We propose a predictive sliding mode control (PSMC) scheme for attitude control of hypersonic vehicle (HV) with system uncertainties and external disturbances based on an improved fuzzy disturbance observer (IFDO). First, for a class of uncertain affine nonlinear systems with system uncertainties and external disturbances, we propose a predictive sliding mode control based on fuzzy disturbance observer (FDO-PSMC), which is used to estimate the composite disturbances containing system uncertainties and external disturbances. Afterward, to enhance the composite disturbances rejection performance, an improved FDO-PSMC (IFDO-PSMC) is proposed by incorporating a hyperbolic tangent function with FDO to compensate for the approximate error of FDO. Finally, considering the actuator dynamics, the proposed IFDO-PSMC is applied to attitude control system design for HV to track the guidance commands with high precision and strong robustness. Simulation results demonstrate the effectiveness and robustness of the proposed attitude control scheme.

Near space is the airspace of Earth altitudes from 20 km to 100 km, which has shown strategy and spatial superiority with the prosperous development of aerospace technology [

The sliding mode control (SMC) is insensitive to system uncertainties and disturbances. It is one of the most important approaches to the control of systems with modeling imprecision, and it has been widely applied to the flight control system design [

For the design of control system for the HV, many advanced control methods mainly focus on the stability or robust stability rather than considering the system uncertainties and disturbances explicitly in the controller design [

Motivated by the precise and robust attitude control demand of the HV with uncertain model and external disturbances, this paper considers the composite disturbances in flight control system design of the HV to improve the robust control performance. Three major contributions are presented as follows.

We propose a predictive sliding mode control based on fuzzy disturbance observer (FDO-PSMC) method for a class of uncertain affine nonlinear systems with system uncertainties and external disturbances. The composite disturbances are considered, which result in poor performance and instability of the control system.

To address the problems which are brought by the composite disturbances, an improved FDO (IFDO) is proposed through utilizing the special properties of a hyperbolic tangent function to compensate for the approximate error of FDO. By using IFDO, the composite disturbances can be approximated effectively.

Considering the actuator dynamics, we apply the improved fuzzy disturbance observer based predictive sliding mode control (IFDO-PSMC) scheme to the attitude control system design for the HV. Numerical simulation verifies the surpassing performance of the proposed control scheme.

The rest of this paper is organized as follows. In Section

Suppose that the fuel slosh is not considered and the products of inertia are negligible [

For the convenience of control system design,

To develop the predictive sliding mode control, we consider the following MIMO uncertain affine nonlinear system with external disturbances:

Define

Without loss of generality, the equilibrium of uncertain nonlinear system (

The vector relative degree of system (

For all

The following

To facilitate the process of control system design, the following reasonable assumptions are required before developing predictive sliding mode control of the uncertain MIMO nonlinear system (

All states are available; moreover, the output and reference signals are also continuously differentiable.

The zero dynamics are stable.

The vector relative degree is

According to Assumption

Associate the

Furthermore, the sliding surface vector is defined as

For the sake of simplified notation, define

Then the vector

Consequently, differentiating the sliding surface vector, we obtain

Within the moving time frame, the sliding surface

For the derivation of the control law, the receding-horizon performance index at the time

The necessary condition for the optimal control to minimize (

According to (

If

For the convenience of notation,

The fuzzy inference engine adopts the fuzzy if-then rules to perform a mapping from an input linguistic vector

By adopting a center-average and singleton fuzzifier and the product inference, the output of the fuzzy system can be written as

For any given real continuous function

According to Lemma

Let

Consequently, the composite disturbances

Through adjusting the parameter vector

Consider the following dynamic system:

Define the disturbance observation error

Then, the FDO-PSMC is proposed as

Invoking (

Invoking (

Assume that the disturbance of (

Consider the Lyapunov function candidate:

Invoking (

Considering the fact

Consequently, we obtain

If

In order to make sure that the FDO

A projection operator (

The adjustable parameter vector of the FDO (

For all

The hyperbolic tangent function is incorporated to compensate for the approximate error and improve the precision of FDO. Consider the following dynamic system:

Define the disturbance observation error

The IFDO-PSMC is proposed as

Invoking (

Invoking (

Assume that the disturbance of the system (

Consider the Lyapunov function candidate:

According to Lemma

Consequently, we obtain

If

The composite disturbances can be approximated effectively by adjusting the parameter law (

The structure of the IFDO-PSMC flight control system is shown in Figure

IFDO-PSMC based flight control system.

The states of the attitude model (

According to the PSMC approach, (

Then, the sliding surface can be selected as

Substituting (

In order to improve performance of the flight control system, the adaptive compensation controller based on IFDO is designed as

Accordingly, a fuzzy system can be designed to approximate the composite disturbances

Considering the adaptive parameter law (

Assume that the HV attitude model satisfies Assumptions

Theorem

By means of the designed IFDO-PSMC system (

The HV attitude system tracks the guidance commands by controlling actuator to generate deflection moments; then, the HV is driven to change the attitude angles. However, there exist actuator dynamics to generate the input moments

Actuator model.

To validate the designed HV attitude control system, simulation studies are conducted to track the guidance commands

The damping

To exhibit the superiority of the proposed scheme, the variation of the aerodynamic coefficients, aerodynamic moment coefficients, atmosphere density, thrust coefficients, and moments of inertia is assumed to be −50%, −50%, +50%, −30%, and −10%, which are much more rigorous than those considered in [

The simulation time is set to be 20 s and the update step of the controller is 0.01 s. The predictive sliding mode controller design parameters are chosen as

Comparison of tracking curves and control inputs under SMC and PSMC in nominal condition.

Comparison of tracking curves and control inputs under SMC and PSMC in the presence of system uncertainties.

Comparison of tracking curves under PSMC, FDO-PSMC, and IFDO-PSMC in the presence of system uncertainties and external disturbances.

Figure

Figure

Figure

It can be concluded from the above-mentioned simulation analysis that the proposed IFDO-PSMC flight control scheme is valid.

An effective control scheme based on PSMC and IFDO is proposed for the HV with high coupling, serious nonlinearity, strong uncertainty, unknown disturbance, and actuator dynamics. PSMC takes merits of the strong robustness of sliding model control and the outstanding optimization performance of predictive control, which seems to be a very promising candidate for HV control system design. PSMC and FDO are combined to solve the system uncertainties and external disturbance problems. Furthermore, we improve the FDO by incorporating a hyperbolic tangent function with FDO. Simulation results show that IFDO can better approximate the disturbance than FDO and can assure the control performance of HV attitude control system in the presence of rigorous system uncertainties and strong external disturbances.

The authors declare that there is no conflict of interests regarding the publication of this paper.