Adaptive fault tolerant control for hypersonic flight vehicle system with state constraints

doi:10.1016/j.jfranklin.2020.07.014

Journal of the Franklin Institute

Volume 357, Issue 14, September 2020, Pages 9351-9377

https://doi.org/10.1016/j.jfranklin.2020.07.014 Get rights and content

Highlights

•
A fault-tolerant control scheme is proposed for HFVs with flexible dynamics, parameter uncertainties, faults and state constraints.
•
The proposed method transforms the MIMO model properly such that the BLF based control design can be successfully employed to solve the problem of state constraints.
•
Considering two types of actuator faults, an adaptive fault compensation mechanism is introduced to the BLFs-based controller.

Abstract

In this paper, an adaptive fault tolerant control (FTC) scheme based on barrier Lyapunov functions (BLFs) for the hypersonic flight vehicle (HFV) with state constraints is proposed. Complexities of the aerodynamical uncertainties, external disturbances and flexible dynamics are taken into account in the controller design process. The paper deals with the MIMO system properly so that the backstepping technique based on BLFs can be successfully used for the issue of state constraints without neglecting the coupling of HFV system. To aim at the unknown faults of the elevators, an adaptive FTC mechanism is introduced to the BLFs-based controller, which increases the reliability of the system. Finally, simulations are conducted to verify the validity of the designed controller.

Introduction

Nowadays, a growing number of countries have began to regard hypersonic technology as the main standard in the aerospace field, because HFVs have strong military as well as civil applications. However, there are many challenges in the controller design of HFV [1].

Firstly, due to the fuselage/propulsion integrated design of HFV, the dynamics of HFV have strong nonlinearity [2], [3], strong coupling [4], [5], [6] and strong uncertainty [7], [8], [9], which increase the difficulty of the controller design. Secondly, as the complexity of aircraft systems continues to increase, FTC should be used to deal with the effects caused by faults [10], [11]. Meanwhile, the states of HFVs need to be restricted so that they can meet engine operating conditions [12]. As pointed out in the literature [12], excessive AOA may lead to a sharp drop in intake air flow, which can even cause the engine not to start. Therefore, state constraints must be considered when designing the controllers for the HFV.

In recent years, BLFs and the improved forms have been proposed and applied for nonlinear systems [13], [14], [15], [16], [17], [18], [19]. BLFs-based backstepping methods can achieve satisfactory effect in constraining states with relatively easy calculations. The basic idea is when the independent variables tend to approach some regional boundaries, the values of BLFs tend to approach infinity. If the BLFs are ensured bounded, the purpose of constraining states can be achieved.

BLFs method can only be used to constrain states which have clear tracking targets, because the constraints are actually put on the tracking errors. Therefore, the method was originally used for output constraint [13], and then it was used for state constraints on strict feedback systems [15]. Recently, some researchers tried to use BLFs-based method on MIMO systems [20], [21], [22]. For example, in [23], for a MIMO system (marine surface vessel), a BLFs-based block backstepping controller was employed for state constraints. In [24], DongJuan Li was inspired by [25] and proposed a BLFs-based decoupling backstepping method, which can achieve state constraints on some special forms of MIMO systems.

BLFs-based methods have gradually attracted the attention of scholars who study the control of HFV [26], [27], [28], [29], [30]. In particular, in [26], the author proposed a BLFs-based composite learning method, which realizes AOA constraint for the longitudinal model of HFV. In [27], the BLFs-based backstepping method were used to achieve the full state constraints of the flexible HFV system. Time-varying BLFs are introduced in [30] to make AOA meet velocity dependent constraint so that the scramjet can be kept away from inlet un-start. However, all of the above papers ignore the coupling of HFV longitudinal model and divide the MIMO system into SISO strict feedback systems. The dynamics of HFV are characterized by strong coupling, and ignoring the coupling between altitude dynamics and velocity dynamics may reduce the accuracy of the system. How to achieve state constraints while ensuring the accuracy of the system is the main work of this paper.

Sliding mode control (SMC) is commonly used in designing the controllers for nonlinear systems [31], [32], [33], [34]. In [35], the integral term was firstly introduced into the sliding surface to reduce the steady-state error and enhance the robustness. The algorithm is simple and can deal with the uncertainties of HFV effectively, so it is widely used in the field of HFV control. In [4], the author designed an adaptive sliding mode controller for the HFV’s longitudinal model with disturbances and parameter uncertainties. In cruise condition, the tracking curves of altitude and velocity are evaluated, and validity of the method is verified. In [36], a SMC-based strategy is proposed to achieve fast attitude tracking for a HFV with unknown external disturbances. Combined with the adaptive method, the controllers are designed for the outer and inner loops of the HFV system respectively. In [37], a control method for HFV based on terminal sliding mode is proposed. The nonlinear disturbance observer (NDO) is designed to estimate the uncertain parameters and external disturbances of HFV system, and the output of NDO is used to design the controller to improve the robustness of the system.

