空天飞行器基于模糊理论的鲁棒自适应控制研究
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摘要
空天飞行器(ASV)是各国正在大力发展的新型飞行器,美欧等国都有各自的空天研究计划,并取得了不少研究进展,而我国在高超声速飞行器方面尚处于起步阶段。空天飞行器在运行中表现出的多任务、多工作模式、大范围高速机动等特点使得控制系统设计成为一项极具挑战的研究课题。围绕这一基础科学问题,本文在空天飞行器T-S模糊建模与分析、不确定非线性系统模糊控制、T-S模糊系统建模训练以及模糊自适应控制系统设计四个方面开展了较为深入的研究。
首先,根据国内外公开发表的文献资料及我们实验室的已有成果,建立起ASV再入段完整的动力学方程和运动学方程,其中气动力系数和力矩系数是迎角、马赫数及气动舵面偏角的函数,发动机模型为反作用发动机的组合推进装置,飞行器的质心、惯性矩是飞行器质量的时变函数。开环分析表明整个模型能够体现出ASV复杂的非线性、强耦合、快速时变以及不确定性等特点,具有一定的代表性,可以满足未来ASV先进制导和控制等问题的理论研究和仿真验证的需要。
其次,基于T-S模糊逼近理论,通过分析ASV再入段的姿态运动的特点,确立了相应的模糊规则、模糊隶属度函数以及各模糊规则下的模糊子系统,建立了基于T-S模糊模型的ASV再入姿态的运动模型和仿真平台,为后文的控制器设计与分析奠定基础。
接着,基于已建立的ASV再入姿态的T-S模糊模型,在区域极点配置理论分析的指导下提出了具有极点约束的T-S模糊保性能控制新策略,并利用H∞控制抑制外界干扰,给出了一种模糊鲁棒控制的设计方法。通过Lyapunov理论证明,闭环系统所有状态渐进稳定。根据不同的性能指标要求,分别设计了ASV姿态系统的状态反馈和输出反馈控制器。
随后,提出了新的基于模糊前馈的模糊鲁棒跟踪方案。首先结合T-S模糊系统的优势将线性系统的前馈控制方案推广至非线性系统,避免了基于线性矩阵不等式(LMI)的T-S模糊跟踪控制方案中需要引入的增广系统,减少了系统设计的维数,降低了设计保守性,并采用Lyapunov方法严格证明出系统跟踪误差渐进稳定,考虑系统不确定性及外界干扰,设计出被控系统的模糊鲁棒跟踪控制器,并在针对复杂非线性系统输出跟踪和ASV姿态角跟踪问题的仿真中验证了方法的有效性。
然后,为了使得建立的模糊模型能够适应系统参数的变化,提出了一种新的L-M算法,并研究了其在T-S模糊建模中的应用。基于标准的L-M算法,在局部误差界的条件下,根据迭代参数取值的不同,定义迭代步长为逼近误差的函数,给出了改进后的L-M算法的参数迭代公式,并从理论上分析了它的收敛性是二次的。最后将所提算法应用于ASV姿态动态系统的模糊建模,训练时各线性系统参数和模糊隶属度函数参数均可在线调节。此外,训练时不过分依赖专家经验,与标准L-M算法相比,收敛速率明显加快,逼近精度高。
最后,研究了一种新的自适应调节律,在线调节模糊自适应控制的相关参数,与梯度法自适应调节律相比,参数收敛速度明显加快,针对复杂非线性系统的跟踪控制问题,设计出稳定的间接自适应模糊控制器,并有效改善了由于参数收敛速度慢而带来的系统振荡。接着将此方案推广至包含未建模动态的多输入多输出(MIMO)非线性系统,设计了ASV的姿态模糊自适应控制器。此外,考虑外界干扰对系统的影响,引入了鲁棒控制项,进一步改善了控制效果。
At present, many countries in the world are speeding up their efforts in the research on next generation reusable flight vehicles-aerospace vehicles (ASVs). The United States and European countries have their own aerospace projects and have achieved significant research progress, while, the research on hypersonic vehicles in our country is at in the initial stage. The control system design for the ASVs is a challenge research topic due to their multi-mission profiles, large attitude maneuvers and complicated flight conditions. In this dissertation, four relative problems, i.e. Takagi-Sugeno (T-S) fuzzy modeling and analysis for a conceptual ASV,fuzzy control for uncertain nonlinear system, T-S fuzzy system modeling training and fuzzy adaptive control system design, are studied.
First of all, a whole of kinetic equations and motion equations during the reentry phase of an ASV are presented based on the publicated literatures and the contributions of our lab. The coefficients of aerodynamic force and moment are given as functions of angle of attack, Mach number and control surface deflections. The propulsion system is a combination of reaction engine. Rigid-body mass moments of inertia and center of gravity location are time-varying functions of vehicle weight. Open-loop dynamics demonstrate that the proposed model can embody the characteristics of ASV, such as complicated nonlinearity, strong coupling, fast time-varying and uncertainties. The model has a certain representative and can be used to meet the requirements of research and simulation for advanced guidance and control problems.
