智能分数阶滑模控制及系统参数整定方法的研究
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摘要
滑模变结构控制最突出的优点是系统状态一旦进入滑模运动，对系统扰动及参数变化具有完全鲁棒性。同时，设计方法简单，易于实现。这些优越特性使滑模控制理论成为控制界的重要研究分支。但是，滑模控制系统中的抖震问题限制了它在实际工程中的应用。因此，滑模变结构控制系统中抖震削弱或消除一直是工程实际问题的实时控制中一个研究热点，本文的研究具有重要的意义。
针对传统滑模变结构控制系统中的抖震问题，本文把分数阶微积分理论引入到滑模控制方法当中，提出了分数阶滑模控制策略，给出了分数阶系统的稳定性分析及其削减抖震的机理分析。考虑不确定系统上界难于测量以及开关增益对抖震的影响，利用智能控制算法的优点，给出了分数阶滑模控制系统的参数整定方法。深入分析传统滑模控制系统抖震产生的机理，提出了无抖震分数阶滑模控制算法，给出了控制系统相对一定控制对象的参数整定规则。本文结合分数阶微积分理论、智能控制算法和滑模控制算法，深入研究了消除抖震并具有完全鲁棒性的滑模控制系统以及其参数整定方法，具体研究内容如下：
深入分析了传统一阶滑模控制系统中的抖震现象，根据一阶滑模抖震产生机理，提出混合一阶与二阶滑模控制系统，给出了稳定性证明和该混合控制器的滑模逼近条件，分析了该混合控制系统相对于单一一阶或二阶滑模控制系统在削减抖震的优势。基于永磁同步电机伺服系统进行了仿真分析和实验验证，结果说明了该控制方法相对单一阶滑模控制系统减少了抖震。
纵然采用混合一阶与二阶滑模控制方法，系统的抖震也相当剧烈。利用分数阶系统在滑模运动中能以比整数阶系统较慢的能量传递速度特性，设计分数阶切换流形，驱使系统状态较为缓慢地收敛到零点。分数阶微积分的引入在提高系统性能的同时也增加了系统参数的整定难度，基于经典控制理论，给出了分数阶滑模等效控制器的参数整定规则；利用模糊推理算法，给出了切换增益的整定方法。考虑到分数阶滑模控制系统在滑模逼近阶段对系统扰动和参数变化不具有很强的鲁棒性，设计全控制域的完全鲁棒性分数阶滑模控制策略。仿真和实验结果说明了分数阶滑模控制系统能有效地削减抖震。
传统滑模控制系统滑模运动逼近条件的建立依赖于被控对象的数学模型，然而对于未知上界的不确定系统或者高阶系统，滑模逼近条件的建立显得过于复杂。考虑到模糊控制系统不依赖系统数学模型，且能利用专家经验，把滑模控制理论的优点融合到模糊控制当中，并利用分数阶微积分的优越特性，建立基于分数阶滑模面的模糊滑模控制系统。针对扰动和系统参数变化的不确定性，利用模糊推理算法实时整定不确定参数值，使得基于等效控制的分数阶滑模控制系统保持在最小抖震状态。仿真和实验结果说明，基于分数阶滑模面的模糊控制系统能柔化系统的抖震，并保证系统在最少输入信号的情况下也能保持传统滑模控制系统的鲁棒性；基于等效控制的模糊分数阶滑模系统能根据系统参数和扰动的变化实现最小抖震的控制。
考虑到模糊规则的建立要求一定的专家经验，利用神经网络的学习功能，设计基于神经网络参数整定的分数阶滑模控制系统。深入分析分数阶系统与整数阶系统的稳定性，提出利用整数阶系统的镇定方法研究分数阶系统的稳定性。尽管模糊推理系统不依赖被控对象数学模型，但存在一定的静差。利用神经网络能逼近任意非线性函数的优点，提出基于分数阶切换流形的神经网络控制系统。仿真和实验结果说明了神经网络分数阶滑模控制系统不但能削减抖震，而且能达到较高的综合控制性能。
尽管采用模糊推理和神经网络控制等人工智能算法，基于开关切换作用的滑模控制系统依然存在抖震问题。采用分数阶PI~λD~μ控制律驱使系统在任意初始状态都能达到给定的滑模面，理论证明了系统状态轨迹进入滑模运动后，在满足一定条件下，控制系统对扰动和参数变化具有完全鲁棒性。给出了基于经典控制理论的控制器参数整定方法和基于模糊推理机制的滑模面参数自整定算法。仿真和实验结果说明了该基于滑模面的分数阶控制系统不但能根除抖震，而且保持了传统滑模控制系统对扰动和参数变化的鲁棒性。
One of the most distinguished features of the sliding mode control(SMC) is that afterreaching the sliding mode, the system is robust to parameter uncertainties and disturbances.And the control algorithm is simple and easy to be realized. All these fetures of SMC lead tothe importamt position of SMC theory. However, the chattering existed in SMC system limitsits application. Thus, counteracting the chattering for SMC system interests many researchers.And the study of this paper focusing on reducing the chattering is valuable.
