过驱动系统控制分配理论及其应用
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摘要
具有冗余执行机构的过驱动系统广泛存在于航空航天、航海、汽车、机器人以及工业过程等应用领域。控制分配是过驱动控制系统设计和分析的关键问题,也是当前控制领域的研究热点之一。引入控制分配的过驱动控制系统设计可分解为基本控制律设计和控制分配算法设计两部分。其中,基本控制律根据对象动力学特性和控制目标得到总的控制指令(称为伪指令);控制分配算法则是在综合考虑执行机构物理约束(偏转位置、速率等)的基础上,将伪指令合理分配至冗余的执行机构中,以获得期望的系统响应。随着控制对象本身以及其工作环境的日益复杂化,传统控制分配算法已逐渐不能适应目前系统的要求,先进的控制分配算法及其相关问题研究的重要性日益突显。
论文研究了过驱动系统的控制分配问题,分析了目前控制分配算法中存在的局限性,并针对不确定性建模下的鲁棒控制分配、典型非线性条件下的非线性控制分配以及考虑执行器动态响应过程的动态控制分配等问题开展研究,得到了一些新的结果;将部分研究结果应用于具有多操纵面的飞行器控制系统设计中,验证了其有效性。论文的主要研究工作包括:
(1)针对不确定性建模问题,以具有多操纵面的飞机为受控对象,在分析现有控制分配算法局限性的基础上,应用鲁棒优化理论研究不确定性建模下的控制分配问题。研究了原始不确定鲁棒优化模型的建立和基于椭球不确定集的鲁棒对等式的转化问题,并推广到锥不确定集的情况;讨论了鲁棒控制分配算法的数值求解方法及其计算复杂度;针对多操纵面布局飞机的控制分配问题与传统算法进行了仿真比较,结果表明鲁棒优化算法能有效降低控制效率矩阵存在不确定性的影响,使分配结果更为合理,从而具有更好的鲁棒性。
(2)针对多操纵面布局飞行器中操纵面存在耦合效应导致舵效呈非线性的情况,研究了基于耦合补偿的非线性控制分配方法。针对该问题中以误差最小化作为线性目标函数,约束函数为二阶非线性、连续可微凸函数的特点,提出一种基于序列线性规划的控制分配算法,将原非线性规划问题转化为一系列线性规划子问题进行求解,从而实现了飞行器控制分配的耦合非线性补偿,使得分配性能得到了有效提高。
(3)研究了直接非单调非线性情况下的控制分配问题。传统的线性控制分配算法是基于控制力矩与执行器偏转位置存在精确的线性函数关系的假设之上得到的。然而,控制力矩与执行器偏转位置的关系本质上是非线性的,特别是执行器出现故障时。针对非单调非线性控制分配问题,提出一种基于微分进化的非线性控制分配策略,研究了问题的转化描述,给出了算法步骤,并以具有多操纵面的飞机模型为对象,与传统算法进行了性能比较,验证了提出方法的有效性。
(4)研究了执行器动态响应过程不可忽略情形下的控制分配问题。基于数据驱动的子空间辨识方法和预测控制理论,提出了一种考虑执行器动态响应过程的动态控制分配方法。在考虑范数有界不确定性的在线子空间辨识的基础上,对执行器动力学特性进行不确定性建模,再结合预测控制理论进行动态控制分配。从而将执行机构的动力学建模、控制量分配和执行机构控制律的设计包含在一个子系统框架内,对执行机构的模型不确定性具有更好的鲁棒性,并给出仿真实例验证了算法的有效性。
(5)将Backstepping方法与在线控制分配方法相结合应用于多操纵面布局飞机的飞行控制器设计中。建立了多操纵面布局飞行器的严格反馈模型,采用Backstepping方法设计了基本控制律,并进行了稳定性证明,利用最小二乘法在线估计执行器效率,实现在线控制分配,仿真结果验证了方法的有效性、鲁棒性以及操纵面故障情况下的控制重构性能。
Overactuated systems with redundant control effectors can be found in many places, such as aerospace, marine vessels, automatic vehicles, robotics and industrial process applications. In this kind of system, control allocation is one of key problems for design and analysis, and has been one of the important and hot research topics in control theory and engineering. Using control allocation, it is possible to split control design into two steps: firstly, a control law is designed to specify the total control effort (virtual commands); secondly, a control allocation algorithm is designed to distribute the required control moment over the actuators in order to obtain the desired response. With the increasing complexity of plants and environment, the traditional control allocation algorithms are not suitable for modern system. It is necessary to study advanced control allocation algorithms and overactuated systems related problems.
