再入飞行器末制导与控制技术研究
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摘要
末制导与控制是再入飞行器提高打击精度的重要手段。经过长时间飞行后，飞行器携带的惯性测量装置积累了较大的误差，需要融合末制导测量信息和惯性器件信息，修正飞行器位置、姿态观测误差，以得到更为准确的飞行器运动状态。对于变化的预测目标点，如果按照标准弹道飞行，势必带来较大落点偏差，必须根据相对位置和相对速度来实时生成制导指令。本文以再入飞行器为研究对象，重点研究了末制导与控制技术，主要研究成果如下：
提出了运用伪逆和四元数求解欧拉姿态角速率的方法，得到了奇异情况下欧拉角速率的解。运用最优导引律研究了弹道倾角、弹道偏角与视线高低角、方位角之间的关系，设计了需用攻角、侧滑角制导指令。提出了一种依赖相对视线信息求解转换矩阵的新方法，实现了从攻角、侧滑角制导指令到欧拉姿态角指令的转换。提出了一种滚转通道控制量为零的新制导指令组合。
提出了考虑相对位置和相对速度间夹角信息的剩余时间估算方法。运用最优控制理论得到了最优加速度矢量作用下末端脱靶量的表达式，建立了末端脱靶量与零控脱靶量之间的关系。在最近接近点和直接碰撞路径两种拦截场景下，得到了新的剩余飞行时间的闭式解。当夹角较大时，剩余飞行时间估计误差较传统的一阶近似方法小。
研究了末端攻击角度约束的自适应比例导引律和滑模变结构导引律两种制导律。建立了弹道倾角、航迹偏航角变化率和视线高低角、方位角的比例导引关系，根据俯冲平面和转弯平面的运动特点选择了合适导引参数，提出了基于飞行位置的导引参数自适应更新策略；设计了俯冲、转弯平面内的滑模切换函数和趋近律，给出了滑动模态的存在性证明，得到了视线系下的需要加速度。
设计了基于状态相关Riccati方程(SDRE)方法的姿态控制器。给出了控制器的稳定性和最优性证明，根据SDRE控制器设计思想将再入运动方程写成参数化表达形式，提出了基于状态变量函数的权重矩阵表达式，运用Schur分解法实现了Riccati方程的在线求解，得到了系统的反馈控制律。运用SDRE姿态控制器得到了再入飞行器的舵偏角指令，针对姿态控制效果进行了仿真分析。
研究了输入输出约束情况下的舵机约束预测控制方法。设计了连续预测控制的各项参数，通过将输入输出限制表示成不等式约束的形式，将输入输出约束情况下最优控制量的求解问题转化为标准二次规划问题。设计了舵机约束预测控制器，将舵机的约束控制环节加入到姿态控制回路中，减小了舵机的最大舵偏角、最大舵偏速率等伺服特性对姿态控制回路的影响，取得较好的姿态控制效果。
建立了基于dSPACE实时仿真平台的“舵机+惯组”在回路半实物仿真系统。搭建了半实物仿真环境，解决了姿态模拟、飞控计算机设计、信号采集、仿真模型下载等仿真中的关键问题，测试了接口间的数据传输。仿真系统具有在线调参、实时仿真、目标代码快速原型化、精度高等优点，节约了研制成本，缩短了研制周期。基于仿真数据对再入飞行器的姿态控制效果进行了分析，制导指令生成正确，姿态跟踪效果良好，再入飞行器能够准确到达目标点。
论文较为完整地研究了再入飞行器末制导与控制相关理论问题，研究工作是对高精度制导律和控制律的有益探索，具有一定的理论意义及工程参考价值。
This dissertation is intended to give a systematic study on the terminal guidanceand control for precise impact of reentry vehicles. The Inertial measurement unit willaccumulate errors after long-time flight. More accurate navigation information will beachieved with combined navigation, using inertia navigation and homing seeker.Furthermore, impact point error will be great guided by standard reentry trajectory iftarget point is changing. Then guidance command should be generated on relativeposition and relative velocity. By thoroughly discussing the theories and technicaldifficulties in terminal guidance and control, this study reaches an abundance of regularconclusions.
First, commonly used coordinate system in reentry phase and the transformationmatrix between different coordinate are introduced, the motion equations of reentryvehicle are given. Based on the correlation between Euler angle rates and body anglerates, Euler angle rates are calculated with pseudoinverse and quaternion method whensingularity exists. Guided by optimal guidance law, the angle between velocity vectorand local horizontal and the angle between velocity vector and local vertical plane arecorrelated with elevation/azimuth, and the commanded angle of attack and sideslipangle are derived. In the transformation from attack angle and sideslip angle commandto Euler angle command, the traditional stratrgy relies on inclination angle, flight pathangle and bank angle, a new guidance command generation strategy using relativeposition is researched. Then, a new guidance command combination is generated whichexerts no control effort in roll plane.