For dealing with the chaterring, this paper integrates the advantage of fractional ordercalculus and SMC to propose a fractional order calculus SMC system. The stability andmechanism for descring the chaterring are analysed. Considering the uncertainties impact onchattering, a tuning method based on intenlegent algorithm is proposed to obtain the gain offractional order SMC system. Based on a deep analysis of the chaterring occurring, afractional order SMC is propsed, which is robust with regard to parameters variations anddisturbances as well as eliminating the chaterring. And a tuning method is proposed for thiscontrol scheme. This paper integrates the fractional calculus and intelligent algorithm intoSMC to deal with chattering and give the parameters tuning methods. The research contentsare as follow:
Based on depth analysis of chattering phenomenon existing in the traditional firstorder SMC systems, a hybrid first order and second order SMC system isproposed, the stability proof of the hybrid SMC system is given. The advantages of the hybridcontrol system in descring the chaterring is superior to that of a single first order or secondorder SMC system. Simulations and experiments based on permanent magnet synchronousmotor servo system verificate that the control method is effective.
Using the unique convergence properties that the energy transmission speed of fractionalorder systems is slower than that of integer order system in the sliding phase,a fractional order sliding mode interface is designed to drive the systemstatus slowly converge to zero. Fractional calculus is introduced to enhance the controlperformance, but it also adds the difficulty in parameters tuning. Based on the tradicionalcontrol theory, this paper gives the tuning rules for the control law. And using fuzzy inference algorithm, a tuning method is proposed for switching gain. Since the reaching phase of SMCis sencetive to parameters variations and disturbances, a control scheme based on overallrobustness sliding mode interface is proposed. Simulations and experiments basedon permanent magnet synchronous motor servo system verificate that the control methodrudecues the chaterring effectively.
Since the design of SMC relaies on dynamic model, it is difficult for complex system toyield the control law. Using the advantages of fuzzy inference system and fractional calculus,a fuzzy controller based on fractional order sliding mode interface is proposed. Consideringthe uncertainties, a fuzzy logic inference sysem is adopted to obtain the gain of SMC based onequivalent control law. Simulations and experiments based on permanent magnet synchronousmotor servo system verificate that the control schemes are not only robust to disturbance, butachieve high control performance.
The building of fuzzy controller requires some experiences. It is not easy to apply.Instead, using the learning function of neural network, a tuning method based on neuralnetwork control algorithm is designed to obtain the gain of fractional order SMC system. Anda neural network controller is proposed to deal with the static error existing in fuzzy controlsystem. The stability sproof is given for fractional order system with the stability theory ofinteger order system. Simulations results show that the control schemes achieve high controlperformance under the existence of external disturbances and parameters variations.
