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A new adaptive neural control scheme for hypersonic vehicle with actuators multiple constraints

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Abstract

A new adaptive neural control method, with the actuators multiple constraints of amplitude and rate into consideration, is proposed in this paper for the flexible air-breathing hypersonic vehicle (AHV). In order to better reflect the characteristics of the actual AHV model, we regard the AHV as a completely unknown non-affine system in the control law design process, which is different from the existing AHV control methods, thus ensuring the reliability of the designed control law. On the basis of the implicit function theorem, the radial basis function neural network (RBFNN) is introduced to approximate the model. Meanwhile, the minimum learning parameter algorithm is adopted to adaptively adjust the weight vector of RBFNN, then the design of the ideal control law is completed. When the amplitude and rate of the actuator are saturated, the designed novel auxiliary error compensation system is used to effectively compensate for the ideal control law, and the stability of the closed-loop control system is proved via the Lyapunov stability theory. In addition, to avoid the “explosion of terms” problem in the control law design process, the finite-time-convergence-differentiator is introduced to accurately estimate the differential signal. Finally, the effectiveness of the control method designed in this paper is verified by simulation.

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Abbreviations

m :

Vehicle mass

g :

Gravitational constant

\({{I}_{{yy}}}\) :

Moment of inertia

\({{\zeta }_{i}}\) :

Damping ratio for flexible modes \({{\eta }_{i}}\)

\({{\omega }_{i}}\) :

Natural frequency for flexible modes \({{\eta }_{i}}\)

\({{\tilde{\psi }}_{i}}\) :

Constrained beam coupling constant for \({{\eta }_{i}}\)

\({{L}_\mathrm{f}}\) :

The length of forward beam

\({{L}_\mathrm{a}}\) :

The length of aft beam

\({{\hat{m}}_\mathrm{f}}\) :

Mass distribution of forward beam

\({{\hat{m}}_\mathrm{a}}\) :

Mass distribution of aft beam

\({{\phi }_\mathrm{f}}(\cdot )\) :

Structural mode shape of forward beam

\({{\phi }_\mathrm{a}}(\cdot )\) :

Structural mode shape of aft beam

\(\bar{q}\) :

Dynamic pressure

S :

Reference area

\({{z}_\mathrm{T}}\) :

Thrust moment arm

\(\bar{c}\) :

Aerodynamic chord

\(\bar{\rho }\) :

Air density at height h

\({{h}_{0}}\) :

Nominal altitude

\({{\bar{\rho }}_{0}}\) :

Air density at the altitude \({{h}_{0}}\)

\({1}/{{{h}_{s}}}\) :

Air density decay rate

\({{c}_\mathrm{e}}\) :

Elevator coefficient

\(C_{T}^{{{\alpha }^{i}}}\) :

ith order coefficient of \(\alpha \) in T

\(C_{D}^{{{\alpha }^{i}}}\) :

ith order coefficient of \(\alpha \) in D

\(C_{T}^{{{{\delta }_\text {e} }^{i}}}\) :

ith order coefficient of \({\delta }_\text {e}\) in T

\(C_{D}^{{{{\delta }_\text {e} }^{i}}}\) :

ith order coefficient of \({\delta }_\text {e}\) in D

\(C_{T}^{0}\) :

Constant coefficient in T

\(C_{D}^{0}\) :

Constant coefficient in D

\(C_{L}^{0}\) :

Constant coefficient in L

\(C_{L}^{\alpha }\) :

Coefficient of \(\alpha \) in L

\(C_{L}^{{{\delta }_\text {e}}}\) :

Coefficient of \({{\delta }_\text {e}}\) in L

\(C_{M,\alpha }^{{{\alpha }^{i}}}\) :

ith order coefficient of \(\alpha \) in M

\(C_{M,\alpha }^{0}\) :

Constant coefficient in M

\(N_{j}^{{{\alpha }^{i}}}\) :

ith order contribution of \(\alpha \) to \({{N}_{j}}\)

\(N_{i}^{0}\) :

Constant term in \({{N}_{i}}\)

\(N_{2}^{{{\delta }_\text {e}}}\) :

Contribution of \({{\delta }_\text {e}}\) to \({{N}_{2}}\)

\({{\beta }_{i}}(h,\bar{q})\) :

ith trust fit parameter

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Acknowledgements

The authors would like to express their sincere thanks to the editor and anonymous reviewers for their helpful suggestions for improving the technical note.

Funding

This work was supported by the National Natural Science Foundation of China (Grant nos. 61873278 and 61773398).

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Authors and Affiliations

  1. Graduate School, Air Force Engineering University, Xi’an, 710051, China

    Changxin Luo

  2. Air and Missile Defense College, Air Force Engineering University, Xi’an, 710051, China

    Humin Lei, Jiong Li & Chijun Zhou

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  1. Changxin Luo
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Correspondence to Changxin Luo.

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Luo, C., Lei, H., Li, J. et al. A new adaptive neural control scheme for hypersonic vehicle with actuators multiple constraints. Nonlinear Dyn 100, 3529–3553 (2020). https://doi.org/10.1007/s11071-020-05707-2

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