For HFV system, actuator faults are relatively common and difficult to handle. In complex flight environments, elevators often break down due to wear and tear, so FTC methods are often applied in the papers about controller design for HFV. In [38], backstepping method is used to design the adaptive fault-tolerant controller for HFV system. HFVs elevators need to meet the given matching conditions under the known faults. When the fault information is unknown, the adaptive laws are used to achieve the purpose of fault tolerance. In [39], the author designed a sliding mode observer for HFV model to judge whether any fault occurs and obtain fault information. And then, FTC is realized according to the obtained information. In [40], a FTC strategy based on control allocation algorithm is proposed. Instead of reconfiguring the controller, the method redistributes the control signals to the remaining actuators when a fault occurs, so as to achieve the purpose of fault tolerance. In [10], for a HFV system, a FTC method is proposed based on the nominal feedback linearization to accommodate the impact of unknown fault. In [36], an adaptive FTC scheme is proposed for the HFV system in the presence of unknown faults. A neural network is designed to estimate the unknown additive fault, and the adaptive method is applied to handle the unknown multiplicative fault.

Summarize the main contributions of this paper as follows:

(1)
The paper proposes a BLFs-based adaptive FTC method for the HFV. The controller design challenges such as flexible dynamics, external disturbances, parameter uncertainties, actuator faults and state constraints are taken into consideration.
(2)
This paper uses BLFs to constrain the states of the HFV so that the HFV can remain in its safe flight envelope. Instead of decomposing the HFV system into two SISO subsystems, this paper considers the coupled MIMO system model and proposes a novel way to handle state constraints without neglecting the coupling between the altitude subsystem and the velocity subsystem. The proposed method transforms the MIMO model properly such that the BLFs based technique can be successfully employed to solve the problem of state constraints for the HFV. Also, the closed-loop stability of the MIMO longitudinal model for the HFV under the proposed controller is proved in the paper.
(3)
Furthermore, considering two types of elevator faults, an adaptive FTC mechanism is introduced to the BLFs-based controller. For the double-elevators model, as long as both actuators are not stuck, employed control law can guarantee that required constraints are not violated and outputs track the desired reference commands.

This paper is organized as follows. Description and transformation of HFV model are presented in the Section 2. Fault-tolerant controller design focusing on state constraints and the stability analysis are shown in the Section 3. The simulation results and the conclusion are respectively presented in Sections 4 and 5.

Section snippets

Hypersonic flight vehicle model and problem formulation

This section provides a brief introduction of the flexible HFV’s longitudinal model and the control purpose before designing the controller. Meanwhile, for controller design, some reasonable assumptions are made and the model is transformed.

Controller design and stability analysis

Considering the MIMO system (11) with parameter uncertainties, disturbances, actuator fault and state constraints, the controller is designed in this section. In Section 3.1, basic idea of BLFs and the lemmas required for controller design are shown. In Section 3.2, the procedures of the BLFs-based controller design are presented in details. In Section 3.3, stability analysis is presented.

Simulation

To show the validity of the designed adaptive control strategy for the flexible HFV and show the role of BLFs, this section provides a simulation. According to [41], some vehicle parameters and aerodynamic parameters used in the simulation are as follows: $m = 9375 l b, ρ = 0.24325 \times 10^{- 4}, S = 3603 f t^{2}, \bar{c} = 80, c_{e} = 0.0292, I_{y y} = 7 \times 10^{6} l b \cdot f t, r = 20902244 f t, μ = 3.31929 \times 10^{- 11}$ . Select the initial states as: $h_{0} = 100000 f t,$ $V_{0} = 15000 f t / s,$ $γ_{0} = 0,$ $α_{0} = 0,$ $q_{0} = 0,$ $ζ_{10} = 0,$ $ζ_{20} = 0$ . Consider the influence of the following external

Conclusion

In this paper, an adaptive FTC design focusing on state constraints has been proposed for the flexible HFV. The coupling of the altitude subsystem and the velocity subsystem is taken into consideration, which is not done in others papers. Instead of decomposing the HFV system into two SISO subsystems, this paper transforms MIMO system model properly and proposes a novel way to handle state constraints with BLFs. Meanwhile, the paper solves problem of the parameter uncertainties, external

Declaration of Competing Interest

None.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 61873127 and 61533009), the National Aeronautical Science Foundation of China (No. 2017ZA52013) and the Six Talent Peaks Project in Jiangsu Province (No. HKHT-010).

