有限时间收敛寻的导引律
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摘要
反导导弹通过精确制导实现与目标直接碰撞,利用动能将目标彻底摧毁。在很大的相遇速度下,留给精确制导的时间只限于几秒,这就提出了有限时间收敛高精度制导技术的需求。本文以直接侧向力与气动力复合控制导弹拦截高速机动弹道导弹目标为背景,研究有限时间收敛寻的导引律。
论文首先基于非线性控制系统有限时间稳定性理论,提出了可保证制导系统视线角速率有限时间收敛的充分条件,设计了使视线角速率有限时间收敛到零或零附近边界层内的导引律,理论证明了所提有限时间收敛导引律在三维耦合制导模型下仍是能保证视线角速率有限时间收敛至零。合理调整有限时间收敛导引律的导引参数,可获得不同的使视线角速率收敛到零的速度和制导性能,能在提高制导系统鲁棒性的同时降低制导系统抖动,使得视线角速率在末制导结束前收敛至零,从而确保高制导精度。
考虑到在大气层内飞行的导弹自动驾驶仪都存在动态延迟特性,应用非奇异终端滑模控制和常规滑模控制方法,设计了两种滑模导引律。理论证明了两种导引律都可保证制导系统状态有限时间收敛至滑模面,基于非奇异终端滑模的导引律在滑动模态上视线角速率有限时间收敛至零,基于常规滑模的导引律在滑动模态上视线角速率以指数形式收敛至零。理论分析和仿真结果表明,在不考虑导引头测量噪声的情况下,两种导引律都能有效补偿导弹自动驾驶仪动特性和克服目标机动加速度的影响。
基于平面内弹-目相对运动方程下得到的真比例导引、增广比例导引和滑模变结构导引已得到了广泛的应用,本文通过构造Lyapunov函数证明了其在三维空间耦合制导模型下仍可保证视线角速率渐近收敛至零。进一步考虑导弹自动驾驶仪一阶动态延迟特性,应用非线性反步设计法,针对目标非机动、目标机动加速度可获取和目标机动加速度不可获取的三种情形分别设计了三种三维非线性导引律。在反步设计的过程中,不需要消去三维制导动力学方程中的非线性耦合项,使得导引规律的最终表达形式得以极大简化。所提三维非线性导引律都能有效克服导弹自动驾驶仪的动态延迟特性对制导精度的影响,且导引律中所需控制量都是实际制导过程中可直接测量的量,便于工程应用。
为了提高导弹拦截的杀伤效果,讨论了目标机动下的攻击角度约束导引律设计问题。在不考虑导弹自动驾驶仪动特性下设计了两种攻击角度约束滑模导引律;理论证明了两种导引律都能有限时间收敛到滑动模态,进入滑动模态后第一种滑模导引律可保证视线角以指数形式收敛至期望值和视线角速率以指数形式收敛至零,第二种滑模导引律可保证攻击角度收敛到期望值且终端脱靶量收敛至零。进一步应用非线性反步设计法把上述两种导引律推广到导弹自动驾驶仪存在一阶动态延迟特性的情形;在目标做大机动逃逸,导弹自动驾驶仪存在大滞后下,所设计的导引律都可以期望的攻击角度精确击中目标。
最后,考虑到复合控制导弹直接侧向力具有离散的工作特性,应用离散滑模变结构控制理论,系统设计了三种离散滑模导引律。先推导出了一种不需要获取目标机动加速度信息只需要其界限的离散滑模导引律;为了有效降低制导系统抖动,又提出了只需要知道目标加速度在两个采样周期之间变化界限的离散滑模导引律;由于该导引律在导引头存在测量噪声时容易引起制导系统发散,进一步设计了一种能有效克服测量噪声和目标高机动影响的离散滑模导引律;从理论上证明了上述三种离散滑模导引律都能保证视线角速率有限时间收敛至零的特性;探讨了离散滑模导引律的准滑动模态和导弹停控后脱靶量计算方法,阐述了离散滑模导引律的终端脱靶量满足的范围。
Anti-missile missiles achieve direct collision with targets by precision guidance, and destroy the targets using kinetic energy. Since the relative velocity between the missile and target is great, only a few seconds are available for the precision guidance process. This requires a high precision guidance technique with finite time convergence. In this dissertation, under the background of a blended-controlled missile with tail fins and attitude thrusters intercepting a high speed maneuvering ballistic missile, we designed homing guidance laws with finite time convergence.
