Safety Control System Design of HGV Based on Adaptive TSMC

Introduction

Hypersonic gliding vehicle (HGV) is designed with the aerodynamic configuration of high lift-to-drag ratio, which can be launched into the sub-orbital trajectory either by a booster rocket or a reusable launch vehicle. Without any power, an HGV that can operate in near space with a speed of more than Mach 5, possesses a capacity for “extreme maneuvers.” Benefited from the rapid response and flexible maneuverability, HGVs are recognized as a viable option of long-range delivery, remote rapid strike, and power projection.

One of the major problems is that large uncertainties and perturbations are inherent to the HGV model [108]. The HGV unique characteristics pose a severe challenge for the design of flight control systems. The vast majority of contributions focus on control methodologies, including adaptive control [109, 110], back-stepping and dynamic inversion control [111], linear parameter varying control [112], sliding mode control (SMC) [113], model predictive control [114], robust control [115], and adaptive continuous higher order sliding mode control (HOSMC) [116].

Requirements that drive the desire for HGVs include reliability and maintainability. By contrast, increasing complexity and automation make an HGV more vulnerable to component/system malfunctions across the flight envelope. The safety demand for hypersonic flights has spurred an interest in the control design. Takagi-Sugeno (T-S) fuzzy system and adaptive control have been exploited in the fault-tolerant control (FTC) design of hypersonic flight vehicles [117, 118]. Within the scheme [119], a group of local FTCs are synthesized in response to various faults, while Youla parameterizations are constructed to tolerate arbitrary switching actions among different fault modes of a hypersonic vehicle. A model predictive based FTC is investigated in Ref. [51], by which the reshaped reference can be tracked in the actuator faulty condition.

Two-loop controllers based on SMC are deployed to constitute an active FTC scheme for hypersonic vehicle attitude control. The resulting FTC system can guarantee the asymptotic output tracking in spite of actuator faults [120]. An FTC system on the basis of back-stepping and sliding mode technologies is applied for a hypersonic aircraft. The studied controller can guarantee the safety of the handicapped aircraft and the globally asymptotic tracking performance [121]. Recent effort [122] attempts to design an FTC system with combination of conventional SMC and nonlinear disturbance observer. Note that the actuator amplitude constraints and faults are taken into account over the FTC design phase. Furthermore, terminal SMC (TSMC) techniques are adopted to advance the state of the art of FTC. TSMC can not only possess strong robustness on uncertain dynamics similar to linear SMC, but also guarantee the finite-time convergence of tracking error [123, 124, 125]. Two dynamic TSMCs are designed with respect to the inner and outer loops, handling actuator faults of a hypersonic vehicle [126]. An FTC strategy is determined by resorting to TSMC approach, ensuring that velocity and altitude track the reference signals in finite time after occurrence of actuator malfunctions [127]. The work in Ref. [128], which develops a passive FTC based on TSMC technique, focuses on enhancing the convergence rate.

Despite that previous studies have gained various degrees of success in addressing HGV safety control issues, there still exist some challenges.

• 1) As mentioned in Chapter 1, the amount of fault recovery time, which solely relies on the operating condition and the fault characteristics, is very limited for safety-critical plants [4, 129]. More particularly, the safety restrictions imposed on HGV inputs and outputs may be violated, if faults cannot be accommodated within the allowable amount of time. From this perspective, more emphasis on the HGV safety control design with a timely manner needs to be placed.
• 2) In terms of the time-scale separation principle, it is common practice to approach the HGV safety control problem by independent design of fast inner-loop and slow outer-loop dynamics [130, 131]. In the outer-loop, the angular rate profiles, which are regarded as virtual control signals to the inner-loop, are produced by the kinematics equation of angular motion and the SMC. With respect to the inner loop, another SMC is synthesized such that the commanded angular rate profiles are tracked. Roll, pitch, and yaw torque commands generated by the inner-loop are then allocated into control surface deflection commands. However, how to guarantee the finite-time stability of the overall system is an open issue.
• 3) TSMC is exploited for stabilizing the HGV subject to faults and uncertainties. Nonetheless, in the most of resulting TSMC approaches, a multi-input control problem with m control inputs is transformed into a decoupled problem involving m single input control structures. This type of approach may not be effective due to strong couplings in HGV aerodynamics.

In an attempt to tackle the above-mentioned issues, a TSMC based safety control design approach is proposed against HGV actuator faults and model uncertainties, with particular attention devoted to achieving multivariable design in a composite-loop. The major contributions are briefly outlined as follows.

• 1) Due to lack of wind tunnel facility and flight test experiments, a partial knowledge of the aerodynamic derivatives of hypersonic vehicles is present. The control input matrix in any HGV is composed of control moment coefficients, which are extremely difficult to accurately obtain in comparison of conventional aircraft. Hence, multiplicative uncertainty exists in the HGV control input matrix, inducing a great challenge of control design especially in the event of actuator faults. In this study, the cases of HGV actuator malfunctions and multiplicative uncertainty in control input matrix are simultaneously considered at the safety control design stage. To the best of the authors’ knowledge, there are few papers focusing on this aspect .
• 2) In most of the existing literature, control design of hypersonic vehicles is divided into the inner loop and outer loop design (named dual-loop design) based on time-scale separation principle. However, this type of design cannot ensure the stability of the overall closed-loop system. This study establishes a control-oriented model by integrating the HGV attitude kinematic and dynamic equations. Subsequently, a composite-loop design for HGV attitude tracking control under actuator faults is developed. The finite-time stability of the closed-loop system can be guaranteed from a theoretical perspective.
• 3) A finite-time multivariable TSMC approach based on homogeneity is exploited in the safety control design. With consideration of HGV actuator malfunctions and model uncertainties, a novel integral terminal sliding mode surface is established by introducing the fractional power integral terms. The resulting safety control can ensure the finite-time stability of the HGV, when actuator faults and model uncertainties exist. Moreover, the multivariable integral TSMC formed by vector expression, which is driven directly from the sliding mode reachability condition, is incorporated in the HGV safety control design. This feature is of significance in the sense that the strong couplings are inherent to HGV aerodynamics.

The rest of this chapter is organized as follows. The concepts of finite-time stable system and homogeneity are described in Chapter 5.2. The HGV aerodynamics, actuator fault model, and problem statement are given in Chapter 5.3. The control-oriented model is presented in Chapter 5.4. The HGV safety control scheme is proposed against actuator faults and model uncertainties in Chapter 5.5. In Chapter 5.6, the performance of the developed safety control is evaluated through simulations of a full nonlinear model of the HGV dynamics. Chapter 5.7 includes a discussion of the conclusions.