References (41)

J. He et al.
Adaptive output feedback fault-tolerant control design for hypersonic flight vehicles
J. Frankl. Inst.
(2015)
J. He et al.
Fault-tolerant control with mixed aerodynamic surfaces and RCS jets for hypersonic reentry vehicles
Chin. J. Aeronaut.
(2017)
K.P. Tee et al.
Barrier Lyapunov functions for the control of output constrained nonlinear systems
Automatica
(2009)
K.P. Tee et al.
Control of nonlinear systems with time-varying output constraints
Automatica
(2011)
W. He et al.
Cooperative control of a nonuniform gantry crane with constrained tension
Automatica
(2016)
H. An et al.
Control of a time-varying hypersonic vehicle model subject to inlet un-start condition
J. Frankl. Inst.
(2018)
Y. Wu et al.
Adaptive terminal sliding mode control for hypersonic flight vehicles with strictly lower convex function based nonlinear disturbance observer
ISA Trans.
(2017)
H. Alwi et al.
Fault tolerant control using sliding modes with on-line control allocation
Automatica
(2008)
L. Huang et al.
Challenges of control science in near space hypersonic aircrafts
Control Theory Appl.
(2011)
M.A. Bolender et al.
Nonlinear longitudinal dynamical model of an airbreathing hypersonic vehicle
J. Spacecraft Rockets
(2012)

L. Fiorentini et al.

Nonlinear robust adaptive control of flexible air-breathing hypersonic vehicles

J. Guid. Control Dyn.

(2009)

H. Xu et al.

Adaptive sliding mode control design for a hypersonic flight vehicle

J. Guid. Control Dyn.

(2004)

H. Buschek et al.

Uncertainty modeling and fixed-order controller design for a hypersonic vehicle model

J. Guid. Control Dyn.

(2012)

W. Zhen et al.

Longitudinal coordinated control of hypersonic flight vehicle based on coupling analysis

J. Jilin Univ. (Inf. Sci. Ed.)

(2016)

W.A. Butt et al.

Adaptive dynamic surface control of a hypersonic flight vehicle with improved tracking

Asian J. Control

(2013)

B. Xu

Robust adaptive neural control of flexible hypersonic flight vehicle with dead-zone input nonlinearity

Nonlinear Dyn.

(2015)

Q. Zong et al.

Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty

Nonlinear Dyn.

(2014)

Z. Feng et al.

Robust attitude control design for a hypersonic vehicle with multi-constraints

J. Astronaut.

(2017)

K.P. Tee et al.

Control of nonlinear systems with partial state constraints using a barrier Lyapunov function

Int. J. Control

(2011)

B.S. Kim et al.

Adaptive control of nonlinear pure-feedback systems with output constraints: Integral barrier Lyapunov functional approach

Int. J. Control Autom. Syst.

(2015)

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View full text

Adaptive fault tolerant control for hypersonic flight vehicle system with state constraints

Highlights

Abstract

Introduction

Section snippets

Hypersonic flight vehicle model and problem formulation

Controller design and stability analysis

Simulation

Conclusion

Declaration of Competing Interest

Acknowledgments

J. Frankl. Inst.

Chin. J. Aeronaut.

Automatica

Automatica

Automatica

J. Frankl. Inst.

ISA Trans.

Automatica

Challenges of control science in near space hypersonic aircrafts

Control Theory Appl.

Nonlinear longitudinal dynamical model of an airbreathing hypersonic vehicle

J. Spacecraft Rockets

Nonlinear robust adaptive control of flexible air-breathing hypersonic vehicles

J. Guid. Control Dyn.

Adaptive sliding mode control design for a hypersonic flight vehicle

J. Guid. Control Dyn.

Uncertainty modeling and fixed-order controller design for a hypersonic vehicle model

J. Guid. Control Dyn.

Longitudinal coordinated control of hypersonic flight vehicle based on coupling analysis

J. Jilin Univ. (Inf. Sci. Ed.)

Adaptive dynamic surface control of a hypersonic flight vehicle with improved tracking

Asian J. Control

Robust adaptive neural control of flexible hypersonic flight vehicle with dead-zone input nonlinearity

Nonlinear Dyn.

Robust adaptive dynamic surface control design for a flexible air-breathing hypersonic vehicle with input constraints and uncertainty

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