Even though the intelligent algorithm is used to design the fractional order SMC, thechaterring can not be elminated. This paper proposed a continue PI~λD~μcontrol law to replacethe switching control action. It can drive the system states to given sliding interface whereverthe initial states are. The given lemma shows validate that when some conditions are satisfied,this control schem is robut with regard to disturbances and parameters variations. And thetuning method for controller parameters is given. Simulations results show that the controlschemes achieve high control performance under the existence of external disturbances andparameters variations.
针对传统滑模变结构控制系统中的抖震问题，本文把分数阶微积分理论引入到滑模控制方法当中，提出了分数阶滑模控制策略，给出了分数阶系统的稳定性分析及其削减抖震的机理分析。考虑不确定系统上界难于测量以及开关增益对抖震的影响，利用智能控制算法的优点，给出了分数阶滑模控制系统的参数整定方法。深入分析传统滑模控制系统抖震产生的机理，提出了无抖震分数阶滑模控制算法，给出了控制系统相对一定控制对象的参数整定规则。本文结合分数阶微积分理论、智能控制算法和滑模控制算法，深入研究了消除抖震并具有完全鲁棒性的滑模控制系统以及其参数整定方法，具体研究内容如下：
深入分析了传统一阶滑模控制系统中的抖震现象，根据一阶滑模抖震产生机理，提出混合一阶与二阶滑模控制系统，给出了稳定性证明和该混合控制器的滑模逼近条件，分析了该混合控制系统相对于单一一阶或二阶滑模控制系统在削减抖震的优势。基于永磁同步电机伺服系统进行了仿真分析和实验验证，结果说明了该控制方法相对单一阶滑模控制系统减少了抖震。
纵然采用混合一阶与二阶滑模控制方法，系统的抖震也相当剧烈。利用分数阶系统在滑模运动中能以比整数阶系统较慢的能量传递速度特性，设计分数阶切换流形，驱使系统状态较为缓慢地收敛到零点。分数阶微积分的引入在提高系统性能的同时也增加了系统参数的整定难度，基于经典控制理论，给出了分数阶滑模等效控制器的参数整定规则；利用模糊推理算法，给出了切换增益的整定方法。考虑到分数阶滑模控制系统在滑模逼近阶段对系统扰动和参数变化不具有很强的鲁棒性，设计全控制域的完全鲁棒性分数阶滑模控制策略。仿真和实验结果说明了分数阶滑模控制系统能有效地削减抖震。
传统滑模控制系统滑模运动逼近条件的建立依赖于被控对象的数学模型，然而对于未知上界的不确定系统或者高阶系统，滑模逼近条件的建立显得过于复杂。考虑到模糊控制系统不依赖系统数学模型，且能利用专家经验，把滑模控制理论的优点融合到模糊控制当中，并利用分数阶微积分的优越特性，建立基于分数阶滑模面的模糊滑模控制系统。针对扰动和系统参数变化的不确定性，利用模糊推理算法实时整定不确定参数值，使得基于等效控制的分数阶滑模控制系统保持在最小抖震状态。仿真和实验结果说明，基于分数阶滑模面的模糊控制系统能柔化系统的抖震，并保证系统在最少输入信号的情况下也能保持传统滑模控制系统的鲁棒性；基于等效控制的模糊分数阶滑模系统能根据系统参数和扰动的变化实现最小抖震的控制。
考虑到模糊规则的建立要求一定的专家经验，利用神经网络的学习功能，设计基于神经网络参数整定的分数阶滑模控制系统。深入分析分数阶系统与整数阶系统的稳定性，提出利用整数阶系统的镇定方法研究分数阶系统的稳定性。尽管模糊推理系统不依赖被控对象数学模型，但存在一定的静差。利用神经网络能逼近任意非线性函数的优点，提出基于分数阶切换流形的神经网络控制系统。仿真和实验结果说明了神经网络分数阶滑模控制系统不但能削减抖震，而且能达到较高的综合控制性能。
尽管采用模糊推理和神经网络控制等人工智能算法，基于开关切换作用的滑模控制系统依然存在抖震问题。采用分数阶PI~λD~μ控制律驱使系统在任意初始状态都能达到给定的滑模面，理论证明了系统状态轨迹进入滑模运动后，在满足一定条件下，控制系统对扰动和参数变化具有完全鲁棒性。给出了基于经典控制理论的控制器参数整定方法和基于模糊推理机制的滑模面参数自整定算法。仿真和实验结果说明了该基于滑模面的分数阶控制系统不但能根除抖震，而且保持了传统滑模控制系统对扰动和参数变化的鲁棒性。
One of the most distinguished features of the sliding mode control(SMC) is that afterreaching the sliding mode, the system is robust to parameter uncertainties and disturbances.And the control algorithm is simple and easy to be realized. All these fetures of SMC lead tothe importamt position of SMC theory. However, the chattering existed in SMC system limitsits application. Thus, counteracting the chattering for SMC system interests many researchers.And the study of this paper focusing on reducing the chattering is valuable.
