非线性模型预测控制（NMPC）在微型飞行器自适应控制中的应用
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摘要
随着空间事业的发展，飞行器的规模越来越大，对姿态控制性能的要求也越来越高。飞行器是在一定的空间环境中飞行，而空间环境中充满着各种物理介质，对飞行器的姿态运动产生不同程度的影响，所以空间飞行器的姿态控制相当复杂，它受到如下因素的制约：(ⅰ)带时延的非线性动态特性(ⅱ)模型和参数的不确定性(ⅲ)燃料的激荡性以及燃料消耗所引起飞行器的质量变化(ⅳ)推力和输入力矩的约束性(ⅴ)额定角速度约束和姿态约束(ⅵ)在故障发生的情况下自动重新配置的必要性。当前飞行器主要的控制方法是基于近似时不变线性系统的频域分析法(如PID控制)，这种方法的优点是简单且易于稳定性和鲁棒性分析，但它所达到的低性能和低效率却转化成了飞行器控制过程的附加载荷，还远不够满足当前飞行器控制的要求。非线性模型预测控制NMPC(Nonlinear Model Predictive Control)是求解多变量非线性系统的一种有效方法，目前已成功地应用于包括复杂的非线性并带有高安全性和激励约束的工业过程(如石油化工领域、航空航天领域等)控制，其控制所能达到的高稳定性和强鲁棒性已在近期的许多刊物上分析过。非线性模型预测控制(NMPC)的优点和它能在故障情况下自动重新配置的灵活性使得它能完成未来空间飞行器自适应控制的使命。模型预测控制法所能达到的性能和效率也能满足当前和未来空间飞行器控制的要求。
本文的主要研究工作是探讨非线性模型预测控制(NMPC)应用于空间飞行器自适应控制的可行性及对提高控制精度和减少燃料使用方面的优越性，同时利用函数空间模型预测控制算法(F-MPC)对空间飞行器的位置和姿态控制进行仿真，具体内容如下：
一．空间飞行器姿态和轨迹控制问题的数学分析、建模以及仿真。
二．非线性模型预测控制器的设计。
三．对控制器的调试和测试(包括对控制器的稳定性和鲁棒性的分析)。
四．验证非线性模型预测控制(NMPC)应用于空间飞行器控制的可行性及其节省燃料和高控制精度的优越性。
五．提出本课题的后续研究课题。
本文运用非线性模型预测控制理论对空间飞行器位置和姿态的控制进行了系统的分析、研究和计算机仿真，在以下两个方面取得显著成效：
1．飞行器动力学模型的特性使得标准的MPC算法无法直接用于飞行器的控制。本文提出了几种方法用于解决这一问题。在控制对象内部嵌入稳定模型，MPC法可成功地应用于飞行器的速度控制。
2．使用一种基于空间函数最优化的函数空间模型预测控制新算法(F-MPC)控制飞行器的姿态。该算法用于飞行器的精点控制可获得满意的效果，也可用于完成飞行器的旋转控制任务，例如该算法用于飞行器的精点控制可使点误差小于0.05度。该算法的一个重要优点是能解决飞行器姿态控制过程中所产生的一些难题。例如：如果飞行器三轴推力器中的某一轴发生故障，那么常规的反馈算法将无法把飞行器定位到给定的方向，但F-MPC算法则可胜任这一任务。根据仿真结果可推出以下结论：
Ⅰ．由于未来空间飞行器控制在成本和控制性能方面都有较严格的要求，故当前需要通过使用模型预测控制来改善传统的控制方法使控制权限、组件使用和寿命等达到最优化。
Ⅱ．在未来的飞行器控制使命中，要求期望控制成本大大降低，这就需要减少重要的反馈传感器的使用，例如用于速度反馈的高质量陀螺仪等，也使得飞行器控制在如无反馈信息等的情况下为保持控制性能而依赖于预测控制技术。尽管如此，有效的状态估计的相关性技术和系统识别技术仍然在提高控制性能方面扮演着重要的角色。
Ⅲ．用于工业过程控制的MPC标准公式(线性化动力学)不能直接应用于飞行器的动力学控制。通过对本课题的研究，并结合计算机仿真来证明非线性模型预测控制法可以而且能够完成未来空间飞行
厦门大学硕士论义 摘 要
器的控制使命并满足其控制要求，使得用PID控制和现代控制对空间飞行器的控制过程所遇到的问题得
以解决，这些研究成果将对开拓非线性模型预测控制（NMPC）在我国工业领域的应用产生积极的影响。
With the development of the scales of spacecraft projects,the demands for spacecraft attitude control are becoming more and more important today. Spacecrafts are working in the space environment,which is full of sorts of physical mediums. And these mediums will impact on the altitude movement of spacecraft. Spacecraft attitude control during propulsive maneuvers is complicated due to several factors as listed below:(i) nonlinear dynamics with time delays,(ii) modeling and parameter uncertainties,(iii) flexible modes due to fuel sloshing and appendages,(vi) constraints on propulsive force and torque inputs,(v) constraints on acceptable angular rates and attitude,(iv) autonomous reconfiguration requirements under failure conditions. The current control approaches are based on frequency domain methods such as PID control which assumes linear time invariant system dynamics. The advantages of these approaches are simplicity and ease of stability and robustness analysis. However,the decrease in performanc
e and poor efficiency translates to additional payload and cannot meet the demand of current spacecraft control. Nonlinear Model Predictive Control (NMPC) is an effective method of solving multi-variable nonlinear system and has been used successfully in a number of industrial applications involving complex nonlinear processes such as petroleum chemical engineering and spaceflight domains with hard safety and actuator constraints. The remarkable stability and robustness properties of MPC observed in practice have been analyzed in a number of recent publications. The optimality of Nonlinear MPC design and its flexibility for reconfiguration make it an idea candidate for future spacecraft missions like attitude control using thrusters.