Based on optimal control theory, this dissertation proposes a new time-to-goestimation algorithm. The terminal miss distance with optimal control effort and thecorrelation between terminal miss and zero-effort-miss are derived. With two differentintercept strategies called point of closet approach and straight collision path, two newequations of time-to-go estimation are given, these two equations make use of theincluded angle between relative position and relative velocity vector. When the includedangle is great, these two equations return less estimation error than traditional first-orderapproximation.
Two guidance laws with terminal impact angle constraints are proposed usingadaptive proportional guidance and sliding mode control. The correlation betweeninclination/flight path anlge and elevation/azimuth is constructed based on proportionalguidance. Proper guidance parameter is selected in diving plane and tuming plane, andthe guidance parameter is updated with reentry trajectory. The sliding surface andreaching law for sliding mode in diving plane and turning plane are designed, and suchdesign satisfy the reaching condition for the sliding surface. The needed accelerations in target coordinate are given.
To get better tracking performance of attitude command over the reentry phase ofvehicles, this dissertation carries on the use of state-dependent Riccati equation (SDRE)method for attitude controller design of reentry vehicles. SDRE control method employsfactorization of the nonlinear dynamics into a state vector and state dependent matrixvalued function, stability and optimality of SDRE controller are certificated. After theconstruction of SDRE, the solution to Riccatti equation is calculated real-timely withSchur decomposition method. State feedback control law u(x) is derived with linearquadratic regulator (LQR) method. State-dependent coefficients are derived based onreentry motion equations in pitch and yaw channels, and the rudder deflections are gotwith SDRE controller.
Based on generalized predictive control(GPC), constrained predictive control isresearched when input, output and control are constrained. Then the solution to optimalinput is got with quadratic programming. Constrained predictive controller is developedbased on the transfer function of the actuator, then the new predictive controller is addedin the attitude control, and better control performance is achieved.
At last, the dissertation conducts a hardware-in-the-loop simulation based ondSPACE environment. The actuators and inertial measurement unit are added in thesimulation loop, and guidance command and control output are calculated by on-boardcomputer. dSPACE system has such advantages as changing parameter value onlinely,rapid target prototype and high precision. Control performance are discussed based onsimulation data.
To conclude, this dissertation gives a rather complete discussion on issuesconcerning terminal guidance and control both theoretically and pragmatically. Thisresearch work bears great significance in the theory development as well as engineeringpractice.
提出了运用伪逆和四元数求解欧拉姿态角速率的方法，得到了奇异情况下欧拉角速率的解。运用最优导引律研究了弹道倾角、弹道偏角与视线高低角、方位角之间的关系，设计了需用攻角、侧滑角制导指令。提出了一种依赖相对视线信息求解转换矩阵的新方法，实现了从攻角、侧滑角制导指令到欧拉姿态角指令的转换。提出了一种滚转通道控制量为零的新制导指令组合。
提出了考虑相对位置和相对速度间夹角信息的剩余时间估算方法。运用最优控制理论得到了最优加速度矢量作用下末端脱靶量的表达式，建立了末端脱靶量与零控脱靶量之间的关系。在最近接近点和直接碰撞路径两种拦截场景下，得到了新的剩余飞行时间的闭式解。当夹角较大时，剩余飞行时间估计误差较传统的一阶近似方法小。
研究了末端攻击角度约束的自适应比例导引律和滑模变结构导引律两种制导律。建立了弹道倾角、航迹偏航角变化率和视线高低角、方位角的比例导引关系，根据俯冲平面和转弯平面的运动特点选择了合适导引参数，提出了基于飞行位置的导引参数自适应更新策略；设计了俯冲、转弯平面内的滑模切换函数和趋近律，给出了滑动模态的存在性证明，得到了视线系下的需要加速度。
设计了基于状态相关Riccati方程(SDRE)方法的姿态控制器。给出了控制器的稳定性和最优性证明，根据SDRE控制器设计思想将再入运动方程写成参数化表达形式，提出了基于状态变量函数的权重矩阵表达式，运用Schur分解法实现了Riccati方程的在线求解，得到了系统的反馈控制律。运用SDRE姿态控制器得到了再入飞行器的舵偏角指令，针对姿态控制效果进行了仿真分析。
研究了输入输出约束情况下的舵机约束预测控制方法。设计了连续预测控制的各项参数，通过将输入输出限制表示成不等式约束的形式，将输入输出约束情况下最优控制量的求解问题转化为标准二次规划问题。设计了舵机约束预测控制器，将舵机的约束控制环节加入到姿态控制回路中，减小了舵机的最大舵偏角、最大舵偏速率等伺服特性对姿态控制回路的影响，取得较好的姿态控制效果。
建立了基于dSPACE实时仿真平台的“舵机+惯组”在回路半实物仿真系统。搭建了半实物仿真环境，解决了姿态模拟、飞控计算机设计、信号采集、仿真模型下载等仿真中的关键问题，测试了接口间的数据传输。仿真系统具有在线调参、实时仿真、目标代码快速原型化、精度高等优点，节约了研制成本，缩短了研制周期。基于仿真数据对再入飞行器的姿态控制效果进行了分析，制导指令生成正确，姿态跟踪效果良好，再入飞行器能够准确到达目标点。
论文较为完整地研究了再入飞行器末制导与控制相关理论问题，研究工作是对高精度制导律和控制律的有益探索，具有一定的理论意义及工程参考价值。
