非线性系统的约束控制及其应用研究

发布时间：2018-01-05 13:05

本文关键词：非线性系统的约束控制及其应用研究　出处：《西北工业大学》2016年博士论文　论文类型：学位论文

【摘要】：由于控制对象物理局限性、系统干扰和系统安全等因素的影响,实际控制系统不可避免地会受到输入、输出或状态约束等约束特性的限制。这些系统约束的存在使得控制器的设计更加复杂与困难,非线性系统的约束控制也成为非线性控制领域的研究热点。基于障碍Lyapunov函数(Barrier Lyapunov Function)的约束控制方法因其不需要系统的精确解而被广泛用来处理状态约束与输出约束的问题,但是该控制方法采用的backstepping技术需要对虚拟稳定函数进行重复求导带来了系数膨胀的问题。动态面技术通过引入一阶滤波器来获得微分项,从而很好地避免了这个问题。本文基于非对称障碍Lyapunov函数,结合动态面技术,针对具有输出约束特性的非线性系统的控制理论与应用,主要研究了一类具有严格反馈形式的非线性系统的时变输出约束控制和一类具有不确定系统参数的非线性系统的输出约束控制问题。并针对无刷直流电机中复杂的非线性环节和不确定的负载转矩问题,设计了基于分数阶微积分的负载转矩观测器,提出了无刷直流电机系统的改进动态面控制方案。针对飞机全电刹车系统,直接考虑系统工作的稳定区域问题,在已有滑移率控制方法的基础上,提出了滑移率输出约束控制策略,从根本上避免了抱死现象的发生。同时针对结合系数的不确定性问题,设计了自适应的滑移率输出约束控制方案,提高了刹车效率和系统鲁棒性。本文的具体工作归纳如下:1.阐述了非线性控制理论的研究现状及其发展趋势,并对无刷直流电机系统的研究现状和飞机全电刹车系统的研究情况进行了综述。2.针对一类具有严格反馈形式的N阶非线性系统,在具有时变输出约束条件下,基于非对称障碍Lyapunov函数,设计了动态面控制器。设计过程中引入的非对称障碍Lyapunov函数,放宽了对系统初始条件的约束限制,并且沿闭环系统轨线,获得Lyapunov函数的导数是负半定的,从而使得控制系统既不违背系统的约束,又使闭环系统的跟踪误差最终一致有界稳定并收敛到零的很小邻域。引进动态面技术后,降低了对稳定函数高阶可微的要求和跟踪误差变换函数高能量的要求,简化了控制器设计的复杂性。仿真算例验证了基于非对称障碍Lyapunov函数的动态面控制方法具有良好的跟踪性能。与单纯基于非对称障碍Lyapunov函数的控制方法相比,该控制器结构简单,并具有较好的抗干扰能力。3.针对一类具有输出约束和不确定参数的非线性系统的控制问题。基于非对称障碍Lyapunov函数,提出了一种通过在线估计修正未知的不确定参数的自适应约束动态面控制策略,并详细给出了控制器设计过程中控制参数的选取方法。该控制器结构简单,计算量少,同时能确保输出约束的有界性,能够使闭环系统的跟踪误差最终一致有界稳定且收敛到零的很小邻域。最后通过仿真算例进一步阐明了所提出方法的有效性以及鲁棒性。4.针对具有强烈非线性和不确定性的无刷直流电机系统,将本文提出的非对称障碍Lyapunov函数动态面约束控制方法,在horsepower dynamometer实验平台上进行了实验验证。对负载转矩这一电机系统的重要不确定性因素,利用分数阶微积分设计了一种自适应负载转矩观测器,对负载转矩进行了观测,有效的补偿了负载变化给系统带来的控制扰动。实验结果表明分数阶负载转矩观测器对系统的负载扰动和电机参数变化具有响应速度快、跟踪能力强、控制精度高、自适应能力强等特点,并且简单易用,在工程上有一定的实用价值。通过两组仿真实验,阐述了基于障碍Lyapunov函数和动态面技术的输出约束控制方法在实际系统中的优势。5.对飞机防滑刹车系统的滑移率输出约束控制问题进行了研究。首次通过直接考虑滑移率的稳定区域和不稳定区域来设计控制器,提出了以约束滑移率工作在稳定区域的约束控制策略。在建立的飞机防滑刹车系统全状态模型的基础上,针对跑道状态已知的情形,提出了直接考虑刹车系统的工作区域来处理飞机全电刹车系统的滑移率输出约束控制问题;针对跑道状态未知的情形,提出了基于结合系数和滑移率之间不确定关系的自适应约束控制方法,该方法能够在线快速估计轮胎与跑道间的结合系数。最后通过一系列仿真实验说明了所提控制方案的有效性。
[Abstract]:Because the control object of physical limitations, influence of interference and system security system and other factors, the actual control system will inevitably be affected by input, output or state constraints. These characteristics limit the system constraint makes the controller design is more complex and difficult, constrained nonlinear control system has become a research hotspot in the field of nonlinear control. Lyapunov (Barrier Lyapunov Function) function based on constraint control method for exact solutions of the system are not needed and is widely used to deal with state constraints and output constraints, but the control method adopts backstepping technology to virtual stable function of repeated differentiation brings expansion coefficient problems. By introducing a first-order dynamic surface technology to obtain a differential filter, so as to avoid this problem. In this paper, based on the Lyapunov asymmetric barrier Function, combined with dynamic surface technology, control theory and application for nonlinear systems with constraints on the output characteristics of the output, a class of constrained control problem of nonlinear systems in strict feedback form the time-varying output constraints and control of a class of nonlinear systems with uncertain parameters is nonlinear. And for the complicated process of Brushless DC motor and uncertain load torque, a load torque observer is designed based on fractional calculus, we proposed an improved dynamic surface control scheme of Brushless DC motor system. According to the aircraft electric braking system, considering the stable region of the system, based on the existing slip ratio control method, is put forward the slip ratio control strategy and output constraints, fundamentally avoids the occurrence of locking phenomenon. At the same time to solve the uncertainty problem of combination coefficient, was designed. The slip rate output constraint control scheme can improve braking efficiency and robustness of the system. The main work of this paper is summarized as follows: 1. describes the research status and development trend of nonlinear control theory, and the