非线性高阶滑动模式控制器设计：适用于高超音速飞行器的跟踪控制

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"Adaptive High Order Sliding Mode Controller Design for Hypersonic Vehicle" 这篇研究论文提出了一种针对高超音速飞行器的非线性鲁棒控制策略，旨在跟踪高度和空速的阶跃变化响应。高超音速飞行器模型具有非线性、多变量、不稳定且包含不确定参数的特点。首先，通过输入-输出（I/O）线性化技术对飞行器模型进行分析。然后，基于齐次理论设计滑模面。接下来，提出了自适应高阶滑模控制器，以应对具有边界不确定性但其边界未知提前的高超音速飞行器的跟踪问题。此外，通过李雅普诺夫理论证明了系统的稳定性。最后，通过仿真结果展示了所提控制策略的有效性。一、引言可靠且成本效益高的太空接入需求，无论是民用还是军用，都激发了对高超音速飞行器新的兴趣。过去几十年，美国空军和NASA在高超音速飞行器的研发和设计上投入了大量精力。尽管已有显著进展，但高超音速飞行器的控制仍然是一个极具挑战性的领域，尤其是在处理不确定性因素时。传统控制方法可能无法有效应对这些复杂情况，因此需要开发新型控制策略。二、方法概述 1. 输入-输出线性化：这是一种非线性系统分析方法，通过对系统的输入和输出关系进行线性化处理，将非线性系统转化为线性可等效的系统，便于设计控制器。 2. 齐次理论：滑模控制的一种扩展，齐次系统具有对尺度变换的不变性，可以用来设计滑模面，使得控制器对参数不确定性具有一定的鲁棒性。 3. 高阶滑模控制器：相比于传统的第一阶滑模控制器，高阶滑模控制器能更快地驱动系统状态到达滑模面上，从而提高控制性能和抗干扰能力。同时，它通过自适应机制适应系统的不确定性，即使系统的边界未知也能有效工作。 4. 李雅普诺夫稳定性分析：李雅普诺夫稳定性理论是系统稳定性分析的基础工具，通过构造合适的李雅普诺夫函数，可以证明控制系统在不确定性存在的情况下仍能保持稳定。三、仿真结果与讨论仿真结果表明，所提出的自适应高阶滑模控制策略能够有效地使高超音速飞行器跟踪设定的高度和空速变化，同时在面对不确定性时保持良好的控制性能。这验证了该策略在实际应用中的潜力和有效性。总结，这篇研究论文为高超音速飞行器的控制提供了创新解决方案，特别是在处理不确定性方面。自适应高阶滑模控制策略的提出，为未来高超音速飞行器的控制设计提供了新的思路和理论支持。

Equation Chapter 1 Section 1

Abstract—A nonlinear robust control strategy for hypersonic

vehicle in tracking the responses to a step change in altitude

and airspeed is proposed. The vehicle model is nonlinear,

multivariable, unstable, and includes uncertain parameters.

Firstly, the analysis is conducted for the hypersonic vehicle

model via input-output (I/O) linearized technique. Secondly,

the sliding mode manifold is designed based on the

homogeneity theory. Then, the adaptive high order sliding

mode controller is proposed to achieve the tracking for

hypersonic vehicle with bounded uncertainty but its boundary

is not known in advance. Furthermore, the stability of the

system is proved via Lyapunov theory. Finally, the simulation

results are provided to demonstrate the effectiveness of the

proposed control strategy.

I. INTRODUCTION

The need for a reliable and cost-effective access to space

for both civilian and military applications has spurred a

renewed interest in hypersonic vehicle. A considerable effort

has been made by the U.S. Air Force and NASA to further

their development and design during the last decades.

Although the recent success of NASA’s X-43A experimental

vehicle, the design of control systems for hypersonic vehicles

is a challenging task due to the fact that the dynamics of

hypersonic vehicles is highly nonlinear, coupled and partly

unpredictable.

