回滞非线性系统的鲁棒控制
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摘要
早在上个世纪六十年代就有人提出回滞非线性系统控制问题，但因当时人们对控制的要求比较低，对回滞非线性系统的控制可通过选择适当的器件和用线性化系统近似代替回滞非线性来进行。对于精度要求不高的场合，可采用电阻和电容桥路或者电荷控制等方法来削弱回滞。近年来，由于精密加工和各种国防系统对控制精度要求的不断提高，从材料本身已很难克服回滞特性对控制系统性能的影响，因此从控制角度研究回滞非线性系统的控制以克服回滞对系统性能的影响，以适应目前各种精密控制对象对系统性能的高要求，是一具有重要理论意义和应用价值的课题，目前已引起国内外控制和机械工程界的高度重视。此外，回滞也存在于其他许多领域，比如在经济领域和生理学方面。
具有回滞特性的系统是不可微分的非线性系统，所以不能采用可微分的非线性和线性系统的控制理论和方法来进行研究。本文通过对回滞特性的研究，从控制角度提出了回滞的通用模型，它由两部分组成：线性部分和已知上界的不确定非线性部分。此时回滞系统可以看作是输入不确定非线性系统，从而可以采用一般非线性系统的鲁棒控制方法来研究。
滑模控制由于算法简单、响应快速和抗干扰性能好，特别适用于解决非线性不确定系统的鲁棒控制问题。但其抖动问题却可能造成系统硬件的损坏，甚至导致系统的不稳定，因而大大限制了它在实际控制问题中的应用。同时由于滑模控制的算法中，求控制律和滑动流形存在交叉问题，所以对于高阶的系统，其设计过程也变得较为复杂。本文利用Ackermann's Formula首先对滑模控制的算法进行改进，使得算法中不存在交叉问题，然后提出的模型参考滑模控制可以很好地削弱回滞特性，回滞系统的鲁棒控制研究要解决的核心问题最终还是归为解决滑模控制中抖振和收敛问题，为此，本文最后研究了有限时间收敛机理和具有较强鲁棒性的低抖振非奇异终端滑模控制。
本文作为国家自然科学基金(60374016)资助项目“具动态回滞非线性系统的建模与控制问题研究”和广东省自然科学基金(020848)资助项目“高阶滑模控制策略及在不确定控制系统中的应用研究”的研究内容之一，从控制角度给出回滞的一般模型，对回滞非线性系统鲁棒控制进行了研究和探索，包括对回滞逆模型前馈补偿控制的PID控制的改进和基于滑模控制的模型参考控制和终端滑模控制等。所提出的控制思路和对应方法可以有效的削弱回滞，达到控制的目的。
The problem of control on nonlinear systems with hysteresis has been put forward since 1960's. Nonlinear systems with hysteresis could been controlled by choosing appropriate apparatuses and approximately replacing systems with hysteresis by linearization systems in lower demand on control. In the situation of demand on low precision, using resistance and capacitance bridge circuit or charge control could mitigate hysteresis. It is difficult from material to come over the effect caused by hysteresis on performance of controlled systems, with higher and higher demand on control precision in high precision process and all kinds of national defense systems recently. So it is task with important theory significance and application value, to study form control consideration the control of nonlinear systems with hysteresis to come over the effect by hysteresis on systematic performance, and gets highly attention in control and mechanic engineering field home and abroad. It can adapt to high demand on systematic performance in all kinds of precision control. However, hysteresis also exits in other field, for instance, economy and physiology.
Systems with hysteresis are nondifferentiable nonlinear systems. So they cannot be studied through control theories and methods used in differentiable nonlinear and linear systems. A general model for hysteresis form control consideration is put forward in this dissertation after studying characteristic of hysteresis, which consists of two parts: linear part and uncertain nonlinear part with known limit. Systems with hysteresis can be looked as nonlinear systems with uncertain input, and studied through robust control theory used in nonlinear systems.
