Adaptive saturated tracking control for solid launch vehicles in ascending based on differential inclusion stabilization

Abstract

The large-range uncertainties of specific impulse, mass flow per second, aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles (SLVs) ascending leads to the deviation of the actual trajectory from the reference one. One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer (ESO) and then modify the control commands. However, ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large, which reduces the guidance accuracy. This paper introduces differential inclusion (DI) and designs a controller to solve the large-range parameter uncertainties problem. When above uncertainties have large ranges, it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set. If the DI system is stabilized, all the subsets are stabilized. Different from the traditional controllers, the parameters of the designed controller are calculated by the uncertain boundaries. Therefore, the controller can solve the problem of large-range parameter uncertainties of in ascending. Firstly, the ascent deviation system is obtained by linearization along the reference trajectory. The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation, which is called DI system. A DI adaptive saturation tracking controller (DIAST) is proposed to stabilize the DI system. Secondly, an improved barrier Lyapunov function (named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations. Compared with traditional barrier Lyapunov function, it can dynamically adjust the boundary of deviation convergence, which improve the convergence rate and accuracy of altitude, velocity and LTIA deviation. In addition, the correction amplitudes of angle of attack (AOA) and angle of sideslip (AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight. In this paper, a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate, which eliminates the adverse effects caused by the saturation. Finally, it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller. Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values. The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm. Compared with Robust Gain-Scheduling Control method, the robustness to the engine parameters are greatly improved and the control variable is smoother.

Keywords

• Solid launch vehicles
• Trajectory tracking
• Adaptive controller
• Differential inclusion