小型无人直升机鲁棒非线性控制研究
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摘要
与其他飞行器相比小型无人直升机具有垂直起降、空中悬停、协调转弯、体积小、重量轻、价格便宜以及隐蔽性强等优点。因而小型无人直升机在军事及民用领域具有广阔的应用潜力。但是，小型无人直升机是一个欠驱动、强耦合、不稳定、时变的高阶非线性系统，对其自主飞行控制的设计仍具有很大的挑战。因此，研究小型无人直升机的自主飞行控制设计问题具有重大科学意义。
本文主要采用理论分析和数值仿真相结合的方法，对小型无人直升机的简化模型与鲁棒非线性控制器设计进行了研究。
首先，本文建立了小型无人直升机14阶非线性数学模型，并将其简化成更简单的线性参数可变（LPV）模型和含有组合干扰的非线性模型以满足控制器设计的需要。
其次，针对线性控制方法的不足，文中利用已建立的小型无人直升机简化LPV模型，提出了一种基于局部H_∞最优LPV速度(LHOV)控制的小型无人直升机LPV控制方法。
再次，考虑到LPV方法存在轨迹跟踪效果较差的缺点，本文基于含有组合干扰的非线性模型利用自适应反步法设计了飞行控制器，并对其稳定性进行了理论证明和仿真分析；然而，反步法存在的“微分爆炸”问题，本文进一步提出了一种鲁棒积分滤波反步法，极大地简化了计算量。
最后，针对鲁棒积分滤波反步法中过多地使用滤波器近似求导可能引起测量高频噪声放大的问题，本文为无人直升机提出了一种具有内外环结构的基于干扰补偿的鲁棒非线性控制方法。该方法既减小了滤波器求导的次数从而消弱了放大测量高频噪声的可能，又简化了计算量从而方便了参数调整。
本文研究工作的主要内容和创新点包括以下几个方面：
1、介绍了国内外小型无人直升机的研究现状，并重点对小型无人直升机飞行控制技术的研究现状进行了阐述与分析。
2、分析了小型无人直升机的动力学特性，建立了小型无人直升机14阶全状态非线性数学模型，并结合控制器设计的需要，将其简化成了更简单的LPV模型和含有组合干扰的非线性模型。
3、第三章利用第二章建立的小型无人直升机简化LPV模型，为水平面飞行设计了一种局部H_∞最优LPV速度控制方法。该方法不仅具有局部H_∞最优功能，即能保证闭环系统进入任意一个固定速度飞行模式后获得H_∞性能最优，还能保证大范围鲁棒稳定。
4、提出了一种自适应反步控制方法。该方法采用自适应律对组合干扰进行在线估计，并将估计值应用于反步法控制器设计中，从而起到补偿干扰，提高闭环系统的鲁棒性和轨迹跟踪性能的作用。
5、考虑自适应反步法计算量过大的问题，第五章提出了一种基于鲁棒积分滤波反步法的飞行控制方法。该方法运用滤波器近似求导，极大地简化了计算量。同时，该方法运用积分项和不连续的鲁棒项来提高闭环系统的抗干扰能力，消除轨迹跟踪静态误差，获得了很好的轨迹跟踪性能。
6、提出一种基于干扰补偿的鲁棒非线性控制方法.该方法运用动态面控制技术，解决了常规反步法计算量过大、参数调整对输出不敏感的问题；采用内外环结构，解决了滤波反步法抗测量干扰能力不足的问题；采用加速度测量信号重构机体坐标下X和Y方向的外力干扰、非线性观测器观测力矩干扰以及误差积分补偿垂向干扰的方式获得了比自适应反步法、鲁棒积分反步法更好的鲁棒性和抗干扰能力。
本文最后，在总结全文的基础上，提出了有待进一步研究和探索的一些问题。
Compared with other aircrafts, small-scale unmanned helicopters have the advantages ofvertical take-off and landing, hovering, coordinated turn, small size, small weight, low cost,strong concealment and so on, which makes it have widely potential applications in both mil-itary and civil fields. However, the small-scale unmanned helicopters are under-actuated,strongly coupled, unstable and time-varying high order nonlinear systems, which makes theautonomous flight controllers’ design with great challenges still. Therefore, study on the au-tonomous flight controller design for the helicopters is of great scientific significance.
The dissertation mainly discusses the model simplification and robust nonlinear control-ler design based on theoretical analysis and numerical simulation.
Firstly, this dissertation establishes for a helicopter a fourteenth-order nonlinear dynamicmodel, which is simplified into a linear parameter varying (LPV) model and a nonlinear mod-el augmented with lumped disturbances to meet the need of the controller design.
Then, since the shortcomings of linear control methods, a local H_∞optical LPV veloc-ity (LHOV) control method is proposed for the small-scale unmanned helicopter based on thesimplified LPV model.
After that, to overcome poor trajectory tracking performance of the LHOV control me-thod, an adaptive backstepping-based flight controller is designed based on the simplifiednonlinear model with lumped disturbances. Furthermore, a robust integral filtering backstep-ping method based flight controller is presented to solve the problem of the differential explo-sion in the adaptive backstepping method.