Next, based on the T-S fuzzy approximation theory and the reentry attitude dynamics of ASV, the fuzzy rules, the membership functions and the fuzzy sub-systems are established. A simulation model for the reentry attitude dynamics based on T-S fuzzy system is presented, and it lays a foundation for the following controller design and analysis.
Then, based on the presented T-S fuzzy model for ASV reentry attitude dynamics, a new design method of T-S fuzzy guaranteed cost control law with pole constraints is proposed under the guidance of regional pole placement theory. The external disturbance is restricted by using H∞control technique, and a new fuzzy robust control design method is presented. The Lyapunov stability theory is used to prove asymptotic stability of all the states of the closed-loop system. With the different requirement of performance index, state feedback and output feedback controller for ASV attitude dynamic system are designed respectively.
The next, a new design technique of fuzzy robust tracking control based on fuzzy feedforward is proposed. By taking the advantages of T-S fuzzy systems, feedforward control scheme for linear system is extended to nonlinear system. Without the need of the augmented system of linear matrix inequality (LMI) based T-S fuzzy tracking control method, the dimension of system design is reduced, and less conservative is achieved. The asymptotic stability of system tracking error is guaranteed by using Lyapunov stability theory. Considering the system uncertainties and external disturbance, a fuzzy robust tracking controller of the controlled system is designed. The simulation results for the output tracking of complex nonlinear system and attitude angles tracking of ASV demonstrate the effectiveness of the proposed method.
Then, to enhance the adaptation of T-S fuzzy model as system parameters changes, a new Levenberg-Marquardt (L-M) algorithm is proposed, which can be used for Takagi-Sugeno fuzzy modeling. Based on standard L-M algorithm and under the condition of local error bound, the iteration step is defined as a function of approximation error according the different values of iteration parameters. A parameter iteration formula of the modified L-M algorithm is given, and its quadratic convergence is analysed theoretically. Then it is applied to training the ASV attitude dynamic systems based on T-S fuzzy model. This method can adjust the parameters of each linear polynomials and fuzzy membership functions on line. In addition, it does not rely on expert experience excessively when using it for systems modeling. Compared the proposed method with the standard L-M method, the convergence speed is accelerated and high approximation precision is achieved.
Finally, a new adaptive regulator is studied. It can adjust the parameters of fuzzy adaptive controller. Compared with gradient adaptive law, the parameter convergence rate is accelerated obviously. Aimed at the problem of output tracking control for complex nonlinear system, a stable indirect adaptive controller is presented and the system oscillations due to the low convergence speed of parameters are effectively improved. Then the control scheme is extended to multi-input multi-output (MIMO) square nonlinear plants with non-modeled dynamics and an attitude indirect fuzzy adaptive controller for ASV is designed. In addition, considering the effect of external disturbance, a robust control term is introduced and the control effect is further improved.
首先,根据国内外公开发表的文献资料及我们实验室的已有成果,建立起ASV再入段完整的动力学方程和运动学方程,其中气动力系数和力矩系数是迎角、马赫数及气动舵面偏角的函数,发动机模型为反作用发动机的组合推进装置,飞行器的质心、惯性矩是飞行器质量的时变函数。开环分析表明整个模型能够体现出ASV复杂的非线性、强耦合、快速时变以及不确定性等特点,具有一定的代表性,可以满足未来ASV先进制导和控制等问题的理论研究和仿真验证的需要。
其次,基于T-S模糊逼近理论,通过分析ASV再入段的姿态运动的特点,确立了相应的模糊规则、模糊隶属度函数以及各模糊规则下的模糊子系统,建立了基于T-S模糊模型的ASV再入姿态的运动模型和仿真平台,为后文的控制器设计与分析奠定基础。
接着,基于已建立的ASV再入姿态的T-S模糊模型,在区域极点配置理论分析的指导下提出了具有极点约束的T-S模糊保性能控制新策略,并利用H∞控制抑制外界干扰,给出了一种模糊鲁棒控制的设计方法。通过Lyapunov理论证明,闭环系统所有状态渐进稳定。根据不同的性能指标要求,分别设计了ASV姿态系统的状态反馈和输出反馈控制器。
随后,提出了新的基于模糊前馈的模糊鲁棒跟踪方案。首先结合T-S模糊系统的优势将线性系统的前馈控制方案推广至非线性系统,避免了基于线性矩阵不等式(LMI)的T-S模糊跟踪控制方案中需要引入的增广系统,减少了系统设计的维数,降低了设计保守性,并采用Lyapunov方法严格证明出系统跟踪误差渐进稳定,考虑系统不确定性及外界干扰,设计出被控系统的模糊鲁棒跟踪控制器,并在针对复杂非线性系统输出跟踪和ASV姿态角跟踪问题的仿真中验证了方法的有效性。
然后,为了使得建立的模糊模型能够适应系统参数的变化,提出了一种新的L-M算法,并研究了其在T-S模糊建模中的应用。基于标准的L-M算法,在局部误差界的条件下,根据迭代参数取值的不同,定义迭代步长为逼近误差的函数,给出了改进后的L-M算法的参数迭代公式,并从理论上分析了它的收敛性是二次的。最后将所提算法应用于ASV姿态动态系统的模糊建模,训练时各线性系统参数和模糊隶属度函数参数均可在线调节。此外,训练时不过分依赖专家经验,与标准L-M算法相比,收敛速率明显加快,逼近精度高。
最后,研究了一种新的自适应调节律,在线调节模糊自适应控制的相关参数,与梯度法自适应调节律相比,参数收敛速度明显加快,针对复杂非线性系统的跟踪控制问题,设计出稳定的间接自适应模糊控制器,并有效改善了由于参数收敛速度慢而带来的系统振荡。接着将此方案推广至包含未建模动态的多输入多输出(MIMO)非线性系统,设计了ASV的姿态模糊自适应控制器。此外,考虑外界干扰对系统的影响,引入了鲁棒控制项,进一步改善了控制效果。