First of all, based on nonlinear control system finite time stability theory, we proposed sufficient conditions for finite time convergence of the line-of-sight angular rate and design guidance laws which ensure the line-of-sight angular rates converge to zero or a small neighborhood of zero before the final time of the guidance process. Theoretically, such guidance laws guarantee the LOS angular rates converge to zero in finite time in both the planar and three-dimensional environments. Reasonable adjust the parameters of the guidance law, we can obtain different convergence speeds and performances and improve the robustness of the guidance system while alleviate the chattering, therefore we can make the LOS angular rates converge to zero before the final time to ensure high guidance precision.
In consideration of the lag of the autopilot of endoatmospheric missiles, two guidance laws based on the non-singular terminal sliding mode control and regular sliding mode control are designed sequentially. Theoretically, both of them guarantee the variables in guidance system converge to sliding surface in finite time, furthermore, the former guarantees the LOS angular rates converge to zero in finite time on the sliding surface while the later guarantees the convergence at an exponential rate. Theoretical analysis and simulation results show that the proposed guidance laws are robust against target maneuvers and are able to compensate the lag of autopilot.
The true proportional navigation guidance law, the augmented proportional navigation guidance law and the adaptive sliding-mode guidance law designed based on the planar target-to-missile relative motion dynamics have been widely used. By a proper construction of a Lyapunov function for the line-of-sight angular rates in the three dimensional guidance dynamics, it is shown that the three guidance laws presented are able to ensure the asymptotic convergence of the angular rates as they are directly applied to the three-dimensional guidance environment. Furthermore, considering the missile autopilot dynamics as a first order lag, we design three dimensional nonlinear guidance laws by using the backstepping technique for three cases: (1) the target does not maneuver; (2) the information of target acceleration can be acquired; and (5) the target acceleration is not available but its bound is known a priori. In the first step of the backstepping design of the control law, there is no need to cancel the nonlinear coupling terms in the three-dimensional guidance dynamics in such way that the final expressions of the proposed guidance laws are significantly simplified. The proposed three dimensional guidance laws are able to effectively compensate the lag of autopilot; moreover, the control inputs are directly measurable thus can be implemented conveniently.
The problem of intercepting maneuvering targets with impact angle constrained flight trajectories is discussed to enhance the hitting precision. First, supposing the missile has an ideal autopilot, we designed two terminal guidance laws with impact angle constrained trajectories. Theoretically, both of them guarantee the LOS angles and LOS angular rates converge to sliding surface in finite time, and one guidance law guarantees the LOS angles converge to expected value and the LOS angular rates converge to zero in finite time at an exponential rate on the sliding surface while the other guarantees the LOS angles converge to expected value and the final miss distance converge to zero. Furthermore, considering the dynamics of missile autopilot as a first order lag, we extended the two guidance laws with autopilot lag. Simulation results showed that the guidance laws with autopilot lag are able to guide a missile to impact either a maneuvering target or a non maneuvering target with a desired angle and a small miss distance.
Finally, considering of the discrete-time dynamical character of lateral thrusters on blended-controlled missile, three discrete sliding-mode guidance laws are proposed by using discrete siding-mode control theory. First, a discrete sliding-mode guidance law which needs not the bound of target acceleration is deduced. The second discrete sliding-mode law is designed with just knowing the possible variation range of target acceleration between two adjacent sampling instants rather than the target acceleration bound. Since the variations of target-to-missile range and the target acceleration are both small variable between two adjacent sampling instants, in the design of the third discrete sliding-mode guidance law all historical missile seeker’s measurements are used to estimate the target acceleration, such that the noises in seeker measurements are effectively smoothen. It is theoretically proved that the proposed discrete sliding-mode guidance laws are finite time convergent. Quasi sliding-mode bands of the discrete sliding-mode guidance laws are discussed, and formulas to calculate the terminal miss distances of discrete sliding-mode guidance laws are presented.