The control allocation problem of overactuated systems is investigated, and the limitation of current methods is analyzed. Several topics, such as robust control allocation under uncertainty modeling, nonlinear control allocation under representative nonlinear condition and dynamic control allocation including actuator dynamics are discussed in this paper. Some new methods are obtained. Some of the results are applied to the flight control system of modern aircraft with multiple effectors. The main research contents are listed as follows:
(1) Aiming at the uncertainty modeling for control effectiveness of aircraft with multiple effectors, a new control allocation algorithm based on robust optimization is proposed when control effectiveness uncertainties are considered. The original robust optimal model is established. Following with the transformation of its robust counterpart with ellipsoidal and the conic quadratic representable uncertainty set are researched. The numerical solution of robust control allocation algorithm is discussed. Simulations on optimal control allocation of aircraft with multiple effectors show that the proposed algorithm can reduce the impact of the control effectiveness uncertainties, so the results are more reasonable.
(2) As the number of control effectors placed on a vehicle increases, the likelihood of the occurrence of control effector interactions increases. In this case, the nonlinearity of control effectiveness can not be ignored. We studied the control allocation problem including control effector interactions. And a compensate algorithm based on sequential linear programming methods is devised to improve the allocation results.
(3) Traditional methods assume that a perfect linear relationship exists between control moments and effector deflections. However, this relationship is intrinsically nonlinear, especially in the event of failure of one or more actuators. In this paper we consider the control allocation problem with nonmonotonic nonlinearities for overactuated systems. To solve this problem, we propose a differential evolution (DE) strategy. The problem formulation and the algorithm’s procedure are studied. Simulation results show that the proposed method outperforms the traditional approaches.
(4) A data driven subspace predictive control allocation approach is proposed for overactuated system with actuator dynamics.Through online subspace identification,uncertainty model is used for description of actuator dynamic characteristic.A novel control allocation with actuator dynamics is designed by using subspace predictive control theory. The actuator modeling, designing of control allocator and the actuator controller are then included in a framework, which increases robustness of the control system.Simulation examples are given to demonstrate the efficiency of the proposed strategy.
(5) The Backstepping method combined with online control allocation is applied to flight control system design of a class of aircrafts with multiple effectors. The strict feedback form of nonlinear dynamic model is introduced. A high level backstepping controller is developed, and the stability is proved. The least squares method is used to estimate the actuator effectiveness and the online control allocation is implemented by using robust algorithm proposed in chapter 3. The simulations show the effectiveness, robustness and the control reconfiguration capability in presence of actuator failure.
论文研究了过驱动系统的控制分配问题,分析了目前控制分配算法中存在的局限性,并针对不确定性建模下的鲁棒控制分配、典型非线性条件下的非线性控制分配以及考虑执行器动态响应过程的动态控制分配等问题开展研究,得到了一些新的结果;将部分研究结果应用于具有多操纵面的飞行器控制系统设计中,验证了其有效性。论文的主要研究工作包括:
(1)针对不确定性建模问题,以具有多操纵面的飞机为受控对象,在分析现有控制分配算法局限性的基础上,应用鲁棒优化理论研究不确定性建模下的控制分配问题。研究了原始不确定鲁棒优化模型的建立和基于椭球不确定集的鲁棒对等式的转化问题,并推广到锥不确定集的情况;讨论了鲁棒控制分配算法的数值求解方法及其计算复杂度;针对多操纵面布局飞机的控制分配问题与传统算法进行了仿真比较,结果表明鲁棒优化算法能有效降低控制效率矩阵存在不确定性的影响,使分配结果更为合理,从而具有更好的鲁棒性。
(2)针对多操纵面布局飞行器中操纵面存在耦合效应导致舵效呈非线性的情况,研究了基于耦合补偿的非线性控制分配方法。针对该问题中以误差最小化作为线性目标函数,约束函数为二阶非线性、连续可微凸函数的特点,提出一种基于序列线性规划的控制分配算法,将原非线性规划问题转化为一系列线性规划子问题进行求解,从而实现了飞行器控制分配的耦合非线性补偿,使得分配性能得到了有效提高。
(3)研究了直接非单调非线性情况下的控制分配问题。传统的线性控制分配算法是基于控制力矩与执行器偏转位置存在精确的线性函数关系的假设之上得到的。然而,控制力矩与执行器偏转位置的关系本质上是非线性的,特别是执行器出现故障时。针对非单调非线性控制分配问题,提出一种基于微分进化的非线性控制分配策略,研究了问题的转化描述,给出了算法步骤,并以具有多操纵面的飞机模型为对象,与传统算法进行了性能比较,验证了提出方法的有效性。
(4)研究了执行器动态响应过程不可忽略情形下的控制分配问题。基于数据驱动的子空间辨识方法和预测控制理论,提出了一种考虑执行器动态响应过程的动态控制分配方法。在考虑范数有界不确定性的在线子空间辨识的基础上,对执行器动力学特性进行不确定性建模,再结合预测控制理论进行动态控制分配。从而将执行机构的动力学建模、控制量分配和执行机构控制律的设计包含在一个子系统框架内,对执行机构的模型不确定性具有更好的鲁棒性,并给出仿真实例验证了算法的有效性。