This thesis presents the feasibility of Nonlinear Model Predictive Control implemented in spacecraft control and the optimality of increasing the control precision and decreasing the fuels expenditure. And the discussions are then focused on the simulation of spacecraft control using Function-space Model Predictive Control algorithm as mentioned below:
1. Problem formulation,modeling and simulation of the spacecraft attitude and trajectory control.
2. Designation of Nonlinear Model Predictive Controllers.
3. Controller Tuning and Testing including Stability and Robustness Analysis.
4. Test results to the implementation of MPC for spacecraft control.
5. The problems to be studied in future are presented.
This thesis studies the spacecraft control using Nonlinear Model Predictive Control and computer simulations are applied in it. The main results fall into two main areas.
1. Application of the standard MPC algorithms was not possible due to the nature of the spacecraft dynamic model. Several methods were proposed to alleviate these difficulties,with varying success. MPC was successfully applied to the spacecraft rate control (setpoint and tracking problems) when applied on an internally stabilized model of the plant dynamics.
2. A new predictive control algorithm,the Function-space Model Predictive Control(F-MPC) method,was developed based on a function-space optimization of the control input for attitude control. This method yielded very promising results on precision pointing tasks,and is also applicable to the slewing task. Pointing errors of less than 0.05 degrees were achievable with off-line nominal control computation . One key advantage of the MPC feedback stabilization algorithm is that it can handle some well known difficult cases that can arise in attitude control. For example,if one of the actuator fails,conventional feedback algorithms can no longer position a spacecraft to arbitrary orientation while this algorithm remains viable.
Preliminary investigations of the MPC approach to attitude control lead to the following conclusions:I . Because of increasingly stringent requirements on the cost and control performance for future missions,
it is imperative to try to improve on the abilities of traditional control methods by using some aspects of model
本文的主要研究工作是探讨非线性模型预测控制(NMPC)应用于空间飞行器自适应控制的可行性及对提高控制精度和减少燃料使用方面的优越性，同时利用函数空间模型预测控制算法(F-MPC)对空间飞行器的位置和姿态控制进行仿真，具体内容如下：
一．空间飞行器姿态和轨迹控制问题的数学分析、建模以及仿真。
二．非线性模型预测控制器的设计。
三．对控制器的调试和测试(包括对控制器的稳定性和鲁棒性的分析)。
四．验证非线性模型预测控制(NMPC)应用于空间飞行器控制的可行性及其节省燃料和高控制精度的优越性。
五．提出本课题的后续研究课题。
本文运用非线性模型预测控制理论对空间飞行器位置和姿态的控制进行了系统的分析、研究和计算机仿真，在以下两个方面取得显著成效：
1．飞行器动力学模型的特性使得标准的MPC算法无法直接用于飞行器的控制。本文提出了几种方法用于解决这一问题。在控制对象内部嵌入稳定模型，MPC法可成功地应用于飞行器的速度控制。
2．使用一种基于空间函数最优化的函数空间模型预测控制新算法(F-MPC)控制飞行器的姿态。该算法用于飞行器的精点控制可获得满意的效果，也可用于完成飞行器的旋转控制任务，例如该算法用于飞行器的精点控制可使点误差小于0.05度。该算法的一个重要优点是能解决飞行器姿态控制过程中所产生的一些难题。例如：如果飞行器三轴推力器中的某一轴发生故障，那么常规的反馈算法将无法把飞行器定位到给定的方向，但F-MPC算法则可胜任这一任务。根据仿真结果可推出以下结论：
Ⅰ．由于未来空间飞行器控制在成本和控制性能方面都有较严格的要求，故当前需要通过使用模型预测控制来改善传统的控制方法使控制权限、组件使用和寿命等达到最优化。
Ⅱ．在未来的飞行器控制使命中，要求期望控制成本大大降低，这就需要减少重要的反馈传感器的使用，例如用于速度反馈的高质量陀螺仪等，也使得飞行器控制在如无反馈信息等的情况下为保持控制性能而依赖于预测控制技术。尽管如此，有效的状态估计的相关性技术和系统识别技术仍然在提高控制性能方面扮演着重要的角色。
Ⅲ．用于工业过程控制的MPC标准公式(线性化动力学)不能直接应用于飞行器的动力学控制。通过对本课题的研究，并结合计算机仿真来证明非线性模型预测控制法可以而且能够完成未来空间飞行
厦门大学硕士论义 摘 要
器的控制使命并满足其控制要求，使得用PID控制和现代控制对空间飞行器的控制过程所遇到的问题得
以解决，这些研究成果将对开拓非线性模型预测控制（NMPC）在我国工业领域的应用产生积极的影响。