Sliding mode control (SMC) is especially suitable to apply in the robust control on nonlinear systems with uncertainty due to simpleness of algorithm, quickness of response and good performance of anti-disturbance. However, chattering which can result in breakage of hardware and even instability in systems greatly limits the application of SMC. At the same time, there exits crossover in getting control law and manifold in algorithm of SMC, and the control design becomes complex, especially in high order systems. Ackermann's Formula is employed to improve algorithm of SMC in this dissertation, and the crossover disappears. Mode-reference SMC is employed then to
具有回滞特性的系统是不可微分的非线性系统，所以不能采用可微分的非线性和线性系统的控制理论和方法来进行研究。本文通过对回滞特性的研究，从控制角度提出了回滞的通用模型，它由两部分组成：线性部分和已知上界的不确定非线性部分。此时回滞系统可以看作是输入不确定非线性系统，从而可以采用一般非线性系统的鲁棒控制方法来研究。
滑模控制由于算法简单、响应快速和抗干扰性能好，特别适用于解决非线性不确定系统的鲁棒控制问题。但其抖动问题却可能造成系统硬件的损坏，甚至导致系统的不稳定，因而大大限制了它在实际控制问题中的应用。同时由于滑模控制的算法中，求控制律和滑动流形存在交叉问题，所以对于高阶的系统，其设计过程也变得较为复杂。本文利用Ackermann's Formula首先对滑模控制的算法进行改进，使得算法中不存在交叉问题，然后提出的模型参考滑模控制可以很好地削弱回滞特性，回滞系统的鲁棒控制研究要解决的核心问题最终还是归为解决滑模控制中抖振和收敛问题，为此，本文最后研究了有限时间收敛机理和具有较强鲁棒性的低抖振非奇异终端滑模控制。
本文作为国家自然科学基金(60374016)资助项目“具动态回滞非线性系统的建模与控制问题研究”和广东省自然科学基金(020848)资助项目“高阶滑模控制策略及在不确定控制系统中的应用研究”的研究内容之一，从控制角度给出回滞的一般模型，对回滞非线性系统鲁棒控制进行了研究和探索，包括对回滞逆模型前馈补偿控制的PID控制的改进和基于滑模控制的模型参考控制和终端滑模控制等。所提出的控制思路和对应方法可以有效的削弱回滞，达到控制的目的。
The problem of control on nonlinear systems with hysteresis has been put forward since 1960's. Nonlinear systems with hysteresis could been controlled by choosing appropriate apparatuses and approximately replacing systems with hysteresis by linearization systems in lower demand on control. In the situation of demand on low precision, using resistance and capacitance bridge circuit or charge control could mitigate hysteresis. It is difficult from material to come over the effect caused by hysteresis on performance of controlled systems, with higher and higher demand on control precision in high precision process and all kinds of national defense systems recently. So it is task with important theory significance and application value, to study form control consideration the control of nonlinear systems with hysteresis to come over the effect by hysteresis on systematic performance, and gets highly attention in control and mechanic engineering field home and abroad. It can adapt to high demand on systematic performance in all kinds of precision control. However, hysteresis also exits in other field, for instance, economy and physiology.
Systems with hysteresis are nondifferentiable nonlinear systems. So they cannot be studied through control theories and methods used in differentiable nonlinear and linear systems. A general model for hysteresis form control consideration is put forward in this dissertation after studying characteristic of hysteresis, which consists of two parts: linear part and uncertain nonlinear part with known limit. Systems with hysteresis can be looked as nonlinear systems with uncertain input, and studied through robust control theory used in nonlinear systems.
Sliding mode control (SMC) is especially suitable to apply in the robust control on nonlinear systems with uncertainty due to simpleness of algorithm, quickness of response and good performance of anti-disturbance. However, chattering which can result in breakage of hardware and even instability in systems greatly limits the application of SMC. At the same time, there exits crossover in getting control law and manifold in algorithm of SMC, and the control design becomes complex, especially in high order systems. Ackermann's Formula is employed to improve algorithm of SMC in this dissertation, and the crossover disappears. Mode-reference SMC is employed then to
引文
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