Tracking control of transition window for aerospace vehicles based on robust preview control

Abstract

The transition window of aerospace vehicles (ASVs) is defined as the connection point of different flight phases or the engine mode transition point. For ASVs, one of the critical problems is the precise tracking of transition window that would enable the engine to implement the mode transition successfully. Since the engine of ASVs is independently controlled, it is required that ASV eliminates both velocity and position tracking errors within a specified time to reach the transition window accurately. In addition, the tracking control of ASVs is affected by uncertain aerodynamic parameter, initial deviation, and control constraint. Therefore, an innovative tracking control of transition window (TWTC) scheme is developed, which is composed of transient reference trajectory generation and control modules. A dynamic transient trajectory is generated to modify the tracking command to expand the initial feasible region. A piecewise robust preview control algorithm is presented for the control module design, which fuses the preview information of the reference signal, control constraint, equality constraint of ASV dynamics, and performance index function. Simulation results of a nonlinear ASV model show the effectiveness of TWTC scheme under uncertain aerodynamic parameters and initial deviations.

Introduction

The air-breathing aerospace vehicles (ASVs) are reusable launch vehicles with the ability of working both within and outside the atmosphere [1]. Due to the wide flight range and the complex engine working conditions of ASVs [2], its ascent trajectory is divided into different flight stages and engine mode transition points [3], [4]. The connection points between flight phases and the engine mode transition points are called the transition windows. The precise tracking of transition window is one of the most critical problems faced by the ascent trajectory tracking of ASVs. Moreover, the slight deviation can cause undesirable tracking results due to the high flight speed. Therefore, a trajectory tracking controller with fast response time and high accuracy is required. Besides, the saturation limitations of actuators, coupled with uncertain aerodynamic parameters and initial deviations, impose severe limitations on the tracking performance. To overcome these difficulties, an effective tracking controller is important to ensure the tracking precision of transition window for ASV.

Several control methods have been used in the design of the tracking controller of ASVs. William et al. [5] and Chai et al. [6] designed real-time online controllers to improve tracking precision. However, the massive amount of online calculation restrict their practical application. The dynamic inversion control theory was applied to design a tracking controller for ASVs, which relied on the exact system model [7]. After considering wind turbulence and uncertain aerodynamic parameters, the control performance was degraded. Jia et al. [8] proposed an improved backstepping method for ASVs, which was able to provide accurate tracking under some unknown aerodynamic parameters and actuator faults. However, the complexity of controller design makes it challenging to implement in engineering. Robust control can effectively solve the uncertainties caused by aerodynamic parameters and external disturbances, but it is difficult to satisfy requirements [9]. Due to the shortcomings of the above control methods and the high requirements of ASV for transition window tracking control (TWTC), it is necessary to design a new control scheme to solve the above problems to obtain a controller that meets the requirements of high precision, strong robustness and fast response.

Preview control is a control method that adapts to the system with known models and requires fast dynamic response, which can fuse the future information of trajectory to improve the control performance [10], [11]. Moreover, the preview feedforward input can be easily added to the existing feedback control system [12]. Z.Y. Zhen designed an optimal preview controller for automatic carrier landing and achieved a great control effect [13], [14]. Hazell and David combined $H_{\infty }$ control theory with preview control theory to obtain a robust preview control (RPC) scheme to solve the tracking problems of systems with interference or uncertainty [12]. In recent years, an increasing amount of attention has been paid to the problem of robust preview control. Takaba [15] studied the preview control of polytopic uncertain discrete-time systems. Ref. [16] studied the preview control based on an auxiliary Riccati equation and the properties of the Hamiltonian matrix. Refs. [17], [18] assumed that the uncertainty matrix was constant to design a preview controller, and the upper bound of the uncertainty matrix that stabilizes the augmented error system was given based on the Lyapunov stability theorem. In this paper, a novel TWTC scheme is developed based on preview control, which can be easily implemented in practical applications compared to Refs. [5], [6], [8]; compared with Refs. [13], [14], it can solve the tracking problem of ASVs with model uncertainties and initial deviations; and compared with Refs. [17], [18], it not only guarantees the stability of the whole switching system but also considers the tracking performance and control constraints. The main contributions are as follows:

1) A new TWTC scheme for ASV is developed to track the transition window accurately within a specific period under the parameter uncertainties and initial deviations. The TWTC scheme is composed of transient reference trajectory generation and control modules. The dynamic transient trajectory generation module can adjust control commands in real-time to avoid actuator saturation and expand the initial feasible region. The control module design based on a piecewise robust preview control algorithm can satisfy the stability and asymptotic tracking property of uncertainty systems.

2) A new piecewise robust preview control algorithm is proposed to ensure the tracking precision of the system with uncertainties, initial deviations and control constraints, which considers the stability of closed-loop system and switching process, tracking performance, and control constraints. The algorithm fuses the preview information of the reference signal, equality constraint of dynamics, and performance index function, which is suitable for solving the fast-tracking problem of piecewise uncertain models.

The paper is organized as follows. In Section 2, the dynamic model of ASV and the transition window tracking problems in ascent phase for ASVs are described, and the piecewise polytopic model is constructed. Then, the piecewise robust preview control algorithm is introduced; moreover, system stability, control constraints, and performance index are analyzed in Section 3. A TWTC scheme of ASV is designed in Section 4. In Section 5, the simulation results verify the desired system performance. The conclusions are drawn in Section 6.