Lastly, to reduce the probability of amplifying the high-frequency measurement noises inthe robust integral filtering backstepping method for the overuse of filters, for the helicopterthis dissertation proposes a robust nonlinear controller with inner-outer loop structure tocompensate disturbances. This controller not only reduces the number of filters to weaken theeffect of amplifying the high-frequency measurement noises, but also reduces calculationworks, which facilitates the control parameter adjustment.
In general, the main contents and primary innovations of this dissertation can be summa-rized as follows:
1. the background of the small-scale unmanned helicopter both domestic and oversea isintroduced, then an emphasis introduction to the development status of the flight control ispresented.
2. A very specific analysis for the dynamic characteristics of the small-scale unmanned helicopter is given, and a fourteenth order full state nonlinear model is established. Then ac-cording to the need of the control design, the dissertation simplifies it to a simpler LPV modeland a simpler nonlinear model which is augmented with lumped disturbances.
3. A LHOV control method is presented for horizontal flight of the small-scale un-manned helicopter. This method not only ensures the robust optimization with the function oflocal H_∞optimal performance, but also satisfies the large range robust stability while theclosed-loop system flights to any fixed velocity flight domain, or switches from one fixed ve-locity flight point to others.
4. Since the LHOV control method has the shortcoming of large trajectory tracking error,a newly adaptive backstepping method is presented to deal with this problem. this methoduses the adaptive law which is used to estimate the disturbances for compensation in back-stepping controller. Therefore, it can improve the robustness and trajectory tracking perfor-mance. Moreover, it is also proved in Chapter4that the closed-loop system is robustly un-iformly ultimately bounded.
5. Considering the large calculation works that the adaptive backstepping method has, arobust integral filtering backstepping controller is proposed in Chapter5. This controller usescommand filters to compute the time derivatives of the virtual controllers to reduce the calcu-lation works. Moreover, it improves the capability of disturbance rejection and removes thestable-state error of the tracking trajectory by adding an integral term and a discontinuous ro-bust term. evidently, it can obtain very good trajectory tracking performance.
6. A robust nonlinear control method based on the disturbance compensation is proposed.This method uses dynamic surface control technique to solve the large calculation works; andapplies the inner-outer structure to reduce the use frequencies of the filters to solve the prob-lem of amplifying the high-frequency measurement noises; uses the acceleration measurementvalue to reconstruct the external force disturbances of the X and Y direction in body-fixedframe, and the nonlinear disturbance observer to observe the moment disturbance and errorintegration to compensate the disturbance of the Z direction in the body-fixed frame. As a re-sult, it obtains better robustness and disturbance rejection capability than adaptive backstep-ping method and robust integral filtering backstepping method.
At last, some problems are proposed for further research and exploration after the sum-mary of this dissertation.
本文主要采用理论分析和数值仿真相结合的方法，对小型无人直升机的简化模型与鲁棒非线性控制器设计进行了研究。
首先，本文建立了小型无人直升机14阶非线性数学模型，并将其简化成更简单的线性参数可变（LPV）模型和含有组合干扰的非线性模型以满足控制器设计的需要。
其次，针对线性控制方法的不足，文中利用已建立的小型无人直升机简化LPV模型，提出了一种基于局部H_∞最优LPV速度(LHOV)控制的小型无人直升机LPV控制方法。
再次，考虑到LPV方法存在轨迹跟踪效果较差的缺点，本文基于含有组合干扰的非线性模型利用自适应反步法设计了飞行控制器，并对其稳定性进行了理论证明和仿真分析；然而，反步法存在的“微分爆炸”问题，本文进一步提出了一种鲁棒积分滤波反步法，极大地简化了计算量。
最后，针对鲁棒积分滤波反步法中过多地使用滤波器近似求导可能引起测量高频噪声放大的问题，本文为无人直升机提出了一种具有内外环结构的基于干扰补偿的鲁棒非线性控制方法。该方法既减小了滤波器求导的次数从而消弱了放大测量高频噪声的可能，又简化了计算量从而方便了参数调整。
本文研究工作的主要内容和创新点包括以下几个方面：
1、介绍了国内外小型无人直升机的研究现状，并重点对小型无人直升机飞行控制技术的研究现状进行了阐述与分析。
2、分析了小型无人直升机的动力学特性，建立了小型无人直升机14阶全状态非线性数学模型，并结合控制器设计的需要，将其简化成了更简单的LPV模型和含有组合干扰的非线性模型。
3、第三章利用第二章建立的小型无人直升机简化LPV模型，为水平面飞行设计了一种局部H_∞最优LPV速度控制方法。该方法不仅具有局部H_∞最优功能，即能保证闭环系统进入任意一个固定速度飞行模式后获得H_∞性能最优，还能保证大范围鲁棒稳定。
4、提出了一种自适应反步控制方法。该方法采用自适应律对组合干扰进行在线估计，并将估计值应用于反步法控制器设计中，从而起到补偿干扰，提高闭环系统的鲁棒性和轨迹跟踪性能的作用。
5、考虑自适应反步法计算量过大的问题，第五章提出了一种基于鲁棒积分滤波反步法的飞行控制方法。该方法运用滤波器近似求导，极大地简化了计算量。同时，该方法运用积分项和不连续的鲁棒项来提高闭环系统的抗干扰能力，消除轨迹跟踪静态误差，获得了很好的轨迹跟踪性能。
6、提出一种基于干扰补偿的鲁棒非线性控制方法.该方法运用动态面控制技术，解决了常规反步法计算量过大、参数调整对输出不敏感的问题；采用内外环结构，解决了滤波反步法抗测量干扰能力不足的问题；采用加速度测量信号重构机体坐标下X和Y方向的外力干扰、非线性观测器观测力矩干扰以及误差积分补偿垂向干扰的方式获得了比自适应反步法、鲁棒积分反步法更好的鲁棒性和抗干扰能力。
本文最后，在总结全文的基础上，提出了有待进一步研究和探索的一些问题。
Compared with other aircrafts, small-scale unmanned helicopters have the advantages ofvertical take-off and landing, hovering, coordinated turn, small size, small weight, low cost,strong concealment and so on, which makes it have widely potential applications in both mil-itary and civil fields. However, the small-scale unmanned helicopters are under-actuated,strongly coupled, unstable and time-varying high order nonlinear systems, which makes theautonomous flight controllers’ design with great challenges still. Therefore, study on the au-tonomous flight controller design for the helicopters is of great scientific significance.