For dealing with the chaterring, this paper integrates the advantage of fractional ordercalculus and SMC to propose a fractional order calculus SMC system. The stability andmechanism for descring the chaterring are analysed. Considering the uncertainties impact onchattering, a tuning method based on intenlegent algorithm is proposed to obtain the gain offractional order SMC system. Based on a deep analysis of the chaterring occurring, afractional order SMC is propsed, which is robust with regard to parameters variations anddisturbances as well as eliminating the chaterring. And a tuning method is proposed for thiscontrol scheme. This paper integrates the fractional calculus and intelligent algorithm intoSMC to deal with chattering and give the parameters tuning methods. The research contentsare as follow:
Based on depth analysis of chattering phenomenon existing in the traditional firstorder SMC systems, a hybrid first order and second order SMC system isproposed, the stability proof of the hybrid SMC system is given. The advantages of the hybridcontrol system in descring the chaterring is superior to that of a single first order or secondorder SMC system. Simulations and experiments based on permanent magnet synchronousmotor servo system verificate that the control method is effective.
Using the unique convergence properties that the energy transmission speed of fractionalorder systems is slower than that of integer order system in the sliding phase,a fractional order sliding mode interface is designed to drive the systemstatus slowly converge to zero. Fractional calculus is introduced to enhance the controlperformance, but it also adds the difficulty in parameters tuning. Based on the tradicionalcontrol theory, this paper gives the tuning rules for the control law. And using fuzzy inference algorithm, a tuning method is proposed for switching gain. Since the reaching phase of SMCis sencetive to parameters variations and disturbances, a control scheme based on overallrobustness sliding mode interface is proposed. Simulations and experiments basedon permanent magnet synchronous motor servo system verificate that the control methodrudecues the chaterring effectively.
Since the design of SMC relaies on dynamic model, it is difficult for complex system toyield the control law. Using the advantages of fuzzy inference system and fractional calculus,a fuzzy controller based on fractional order sliding mode interface is proposed. Consideringthe uncertainties, a fuzzy logic inference sysem is adopted to obtain the gain of SMC based onequivalent control law. Simulations and experiments based on permanent magnet synchronousmotor servo system verificate that the control schemes are not only robust to disturbance, butachieve high control performance.
The building of fuzzy controller requires some experiences. It is not easy to apply.Instead, using the learning function of neural network, a tuning method based on neuralnetwork control algorithm is designed to obtain the gain of fractional order SMC system. Anda neural network controller is proposed to deal with the static error existing in fuzzy controlsystem. The stability sproof is given for fractional order system with the stability theory ofinteger order system. Simulations results show that the control schemes achieve high controlperformance under the existence of external disturbances and parameters variations.
Even though the intelligent algorithm is used to design the fractional order SMC, thechaterring can not be elminated. This paper proposed a continue PI~λD~μcontrol law to replacethe switching control action. It can drive the system states to given sliding interface whereverthe initial states are. The given lemma shows validate that when some conditions are satisfied,this control schem is robut with regard to disturbances and parameters variations. And thetuning method for controller parameters is given. Simulations results show that the controlschemes achieve high control performance under the existence of external disturbances andparameters variations.
引文
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