论文首先基于非线性控制系统有限时间稳定性理论,提出了可保证制导系统视线角速率有限时间收敛的充分条件,设计了使视线角速率有限时间收敛到零或零附近边界层内的导引律,理论证明了所提有限时间收敛导引律在三维耦合制导模型下仍是能保证视线角速率有限时间收敛至零。合理调整有限时间收敛导引律的导引参数,可获得不同的使视线角速率收敛到零的速度和制导性能,能在提高制导系统鲁棒性的同时降低制导系统抖动,使得视线角速率在末制导结束前收敛至零,从而确保高制导精度。
考虑到在大气层内飞行的导弹自动驾驶仪都存在动态延迟特性,应用非奇异终端滑模控制和常规滑模控制方法,设计了两种滑模导引律。理论证明了两种导引律都可保证制导系统状态有限时间收敛至滑模面,基于非奇异终端滑模的导引律在滑动模态上视线角速率有限时间收敛至零,基于常规滑模的导引律在滑动模态上视线角速率以指数形式收敛至零。理论分析和仿真结果表明,在不考虑导引头测量噪声的情况下,两种导引律都能有效补偿导弹自动驾驶仪动特性和克服目标机动加速度的影响。
基于平面内弹-目相对运动方程下得到的真比例导引、增广比例导引和滑模变结构导引已得到了广泛的应用,本文通过构造Lyapunov函数证明了其在三维空间耦合制导模型下仍可保证视线角速率渐近收敛至零。进一步考虑导弹自动驾驶仪一阶动态延迟特性,应用非线性反步设计法,针对目标非机动、目标机动加速度可获取和目标机动加速度不可获取的三种情形分别设计了三种三维非线性导引律。在反步设计的过程中,不需要消去三维制导动力学方程中的非线性耦合项,使得导引规律的最终表达形式得以极大简化。所提三维非线性导引律都能有效克服导弹自动驾驶仪的动态延迟特性对制导精度的影响,且导引律中所需控制量都是实际制导过程中可直接测量的量,便于工程应用。
为了提高导弹拦截的杀伤效果,讨论了目标机动下的攻击角度约束导引律设计问题。在不考虑导弹自动驾驶仪动特性下设计了两种攻击角度约束滑模导引律;理论证明了两种导引律都能有限时间收敛到滑动模态,进入滑动模态后第一种滑模导引律可保证视线角以指数形式收敛至期望值和视线角速率以指数形式收敛至零,第二种滑模导引律可保证攻击角度收敛到期望值且终端脱靶量收敛至零。进一步应用非线性反步设计法把上述两种导引律推广到导弹自动驾驶仪存在一阶动态延迟特性的情形;在目标做大机动逃逸,导弹自动驾驶仪存在大滞后下,所设计的导引律都可以期望的攻击角度精确击中目标。
最后,考虑到复合控制导弹直接侧向力具有离散的工作特性,应用离散滑模变结构控制理论,系统设计了三种离散滑模导引律。先推导出了一种不需要获取目标机动加速度信息只需要其界限的离散滑模导引律;为了有效降低制导系统抖动,又提出了只需要知道目标加速度在两个采样周期之间变化界限的离散滑模导引律;由于该导引律在导引头存在测量噪声时容易引起制导系统发散,进一步设计了一种能有效克服测量噪声和目标高机动影响的离散滑模导引律;从理论上证明了上述三种离散滑模导引律都能保证视线角速率有限时间收敛至零的特性;探讨了离散滑模导引律的准滑动模态和导弹停控后脱靶量计算方法,阐述了离散滑模导引律的终端脱靶量满足的范围。
Anti-missile missiles achieve direct collision with targets by precision guidance, and destroy the targets using kinetic energy. Since the relative velocity between the missile and target is great, only a few seconds are available for the precision guidance process. This requires a high precision guidance technique with finite time convergence. In this dissertation, under the background of a blended-controlled missile with tail fins and attitude thrusters intercepting a high speed maneuvering ballistic missile, we designed homing guidance laws with finite time convergence.