The dissertation mainly discusses the model simplification and robust nonlinear control-ler design based on theoretical analysis and numerical simulation.
Firstly, this dissertation establishes for a helicopter a fourteenth-order nonlinear dynamicmodel, which is simplified into a linear parameter varying (LPV) model and a nonlinear mod-el augmented with lumped disturbances to meet the need of the controller design.
Then, since the shortcomings of linear control methods, a local H_∞optical LPV veloc-ity (LHOV) control method is proposed for the small-scale unmanned helicopter based on thesimplified LPV model.
After that, to overcome poor trajectory tracking performance of the LHOV control me-thod, an adaptive backstepping-based flight controller is designed based on the simplifiednonlinear model with lumped disturbances. Furthermore, a robust integral filtering backstep-ping method based flight controller is presented to solve the problem of the differential explo-sion in the adaptive backstepping method.
Lastly, to reduce the probability of amplifying the high-frequency measurement noises inthe robust integral filtering backstepping method for the overuse of filters, for the helicopterthis dissertation proposes a robust nonlinear controller with inner-outer loop structure tocompensate disturbances. This controller not only reduces the number of filters to weaken theeffect of amplifying the high-frequency measurement noises, but also reduces calculationworks, which facilitates the control parameter adjustment.
In general, the main contents and primary innovations of this dissertation can be summa-rized as follows:
1. the background of the small-scale unmanned helicopter both domestic and oversea isintroduced, then an emphasis introduction to the development status of the flight control ispresented.
2. A very specific analysis for the dynamic characteristics of the small-scale unmanned helicopter is given, and a fourteenth order full state nonlinear model is established. Then ac-cording to the need of the control design, the dissertation simplifies it to a simpler LPV modeland a simpler nonlinear model which is augmented with lumped disturbances.
3. A LHOV control method is presented for horizontal flight of the small-scale un-manned helicopter. This method not only ensures the robust optimization with the function oflocal H_∞optimal performance, but also satisfies the large range robust stability while theclosed-loop system flights to any fixed velocity flight domain, or switches from one fixed ve-locity flight point to others.
4. Since the LHOV control method has the shortcoming of large trajectory tracking error,a newly adaptive backstepping method is presented to deal with this problem. this methoduses the adaptive law which is used to estimate the disturbances for compensation in back-stepping controller. Therefore, it can improve the robustness and trajectory tracking perfor-mance. Moreover, it is also proved in Chapter4that the closed-loop system is robustly un-iformly ultimately bounded.
5. Considering the large calculation works that the adaptive backstepping method has, arobust integral filtering backstepping controller is proposed in Chapter5. This controller usescommand filters to compute the time derivatives of the virtual controllers to reduce the calcu-lation works. Moreover, it improves the capability of disturbance rejection and removes thestable-state error of the tracking trajectory by adding an integral term and a discontinuous ro-bust term. evidently, it can obtain very good trajectory tracking performance.
6. A robust nonlinear control method based on the disturbance compensation is proposed.This method uses dynamic surface control technique to solve the large calculation works; andapplies the inner-outer structure to reduce the use frequencies of the filters to solve the prob-lem of amplifying the high-frequency measurement noises; uses the acceleration measurementvalue to reconstruct the external force disturbances of the X and Y direction in body-fixedframe, and the nonlinear disturbance observer to observe the moment disturbance and errorintegration to compensate the disturbance of the Z direction in the body-fixed frame. As a re-sult, it obtains better robustness and disturbance rejection capability than adaptive backstep-ping method and robust integral filtering backstepping method.
At last, some problems are proposed for further research and exploration after the sum-mary of this dissertation.
引文
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