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新的轨迹规划方法考虑了包含地球自转项在内的多种非线性项,通过将攻角引入规划变量,极大地增强了飞行器的调节能力,下面结合不同的初始和终端条件,开展仿真验证。初始状态为:高度55 km,速度 7 000 m/s;终端约束为:高度30 km,速度2 500 m/s,初始航向角、终端位置和航向角根据任务需求具体确定,其具体取值参考表1。
Case Initial heading angle/(°) Terminal heading angle/(°) Terminal longitude/(°) Terminal latitude/(°) 1 90 65 120 0 2 90 70 120 0 3 90 75 120 0 4 110 135 110 0 5 110 130 110 0 6 110 125 110 0 Table 1. Initial and terminal states
值得注意的是CASE-1,2,3选择初始倾侧角符号为1,而CASE-4,5,6,选择初始倾侧角符号为−1。所有算例的计算时间均小于0.1 s,运行环境为频率3.3 GHz、内存16 G计算机下的MATLAB2016b。图3为地面轨迹曲线,两类算例具有不同的初始航向角和飞行方向,但均满足终端位置要求,飞行路径具有较大的横向机动轨迹,通过调节攻角能够对横向轨迹进行一定的调整。图4为航向角曲线,两类算例的初始航向角相同,经过两次倾侧反转都满足所需要的终端航向角,从航向角曲线也能清晰的看出各算例具有不同的倾侧反转时刻。
计算所获得控制变量如表2所示,攻角都在5 ~ 20°内变化,且根据终端航向角的需求不同,将攻角的调节能力完全发挥出来,航向角和第一次反转时刻也都确定。
Case Angle of attack/(°) Bank angle/(°) Reversal energy 1 9.091 0.6514 −4.559 5E7 2 13.53 0.7008 −4.564 6E7 3 18.55 0.7661 −4.572 3E7 4 11.82 0.6876 −4.258 8E7 5 15.81 0.7970 −4.223 8E7 6 20.64 0.7661 −4.170 40E7 Table 2. Control variables
终端误差如表3所示,可见该算法具有很高的计算精度。综合而言,所提出的方法将攻角纳入控制量,能有效的调节横向机动轨迹,在保证终端位置的条件下,有效调节终端航向角。
Case Longitude/(°) Latitude/(°) Heading angle/(°) CASE-1 2.92E-10 1.53E-6 2.42E-10 CASE-2 2.07E-10 2.70E-7 3.39E-10 CASE-3 7.37E-11 7.00E-7 5.48E-11 CASE-4 4.31E-10 1.07E-7 1.29E-10 CASE-5 8.99E-9 4.21E-8 1.63E-10 CASE-6 5.39E-9 6.65E-7 5.43E-7 Table 3. Terminal error
3D trajectory planning for gliding vehicle using linear pseudospectral model predictive control
doi: 10.3788/IRLA20200279
- Received Date: 2020-04-09
- Rev Recd Date: 2020-05-12
- Available Online: 2020-09-22
- Publish Date: 2020-09-22
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Key words:
- agent technology using high dimensional polynomials /
- linear pseudospectral method /
- entry guidance algorithm /
- model predictive control /
- high lift to drag ratio vehicle
Abstract: A new entry guidance law for the high lift to drag ratio gliding vehicle was proposed on the basis of the linear pseudospectral model predictive control method. Adopting this approach, the vehicle can arrive at the end of the entry flight with the specific heading angle. Moreover, all the typical constraints such as terminal state constraints and path constraints can be satisfied as well. Firstly, the agent technology using high dimensional polynomials was applied to generalize the lift to drag ratio, hence the analytical expression of the lift to drag ratio was obtained with respect to the energy and the angle of attack. Therefore the angle of attack was designed online to adjust the lift to drag ratio, which can enhance the trajectory planning capacity. The whole entry flight was divided into two phases noted as the descent phase and the gliding phase respectively. In the descent phase, in order to limit the maximum heating rate, the angle of attack remains the maximum allowance value and the bank angle was set to zero. During the gliding phase, the linear pseudospectral model predictive control method was applied. The reduced order dynamic model was formulated to predict the terminal state deviation, and the reduced order dynamic equation was linearized to obtain the error propagation equation. Due to the complexity of the integral calculation, Gauss pseudospectral method was used to derive the correction of the control variables. Finally, terminal state deviations involving final position and heading angle can be efficiently eliminated by modifying the angle of attack parameters, the bank angle parameters and the energy parameters of two bank reversal points. This method is simple and easy to implement with high accuracy, and it is convenient for on-line calculation. The simulation results also show that the planning requirements can be satisfied well through this method.