research of aircraft brushless DC motor system of electric braking system are surveyed with strict feedback.2. N order form for a class of nonlinear system, variable output constraints with Lyapunov under asymmetric barrier function based on the design of the dynamic surface controller. The number of Lyapunov non symmetric function obstacle to the design process, to relax the restriction on the initial condition of the system, and the closed-loop system along the trajectory, the derivative Lyapunov function is negative semidefinite, which makes the control system without violating the system constraints, and make the tracking error of the closed-loop system is uniformly ultimately bounded and converges to zero A very small neighborhood. The introduction of dynamic surface technology, reduces the stability function of higher order differentials request and tracking error transform function of high energy, simplifies the controller design. The simulation examples demonstrate the dynamic surface Lyapunov asymmetric barrier function control method has good tracking performance. Based on compared based on the control method of Lyapunov asymmetric barrier function, the controller has the advantages of simple structure, and has a good anti-jamming capability of.3. control problem for a class of nonlinear systems with output constraints and uncertain parameters. The Lyapunov asymmetric barrier function based on a through online estimation of unknown uncertain parameters adaptive dynamic surface constraint the control strategy, and gives the detailed method of selecting parameters of the controller design process. The controller has the advantages of simple structure, less computation, and can ensure the transmission A constraint can make the boundedness of the tracking errors of the closed-loop system is uniformly ultimately bounded stable and converges to a small neighborhood of zero. The simulation results further illustrate the validity of the proposed methods and the robustness against.4. with strong nonlinearity and uncertainty of Brushless DC motor system, dynamic Lyapunov asymmetric the barrier function of plane constraint control method proposed in this paper, experiments were carried out in the horsepower dynamometer experimental platform. The important uncertainties on the load torque the motor system, the use of fractional calculus to design an adaptive load torque observer of load torque were observed, the effective compensation control system for load change bring disturbance. The experimental results show that the fractional load torque observer has fast response to load disturbances and parameter variations with the system. Trace ability, high control precision, self-adaptive, and easy to use, has a certain practical value in engineering. Through two sets of simulation experiments, expounds the problem of the sliding output constraint function and dynamic obstacle Lyapunov surface technology control method in the actual system, the advantages of.5. based on aircraft antiskid braking system the rate of output control is studied. For the first time by directly considering the stable region and unstable region slip rate to design a controller, the control strategy was proposed in the stable region constraints to constrain slip work. Foundation brake system model in aircraft antiskid state on the runway for state known situations is proposed considering the work area slip brake system to handle aircraft electric braking system output rate constraint control problem; the runway state is unknown, is proposed based on The adaptive constraint control method based on the uncertain relationship between coefficient and slip rate can quickly and quickly estimate the combining coefficient between tire and runway. Finally, a series of simulation experiments are carried out to illustrate the effectiveness of the proposed control scheme.

【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP273

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