With the development of the scales of spacecraft projects,the demands for spacecraft attitude control are becoming more and more important today. Spacecrafts are working in the space environment,which is full of sorts of physical mediums. And these mediums will impact on the altitude movement of spacecraft. Spacecraft attitude control during propulsive maneuvers is complicated due to several factors as listed below:(i) nonlinear dynamics with time delays,(ii) modeling and parameter uncertainties,(iii) flexible modes due to fuel sloshing and appendages,(vi) constraints on propulsive force and torque inputs,(v) constraints on acceptable angular rates and attitude,(iv) autonomous reconfiguration requirements under failure conditions. The current control approaches are based on frequency domain methods such as PID control which assumes linear time invariant system dynamics. The advantages of these approaches are simplicity and ease of stability and robustness analysis. However,the decrease in performanc
e and poor efficiency translates to additional payload and cannot meet the demand of current spacecraft control. Nonlinear Model Predictive Control (NMPC) is an effective method of solving multi-variable nonlinear system and has been used successfully in a number of industrial applications involving complex nonlinear processes such as petroleum chemical engineering and spaceflight domains with hard safety and actuator constraints. The remarkable stability and robustness properties of MPC observed in practice have been analyzed in a number of recent publications. The optimality of Nonlinear MPC design and its flexibility for reconfiguration make it an idea candidate for future spacecraft missions like attitude control using thrusters.
This thesis presents the feasibility of Nonlinear Model Predictive Control implemented in spacecraft control and the optimality of increasing the control precision and decreasing the fuels expenditure. And the discussions are then focused on the simulation of spacecraft control using Function-space Model Predictive Control algorithm as mentioned below:
1. Problem formulation,modeling and simulation of the spacecraft attitude and trajectory control.
2. Designation of Nonlinear Model Predictive Controllers.
3. Controller Tuning and Testing including Stability and Robustness Analysis.
4. Test results to the implementation of MPC for spacecraft control.
5. The problems to be studied in future are presented.
This thesis studies the spacecraft control using Nonlinear Model Predictive Control and computer simulations are applied in it. The main results fall into two main areas.
1. Application of the standard MPC algorithms was not possible due to the nature of the spacecraft dynamic model. Several methods were proposed to alleviate these difficulties,with varying success. MPC was successfully applied to the spacecraft rate control (setpoint and tracking problems) when applied on an internally stabilized model of the plant dynamics.
2. A new predictive control algorithm,the Function-space Model Predictive Control(F-MPC) method,was developed based on a function-space optimization of the control input for attitude control. This method yielded very promising results on precision pointing tasks,and is also applicable to the slewing task. Pointing errors of less than 0.05 degrees were achievable with off-line nominal control computation . One key advantage of the MPC feedback stabilization algorithm is that it can handle some well known difficult cases that can arise in attitude control. For example,if one of the actuator fails,conventional feedback algorithms can no longer position a spacecraft to arbitrary orientation while this algorithm remains viable.
Preliminary investigations of the MPC approach to attitude control lead to the following conclusions:I . Because of increasingly stringent requirements on the cost and control performance for future missions,
it is imperative to try to improve on the abilities of traditional control methods by using some aspects of model
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