Optimal Trajectory Generation and Robust Control of a Launch Vehicle during Ascent Phase

다국어 초록 (Multilingual Abstract)

This research focused on trajectory generation and control of a flexible launch vehicle during ascent flight. An important issue of a launch vehicle design is generating optimal trajectory during its atmospheric ascent flight while satisfying constraints such as aerodynamic load. These constraints become more significant due to wind disturbance, especially in the maximum dynamic pressure region. On the other hand, modern launch vehicles are becoming long and slender for the reduction in structure mass to increase payload. As a result, they possess highly flexible bending modes in addition to aerodynamically unstable rigid body characteristics.

This dissertation proposes a rapid and reliable optimization approach for trajectory generation via sequential virtual motion camouflage (VMC) and non-conservative robust control for an unstable and flexible launch vehicle.

First, an optimal trajectory is generated in a rapid and reliable manner through the introduction of the virtual motion camouflage. VMC uses an observed biological phenomenon called motion camouflage to construct a subspace in which the solution trajectory is generated. By the virtue of this subspace search, the overall dimension of the optimization problem is reduced, which decreases the computational time significantly compared to a traditional direct input programming.

Second, an interactive optimization algorithm is proposed to find a feasible solution easier. For this, the constraint correction step is added after VMC optimization. Since VMC is a subspace problem, a feasible solution may not exist when subspace is not properly constructed. In order to address this concern, a quadratic programming (QP) problem is formulated to find a direction along which the parameters defining the subspace can be improved. Via a computationally fast QP, specific parameters (such as prey and reference point) used in VMC can be refined quickly and sequentially. As a result, the proposed interactive optimization algorithm is less sensitive to the initial guess of the optimization parameters.

Third, a non-conservative 2-DOF H infty controller for an unstable and flexible launch vehicle is proposed. The objectives of the control system are to provide sufficient margins for the launch vehicle dynamics and to enhance the speed of the closed-loop response. For this, a robust control approach is used. The key of the control design is to overcome conservativeness of the robust control. The baseline controllers using the optimal control such as LQG and LQI are designed prior to a robust controller. These optimal controllers are used to find a desirable shape of the sensitivity transfer function in order to reduce conservativeness of the robust control. After implementation and analysis of the baseline controllers, an improved sensitivity weighting function is defined as a non-conventional form with different slopes in the low frequency and around crossover frequency, which results in performance enhancement without loss of robustness. A two-degree-of-freedom H infty controller is designed which uses feedback and feedforward control together to improve tracking performance with the proposed sensitivity weighting function as a target closed-loop shape. The resulting H infty controller stabilizes the unstable rigid body dynamics with sufficient margins in the low frequency, and also uses gain stabilization in addition to phase stabilization to handle the lightly damped bending modes in the high-frequency region.

목차 (Table of Contents)

• 1 Introduction 1
• 1.1 Background and motivations 1
• 1.2 Literature survey 3
• 1.2.1 Optimal trajectory generation for a launch vehicle 3
• 1.2.2 Controller design for a flexible launch vehicle 5
• 1.3 Research objectives and contributions 6
• 1.4 Thesis organization 7
• 2 Launch Vehicle Dynamics 9
• 2.1 Frame and coordinate 9
• 2.2 Rigid body motion 9
• 2.3 Aerodynamic forces and moments 12
• 2.4 Gravity force 14
• 2.5 Thrust forces and moments 14
• 2.6 Flexible bending modes 15
• 3 Optimal Trajectory Generation 16
• 3.1 VMC based trajectory optimization 16
• 3.1.1 Nonlinear constrained trajectory optimization problem 17
• 3.1.2 VMC formulation 17
• 3.2 VMC based trajectory optimization applied to the launch vehicle 21
• 3.2.1 Relationship between launch vehicle dynamics and VMC 21
• 3.2.2 Selection of reference point and virtual prey motion 23
• 3.2.3 Trajectory optimization via VMC 25
• 3.2.4 Sequential VMC: constraint correction 27
• 3.2.5 Comparison study 29
• 3.3 Numerical simulations 31
• 3.3.1 Case 1: No wind disturbance 36
• 3.3.2 Case 2: Z-axis wind disturbance 39
• 3.3.3 Case 3: Y -axis wind disturbance 43
• 3.3.4 Case 4: Z and Y -axes wind disturbance 48
• 3.3.5 Performance comparison 51
• 4 Robust Control 57
• 4.1 Launch vehicle model description 57
• 4.1.1 Rigid body model 58
• 4.1.2 Flexible modes and Actuator 59
• 4.1.3 System properties and design specications 63
• 4.2 Baseline controllers design 65
• 4.2.1 Set-point LQG 65
• 4.2.2 Integral LQG 69
• 4.3 Robust controller design 74
• 4.3.1 H infinity control theory 74
• 4.3.2 Two-degree-of freedom H infinity controller 76
• 4.3.3 Selection of weighting functions: Wp and Wu 77
• 4.3.4 Synthesis results 82
• 4.3.5 Comparison study 88
• 4.4 Numerical simulation 94
• 5 Conclusions 98
• Abstract (in Korean) 106