(5)将Backstepping方法与在线控制分配方法相结合应用于多操纵面布局飞机的飞行控制器设计中。建立了多操纵面布局飞行器的严格反馈模型,采用Backstepping方法设计了基本控制律,并进行了稳定性证明,利用最小二乘法在线估计执行器效率,实现在线控制分配,仿真结果验证了方法的有效性、鲁棒性以及操纵面故障情况下的控制重构性能。
Overactuated systems with redundant control effectors can be found in many places, such as aerospace, marine vessels, automatic vehicles, robotics and industrial process applications. In this kind of system, control allocation is one of key problems for design and analysis, and has been one of the important and hot research topics in control theory and engineering. Using control allocation, it is possible to split control design into two steps: firstly, a control law is designed to specify the total control effort (virtual commands); secondly, a control allocation algorithm is designed to distribute the required control moment over the actuators in order to obtain the desired response. With the increasing complexity of plants and environment, the traditional control allocation algorithms are not suitable for modern system. It is necessary to study advanced control allocation algorithms and overactuated systems related problems.
The control allocation problem of overactuated systems is investigated, and the limitation of current methods is analyzed. Several topics, such as robust control allocation under uncertainty modeling, nonlinear control allocation under representative nonlinear condition and dynamic control allocation including actuator dynamics are discussed in this paper. Some new methods are obtained. Some of the results are applied to the flight control system of modern aircraft with multiple effectors. The main research contents are listed as follows:
(1) Aiming at the uncertainty modeling for control effectiveness of aircraft with multiple effectors, a new control allocation algorithm based on robust optimization is proposed when control effectiveness uncertainties are considered. The original robust optimal model is established. Following with the transformation of its robust counterpart with ellipsoidal and the conic quadratic representable uncertainty set are researched. The numerical solution of robust control allocation algorithm is discussed. Simulations on optimal control allocation of aircraft with multiple effectors show that the proposed algorithm can reduce the impact of the control effectiveness uncertainties, so the results are more reasonable.
(2) As the number of control effectors placed on a vehicle increases, the likelihood of the occurrence of control effector interactions increases. In this case, the nonlinearity of control effectiveness can not be ignored. We studied the control allocation problem including control effector interactions. And a compensate algorithm based on sequential linear programming methods is devised to improve the allocation results.
(3) Traditional methods assume that a perfect linear relationship exists between control moments and effector deflections. However, this relationship is intrinsically nonlinear, especially in the event of failure of one or more actuators. In this paper we consider the control allocation problem with nonmonotonic nonlinearities for overactuated systems. To solve this problem, we propose a differential evolution (DE) strategy. The problem formulation and the algorithm’s procedure are studied. Simulation results show that the proposed method outperforms the traditional approaches.
(4) A data driven subspace predictive control allocation approach is proposed for overactuated system with actuator dynamics.Through online subspace identification,uncertainty model is used for description of actuator dynamic characteristic.A novel control allocation with actuator dynamics is designed by using subspace predictive control theory. The actuator modeling, designing of control allocator and the actuator controller are then included in a framework, which increases robustness of the control system.Simulation examples are given to demonstrate the efficiency of the proposed strategy.
(5) The Backstepping method combined with online control allocation is applied to flight control system design of a class of aircrafts with multiple effectors. The strict feedback form of nonlinear dynamic model is introduced. A high level backstepping controller is developed, and the stability is proved. The least squares method is used to estimate the actuator effectiveness and the online control allocation is implemented by using robust algorithm proposed in chapter 3. The simulations show the effectiveness, robustness and the control reconfiguration capability in presence of actuator failure.
引文
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