Many advance control methods based on robust and

adaptive theory have been extensively used to study the flight

control problem since 1990’s. Such as, Marrison

[1]

used

linear-quadratic stochastic robust control, while Wang

[2]

combined nonlinear dynamic inversion with stochastic

robustness to design the control system for hypersonic

vehicle. To provide robust velocity and altitude tracking in

the presence of parameter uncertainties and varying flight

conditions, the robust output-feedback control is designed in

Ref.[3]. Cliff

[4]

proposed the L1 adaptive control architecture

to compensate for parametric uncertainties and the

unmodeled dynamics for hypersonic vehicle. Thereafter, the

employed both robust and adaptive techniques on a

sequential loop closing methodology is proposed in Ref.[5].

In spite of the extensive development of robust control

methods, Sliding Mode Control (SMC) remains a key choice

for handling bounded uncertainties and unmodeled dynamics

in control problems. However, the pure sliding mode control

presents drawbacks that include large control authority

requirements and control chattering. Xu

[6]

combined the the

* This work has been supported by National Natural Science Foundation

of China (61203012, 61273092, 91016018), Key Grant Project of Chinese

Bailing Tian is with the School of Electric and Automation Engineering,

Tianjin University, Tianjin, China (e-mail: tianbailing121@126.com)

Wenru Fan is with Aeronautical Automation College, Civil Aviation

University of China, Tianjin, China (e-mail: wenrufan@tju.edu.cn).

estimator-based solution with the standard SMC to design an

adaptive sliding mode controller that avoids the chattering

phenomenon and tracks step commands in velocity and

altitude while requiring limited state information. Ronald

[7]

investigated a pseudo-sliding mode flight control design in

the frequency domain, based on the sliding mode control

theory. Furthermore, in order to improve the control

performance, the high order sliding mode control (HOSM)

strategy begins to be applied in flight control system for

hypersonic vehicle. The HOSM keeps the main advantages of

standard SMC, the chattering effect, relative degree

restriction are eliminated and higher order precision is

provided

[8,9]

. Zong proposed the quasi-continuous HOSM

controller for hypersonic cruise vehicle to achieve the track

for the responses to a step change in altitude and airspeed

[10]

Subsequently, the HOSM controller and observer are

synthesized to control the hypersonic vehicle with angle of

attack and flight path angle unmeasurable in Ref.[11].

Although many nonlinear control methods have been used in

hypersonic vehicle, the assumption that the boundary of

uncertainty is known in advance is often used in the design of

flight control. However, the boundary can’t be known exactly

in practical flight control system which makes the control

system design more challenging.

This paper is part of a continuing effort to develop

practical nonlinear robust control method for hypersonic

vehicle with bounded uncertainty but its boundary is not

known in advance. The paper is organized as follows: In Sec.

2 the hypersonic vehicle model is introduced and the control

objective is stated. The input-output decoupling linearization

model is derived for hypersonic vehicle via dynamic

inversion technique in Sec.3. In Sec.4, the adaptive

high-order sliding mode theory is proposed to design

controller to achieve stable tracking in altitude and velocity.

Finally, the simulation results are provided in Sec.5 to verify

the effectiveness of the proposed control strategy and this

paper ends with the conclusion remarks in Sec. 6.

II. PROBLEM FORMULATION

A. Hypersonic Vehicle Model

The longitudinal model of a generic hypersonic vehicle

under study is a conical vehicle designed by National

Aero-Space Plane Program. At the trimmed conditions

15060ft/s, 110000ft, =0.0315rad, 0rad, =0rad)V h q



  （

, the

open-loop dynamics of the vehicle exhibits statically unstable

short-period mode, lightly damped phugoid mode as well as a

mildly unstable height mode

[12]

. Consequently, cruising flight

would be subject to attitude and velocity divergence that

would require stabilized feedback control. Force and moment

coefficients of the vehicle for different Mach numbers, angle

Adaptive High Order Sliding Mode Controller Design for

Hypersonic Vehicle*

Bailing Tian, Member IEEE, Member AIAA, Wenru Fan

2013 10th IEEE International Conference on Control and Automation (ICCA)

Hangzhou, China, June 12-14, 2013

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