems according to expert experience. The control system can be considered as an extension of traditional fuzzy system, and the design method is very simple.
(2) A multi-variable fuzzy logic controller is designed, and a mathematical model is deduced.
Mathematical model of the multi-variable fuzzy logic controller (FLC) is deduced following an inference engine. Relationships between multi-variable FLC and PID controller are built. Therefore, scaling factors (parameters) of multi-variable FLC can be tuned through tuning method of PID controller, and the design method is simple.
(3) Tuning method of multi-variable FLC is proposed based on PID controller.
Tuning based on internal mode control is proposed for stable processes. Phase margin and gain margin tuning method is proposed for unstable processes. For MIMO systems, parameters of PID are used to design parameters of multi-variable FLC thorough decoupling. For DPS, a finite-dimensional approximate model is obtained through time/space variable separation and Galerkin method. The approximate model is used to design multi-variable FLC,and a spatio-temporal controller is synthesized by spatial basis and multi-variable FLC. Enough spatial information is considered in this method and the design method is effective through simulating.
(4) Intelligent tuning methods of multi-variable FLC are researched.
Scaling factors of multi-variable FLC are adaptively adjusted by gradient descent, and neural network is used to identify unknown variables. The simulations show the usefulness of it. Particle swarm optimization is used to tuning parameters of multi-variable FLC for DPS, and a sound performance is obtained from simulations. Stability of multi-variable FLC controlled DPS is analyzed through the mathematical model. The stability conditions are also given for the controlled system.
(5) Probe movement of SPM in nano-manipulation platform is considered as a DPS. Multi-variable FLC is used to control the movement. Performance of multi-variable FLC is better than PID controller in experiment. Therefore, the design of multi-variable FLC are effective.
引文
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