At present, many countries in the world are speeding up their efforts in the research on next generation reusable flight vehicles-aerospace vehicles (ASVs). The United States and European countries have their own aerospace projects and have achieved significant research progress, while, the research on hypersonic vehicles in our country is at in the initial stage. The control system design for the ASVs is a challenge research topic due to their multi-mission profiles, large attitude maneuvers and complicated flight conditions. In this dissertation, four relative problems, i.e. Takagi-Sugeno (T-S) fuzzy modeling and analysis for a conceptual ASV,fuzzy control for uncertain nonlinear system, T-S fuzzy system modeling training and fuzzy adaptive control system design, are studied.
First of all, a whole of kinetic equations and motion equations during the reentry phase of an ASV are presented based on the publicated literatures and the contributions of our lab. The coefficients of aerodynamic force and moment are given as functions of angle of attack, Mach number and control surface deflections. The propulsion system is a combination of reaction engine. Rigid-body mass moments of inertia and center of gravity location are time-varying functions of vehicle weight. Open-loop dynamics demonstrate that the proposed model can embody the characteristics of ASV, such as complicated nonlinearity, strong coupling, fast time-varying and uncertainties. The model has a certain representative and can be used to meet the requirements of research and simulation for advanced guidance and control problems.
Next, based on the T-S fuzzy approximation theory and the reentry attitude dynamics of ASV, the fuzzy rules, the membership functions and the fuzzy sub-systems are established. A simulation model for the reentry attitude dynamics based on T-S fuzzy system is presented, and it lays a foundation for the following controller design and analysis.
Then, based on the presented T-S fuzzy model for ASV reentry attitude dynamics, a new design method of T-S fuzzy guaranteed cost control law with pole constraints is proposed under the guidance of regional pole placement theory. The external disturbance is restricted by using H∞control technique, and a new fuzzy robust control design method is presented. The Lyapunov stability theory is used to prove asymptotic stability of all the states of the closed-loop system. With the different requirement of performance index, state feedback and output feedback controller for ASV attitude dynamic system are designed respectively.
The next, a new design technique of fuzzy robust tracking control based on fuzzy feedforward is proposed. By taking the advantages of T-S fuzzy systems, feedforward control scheme for linear system is extended to nonlinear system. Without the need of the augmented system of linear matrix inequality (LMI) based T-S fuzzy tracking control method, the dimension of system design is reduced, and less conservative is achieved. The asymptotic stability of system tracking error is guaranteed by using Lyapunov stability theory. Considering the system uncertainties and external disturbance, a fuzzy robust tracking controller of the controlled system is designed. The simulation results for the output tracking of complex nonlinear system and attitude angles tracking of ASV demonstrate the effectiveness of the proposed method.
Then, to enhance the adaptation of T-S fuzzy model as system parameters changes, a new Levenberg-Marquardt (L-M) algorithm is proposed, which can be used for Takagi-Sugeno fuzzy modeling. Based on standard L-M algorithm and under the condition of local error bound, the iteration step is defined as a function of approximation error according the different values of iteration parameters. A parameter iteration formula of the modified L-M algorithm is given, and its quadratic convergence is analysed theoretically. Then it is applied to training the ASV attitude dynamic systems based on T-S fuzzy model. This method can adjust the parameters of each linear polynomials and fuzzy membership functions on line. In addition, it does not rely on expert experience excessively when using it for systems modeling. Compared the proposed method with the standard L-M method, the convergence speed is accelerated and high approximation precision is achieved.
Finally, a new adaptive regulator is studied. It can adjust the parameters of fuzzy adaptive controller. Compared with gradient adaptive law, the parameter convergence rate is accelerated obviously. Aimed at the problem of output tracking control for complex nonlinear system, a stable indirect adaptive controller is presented and the system oscillations due to the low convergence speed of parameters are effectively improved. Then the control scheme is extended to multi-input multi-output (MIMO) square nonlinear plants with non-modeled dynamics and an attitude indirect fuzzy adaptive controller for ASV is designed. In addition, considering the effect of external disturbance, a robust control term is introduced and the control effect is further improved.
引文
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