This dissertation is intended to give a systematic study on the terminal guidanceand control for precise impact of reentry vehicles. The Inertial measurement unit willaccumulate errors after long-time flight. More accurate navigation information will beachieved with combined navigation, using inertia navigation and homing seeker.Furthermore, impact point error will be great guided by standard reentry trajectory iftarget point is changing. Then guidance command should be generated on relativeposition and relative velocity. By thoroughly discussing the theories and technicaldifficulties in terminal guidance and control, this study reaches an abundance of regularconclusions.
First, commonly used coordinate system in reentry phase and the transformationmatrix between different coordinate are introduced, the motion equations of reentryvehicle are given. Based on the correlation between Euler angle rates and body anglerates, Euler angle rates are calculated with pseudoinverse and quaternion method whensingularity exists. Guided by optimal guidance law, the angle between velocity vectorand local horizontal and the angle between velocity vector and local vertical plane arecorrelated with elevation/azimuth, and the commanded angle of attack and sideslipangle are derived. In the transformation from attack angle and sideslip angle commandto Euler angle command, the traditional stratrgy relies on inclination angle, flight pathangle and bank angle, a new guidance command generation strategy using relativeposition is researched. Then, a new guidance command combination is generated whichexerts no control effort in roll plane.
Based on optimal control theory, this dissertation proposes a new time-to-goestimation algorithm. The terminal miss distance with optimal control effort and thecorrelation between terminal miss and zero-effort-miss are derived. With two differentintercept strategies called point of closet approach and straight collision path, two newequations of time-to-go estimation are given, these two equations make use of theincluded angle between relative position and relative velocity vector. When the includedangle is great, these two equations return less estimation error than traditional first-orderapproximation.
Two guidance laws with terminal impact angle constraints are proposed usingadaptive proportional guidance and sliding mode control. The correlation betweeninclination/flight path anlge and elevation/azimuth is constructed based on proportionalguidance. Proper guidance parameter is selected in diving plane and tuming plane, andthe guidance parameter is updated with reentry trajectory. The sliding surface andreaching law for sliding mode in diving plane and turning plane are designed, and suchdesign satisfy the reaching condition for the sliding surface. The needed accelerations in target coordinate are given.
To get better tracking performance of attitude command over the reentry phase ofvehicles, this dissertation carries on the use of state-dependent Riccati equation (SDRE)method for attitude controller design of reentry vehicles. SDRE control method employsfactorization of the nonlinear dynamics into a state vector and state dependent matrixvalued function, stability and optimality of SDRE controller are certificated. After theconstruction of SDRE, the solution to Riccatti equation is calculated real-timely withSchur decomposition method. State feedback control law u(x) is derived with linearquadratic regulator (LQR) method. State-dependent coefficients are derived based onreentry motion equations in pitch and yaw channels, and the rudder deflections are gotwith SDRE controller.
Based on generalized predictive control(GPC), constrained predictive control isresearched when input, output and control are constrained. Then the solution to optimalinput is got with quadratic programming. Constrained predictive controller is developedbased on the transfer function of the actuator, then the new predictive controller is addedin the attitude control, and better control performance is achieved.
At last, the dissertation conducts a hardware-in-the-loop simulation based ondSPACE environment. The actuators and inertial measurement unit are added in thesimulation loop, and guidance command and control output are calculated by on-boardcomputer. dSPACE system has such advantages as changing parameter value onlinely,rapid target prototype and high precision. Control performance are discussed based onsimulation data.
To conclude, this dissertation gives a rather complete discussion on issuesconcerning terminal guidance and control both theoretically and pragmatically. Thisresearch work bears great significance in the theory development as well as engineeringpractice.
引文
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