小型无人直升机非线性建模与控制算法研究
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摘要
鉴于小型无人直升机在军事和民用领域的巨大应用前景,本文以模型直升机为平台,设计了一个小型无人直升机实验系统,重点对小型无人直升机的非线性动力学模型和非线性控制算法展开了研究,探索了小型无人直升机自主飞行控制算法的设计过程,目标是建立一个既可以保证飞行安全又可以充分发挥小型无人直升机性能的控制系统,为进一步研究小型无人直升机智能控制系统奠定基础。研究的主要内容包括以下几个方面:
小型无人直升机非线性动力学模型。根据叶素理论和Rotor Disk模型,详细推导了与主旋翼和稳定翼相关的空气动力模型和挥舞运动模型;根据三维非线性Pitt/Peter模型推导了直升机在垂直飞行或悬停飞行时的旋翼入流动力学方程;研究了稳定翼动力学模型,及其与主旋翼之间的耦合关系;应用系统辨识的方法,对含有AVCS(Angular Vector Control System)电子陀螺仪的尾旋翼系统建立了简单的模型。最终建立了一个包含位置、线速度、姿态、角速度、主旋翼入流状态以及主旋翼和稳定翼挥舞运动状态的小型无人直升机非线性动力学模型。
小型无人直升机姿态控制算法。针对模型直升机在姿态控制系统实验平台上的特点,建立了姿态控制实验系统的非线性动力学模型,通过系统辨识的方法确定出了模型中的未知参数。根据实际应用的实时性要求,基于该模型设计了EKF(Extended Kalman Filter)状态观测器。证明了可以通过动态反馈线性化技术,将包含主旋翼和稳定翼挥舞运动状态的姿态动力学系统转换成为一个可控的线性系统。为了减少执行机构的饱和对闭环系统性能的影响,设计了一个启发式控制系统结构。研究了不确性对系统性能的影响,分析了H∞控制器在实际应用中的不足之处。然后,提出了一个ECID(Extended Convex Integrated Design)控制器设计方法,将其应用到反馈线性化后的系统中,设计了一个可以满足多个闭环性能指标的无人直升机姿态控制算法,最后通过实验验证了该算法的有效性和鲁棒性。
小型无人直升机悬停飞行控制算法。对小型无人直升机复杂的理论模型进行了必要的简化,通过系统辨识的方法确定出了模型中的未知参数。基于该模型设计了一个UKF(Unscented Kalman Filter)状态观测器,在线实验验证了该算法的有效性。然后,证明了可以通过动态反馈线性化技术将该非线性系统转换成为线性系统,通过理论推导,证明了小型直升机的机械结构保证了其姿态动力学系统的零动态本质上是稳定的。设计了启发式串级控制系统结构,以解决系统中奇异点对飞行安全性的影响。最后,根据ECID控制器设计方法设计了一个小型无人直升机悬停飞行控制算法,仿真实验说明了该控制算法的鲁棒性。
The small-scale unmanned helicopter has wide prospective of applications in many areas, and is being extensively studied all over the world. This dissertation investigates the nonlinear modeling and controller design of small-scale helicopters and develops an experimental setup to validate the model and the controllers. The ultimate goal is to develop an autonomous flight control system that maximizes the performance of small-scale unmanned helicopters as well as guarantees the flight safety. The main contribution of the dissertation is as follows:
First, we developed a nonlinear model of a small-scale helicopter near hovering. On the basis of the Blade Element theory and Rotor Disk model, the aerodynamics and the flapping dynamics of the main rotor are modeled. Then, the main rotor inflow dynamics is modeled based on the three-state nonlinear Pitt/Peters model. To characterize the model helicopter, the dynamics of the stabilizer bar and the tail rotor with the AVCS (Angular Vector Control System) electronic gyro are also studied in detail.
Next, we developed a nonlinear model of the helicopter on a test bench when the flapping states of the main rotor and the stabilizer bar are considered. The test bench is constructed for experimental testing of the attitude control of the small-scale helicopter. The unknown model parameters are estimated using the EKF (Extended Kalman Filter) with flight test data of the helicopter operating on the test bench. Then, it is proved that the nonlinear model can be globally linearized using the dynamic feedback linearization technique. A heuristic strategy is proposed to reduce the effect of the saturation actuators on the closed-loop performance. Moreover, a robust performance criterion for the experimental system is introduced. Using the Convex Integrated Design (CID) method, it is possible to design a single closed-loop controller that satisfies a set of multiple conflicting performance specifications. However, direct use of the CID method leads to a controller with complicated form which is not suitable for real-time implementation on the helicopter platform. So, we extended the standard CID method to a more general control system framework to solve the conflicting simultaneous performance design problem, which is referred to as ECID (Extended Convex Integrated Design) method. Compared with the standard CID design, the ECID procedure generates a relatively simple controller. Finally, the synthesized controller is tested by simulations and is validated on the experimental small-scale test helicopter. The experimental results demonstrate the expected performance of the proposed controller.
Finally, in order to design a nonlinear controller for small-scale autonomous helicopters, an integrated nonlinear model of a small-scale helicopter for hovering control is developed, and the unknown parameters in the nonlinear model are estimated using the system identification method. To estimate the states in the nonlinear system by using the IMU and GPS sensors, an UKF (Unscented Kalman Filter) observer is designed, whose validity is confirmed by the flight experiments. It is demonstrated that the full nonlinear model can be converted into a controllable linear system via the dynamic feedback linearization technique, and its nonlinear attitude subsystem has a stable zero dynamics. In order to avoid the potential danger caused by the singularities in the feedback linearized system, a cascade control structure is proposed. Finally, a robust controller is designed by applying the ECID method to the cascade system, and simulations are carried out to show the good performance of the controller.