First of all, based on nonlinear control system finite time stability theory, we proposed sufficient conditions for finite time convergence of the line-of-sight angular rate and design guidance laws which ensure the line-of-sight angular rates converge to zero or a small neighborhood of zero before the final time of the guidance process. Theoretically, such guidance laws guarantee the LOS angular rates converge to zero in finite time in both the planar and three-dimensional environments. Reasonable adjust the parameters of the guidance law, we can obtain different convergence speeds and performances and improve the robustness of the guidance system while alleviate the chattering, therefore we can make the LOS angular rates converge to zero before the final time to ensure high guidance precision.
In consideration of the lag of the autopilot of endoatmospheric missiles, two guidance laws based on the non-singular terminal sliding mode control and regular sliding mode control are designed sequentially. Theoretically, both of them guarantee the variables in guidance system converge to sliding surface in finite time, furthermore, the former guarantees the LOS angular rates converge to zero in finite time on the sliding surface while the later guarantees the convergence at an exponential rate. Theoretical analysis and simulation results show that the proposed guidance laws are robust against target maneuvers and are able to compensate the lag of autopilot.
The true proportional navigation guidance law, the augmented proportional navigation guidance law and the adaptive sliding-mode guidance law designed based on the planar target-to-missile relative motion dynamics have been widely used. By a proper construction of a Lyapunov function for the line-of-sight angular rates in the three dimensional guidance dynamics, it is shown that the three guidance laws presented are able to ensure the asymptotic convergence of the angular rates as they are directly applied to the three-dimensional guidance environment. Furthermore, considering the missile autopilot dynamics as a first order lag, we design three dimensional nonlinear guidance laws by using the backstepping technique for three cases: (1) the target does not maneuver; (2) the information of target acceleration can be acquired; and (5) the target acceleration is not available but its bound is known a priori. In the first step of the backstepping design of the control law, there is no need to cancel the nonlinear coupling terms in the three-dimensional guidance dynamics in such way that the final expressions of the proposed guidance laws are significantly simplified. The proposed three dimensional guidance laws are able to effectively compensate the lag of autopilot; moreover, the control inputs are directly measurable thus can be implemented conveniently.
The problem of intercepting maneuvering targets with impact angle constrained flight trajectories is discussed to enhance the hitting precision. First, supposing the missile has an ideal autopilot, we designed two terminal guidance laws with impact angle constrained trajectories. Theoretically, both of them guarantee the LOS angles and LOS angular rates converge to sliding surface in finite time, and one guidance law guarantees the LOS angles converge to expected value and the LOS angular rates converge to zero in finite time at an exponential rate on the sliding surface while the other guarantees the LOS angles converge to expected value and the final miss distance converge to zero. Furthermore, considering the dynamics of missile autopilot as a first order lag, we extended the two guidance laws with autopilot lag. Simulation results showed that the guidance laws with autopilot lag are able to guide a missile to impact either a maneuvering target or a non maneuvering target with a desired angle and a small miss distance.
Finally, considering of the discrete-time dynamical character of lateral thrusters on blended-controlled missile, three discrete sliding-mode guidance laws are proposed by using discrete siding-mode control theory. First, a discrete sliding-mode guidance law which needs not the bound of target acceleration is deduced. The second discrete sliding-mode law is designed with just knowing the possible variation range of target acceleration between two adjacent sampling instants rather than the target acceleration bound. Since the variations of target-to-missile range and the target acceleration are both small variable between two adjacent sampling instants, in the design of the third discrete sliding-mode guidance law all historical missile seeker’s measurements are used to estimate the target acceleration, such that the noises in seeker measurements are effectively smoothen. It is theoretically proved that the proposed discrete sliding-mode guidance laws are finite time convergent. Quasi sliding-mode bands of the discrete sliding-mode guidance laws are discussed, and formulas to calculate the terminal miss distances of discrete sliding-mode guidance laws are presented.
引文
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