小型无人直升机非线性动力学模型。根据叶素理论和Rotor Disk模型,详细推导了与主旋翼和稳定翼相关的空气动力模型和挥舞运动模型;根据三维非线性Pitt/Peter模型推导了直升机在垂直飞行或悬停飞行时的旋翼入流动力学方程;研究了稳定翼动力学模型,及其与主旋翼之间的耦合关系;应用系统辨识的方法,对含有AVCS(Angular Vector Control System)电子陀螺仪的尾旋翼系统建立了简单的模型。最终建立了一个包含位置、线速度、姿态、角速度、主旋翼入流状态以及主旋翼和稳定翼挥舞运动状态的小型无人直升机非线性动力学模型。
小型无人直升机姿态控制算法。针对模型直升机在姿态控制系统实验平台上的特点,建立了姿态控制实验系统的非线性动力学模型,通过系统辨识的方法确定出了模型中的未知参数。根据实际应用的实时性要求,基于该模型设计了EKF(Extended Kalman Filter)状态观测器。证明了可以通过动态反馈线性化技术,将包含主旋翼和稳定翼挥舞运动状态的姿态动力学系统转换成为一个可控的线性系统。为了减少执行机构的饱和对闭环系统性能的影响,设计了一个启发式控制系统结构。研究了不确性对系统性能的影响,分析了H∞控制器在实际应用中的不足之处。然后,提出了一个ECID(Extended Convex Integrated Design)控制器设计方法,将其应用到反馈线性化后的系统中,设计了一个可以满足多个闭环性能指标的无人直升机姿态控制算法,最后通过实验验证了该算法的有效性和鲁棒性。
小型无人直升机悬停飞行控制算法。对小型无人直升机复杂的理论模型进行了必要的简化,通过系统辨识的方法确定出了模型中的未知参数。基于该模型设计了一个UKF(Unscented Kalman Filter)状态观测器,在线实验验证了该算法的有效性。然后,证明了可以通过动态反馈线性化技术将该非线性系统转换成为线性系统,通过理论推导,证明了小型直升机的机械结构保证了其姿态动力学系统的零动态本质上是稳定的。设计了启发式串级控制系统结构,以解决系统中奇异点对飞行安全性的影响。最后,根据ECID控制器设计方法设计了一个小型无人直升机悬停飞行控制算法,仿真实验说明了该控制算法的鲁棒性。
The small-scale unmanned helicopter has wide prospective of applications in many areas, and is being extensively studied all over the world. This dissertation investigates the nonlinear modeling and controller design of small-scale helicopters and develops an experimental setup to validate the model and the controllers. The ultimate goal is to develop an autonomous flight control system that maximizes the performance of small-scale unmanned helicopters as well as guarantees the flight safety. The main contribution of the dissertation is as follows:
First, we developed a nonlinear model of a small-scale helicopter near hovering. On the basis of the Blade Element theory and Rotor Disk model, the aerodynamics and the flapping dynamics of the main rotor are modeled. Then, the main rotor inflow dynamics is modeled based on the three-state nonlinear Pitt/Peters model. To characterize the model helicopter, the dynamics of the stabilizer bar and the tail rotor with the AVCS (Angular Vector Control System) electronic gyro are also studied in detail.
Next, we developed a nonlinear model of the helicopter on a test bench when the flapping states of the main rotor and the stabilizer bar are considered. The test bench is constructed for experimental testing of the attitude control of the small-scale helicopter. The unknown model parameters are estimated using the EKF (Extended Kalman Filter) with flight test data of the helicopter operating on the test bench. Then, it is proved that the nonlinear model can be globally linearized using the dynamic feedback linearization technique. A heuristic strategy is proposed to reduce the effect of the saturation actuators on the closed-loop performance. Moreover, a robust performance criterion for the experimental system is introduced. Using the Convex Integrated Design (CID) method, it is possible to design a single closed-loop controller that satisfies a set of multiple conflicting performance specifications. However, direct use of the CID method leads to a controller with complicated form which is not suitable for real-time implementation on the helicopter platform. So, we extended the standard CID method to a more general control system framework to solve the conflicting simultaneous performance design problem, which is referred to as ECID (Extended Convex Integrated Design) method. Compared with the standard CID design, the ECID procedure generates a relatively simple controller. Finally, the synthesized controller is tested by simulations and is validated on the experimental small-scale test helicopter. The experimental results demonstrate the expected performance of the proposed controller.
Finally, in order to design a nonlinear controller for small-scale autonomous helicopters, an integrated nonlinear model of a small-scale helicopter for hovering control is developed, and the unknown parameters in the nonlinear model are estimated using the system identification method. To estimate the states in the nonlinear system by using the IMU and GPS sensors, an UKF (Unscented Kalman Filter) observer is designed, whose validity is confirmed by the flight experiments. It is demonstrated that the full nonlinear model can be converted into a controllable linear system via the dynamic feedback linearization technique, and its nonlinear attitude subsystem has a stable zero dynamics. In order to avoid the potential danger caused by the singularities in the feedback linearized system, a cascade control structure is proposed. Finally, a robust controller is designed by applying the ECID method to the cascade system, and simulations are carried out to show the good performance of the controller.
引文
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