适应性快速终端滑模控制：不确定系统与输入非线性的解决方案

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"Adaptive Fast Terminal Sliding Mode Control for Uncertain Systems with Input Nonlinearity - 研究论文" 本文探讨了一种针对具有死区和饱和输入非线性的单输入单输出（SISO）不确定系统的一阶终端滑模（TSM）控制策略。研究的核心是提出一种新的自适应TSM控制律，利用积分快速TSM来实现系统不确定性和输入非线性的抑制。通过Lyapunov稳定性理论确保全局达到滑模条件，这意味着系统能够稳定地从任意初始状态到达滑模面。传统的滑模控制在处理不确定性时表现出了强大的鲁棒性，但可能会遇到收敛速度慢、存在奇异性等问题。新提出的控制律克服了这些缺点，具备比线性滑模方法更快的收敛速度，并且避免了TSM的奇异性问题，提高了系统的动态性能。此外，该控制策略不仅限于SISO系统，还进一步扩展到了多输入多输出（MIMO）系统的跟踪控制，如航天器动力学模型。这样的扩展对于解决复杂系统的控制问题具有重要意义，特别是在面对系统参数变化和外部扰动时。关键词：自适应控制，终端滑模控制，输入非线性 1. 引言滑模控制（SMC）作为一种鲁棒控制技术，因其对系统不确定性具有良好的鲁棒性而受到广泛关注。然而，常规的滑模控制在处理具有输入非线性和不确定性的问题时，可能存在收敛速度慢以及在滑模阶段可能出现的不稳定现象。因此，设计一个能快速收敛并有效处理这些挑战的控制策略是控制理论与工程应用中的关键问题。 2. 方法论本文的新颖之处在于设计了一个自适应的终端滑模控制器，通过集成快速滑模机制，确保了系统能够快速地从任何初始状态过渡到滑模表面。同时，控制器的自适应特性使得它可以自动调整参数以适应系统的不确定性。 3. 控制器设计与分析控制律的设计基于Lyapunov稳定性理论，确保了全局稳定性，即无论系统初始状态如何，都能保证系统最终进入并保持在滑模面上。这一设计有效地解决了传统滑模控制可能导致的不稳定和奇异性问题。 4. 扩展至MIMO系统为了证明新方法的通用性，研究将其应用到航天器动力学模型的跟踪控制问题中，展示了在多变量系统中同样具有高效鲁棒控制的能力。 5. 模拟结果与讨论通过仿真结果，证实了所提出的控制方法在抑制不确定性和输入非线性方面具有显著效果，证明了其在实际应用中的有效性。 6. 结论本文提出的新自适应终端滑模控制策略成功地解决了不确定系统中输入非线性的问题，实现了更快的收敛速度，并且避免了奇异性。这种方法在SISO和MIMO系统中的应用表明，它具有广泛的应用前景，特别是在需要高精度和强鲁棒性的控制场景中。这个研究为未来在更复杂的系统中实现高效、鲁棒的滑模控制提供了新的思路和方法。

Adaptive fast terminal SMC for input nonlinearity

Journal of Advanced Computational Intelligence and Intelligent Informatics Vol.0 No.0, 200x

Abstract: This study investigates the terminal sliding

mode (TSM) control for a class of first-order

uncertain systems with dead-zone and saturation.

First, a new adaptive TSM control law was proposed

for the single-input and single-output (SISO) systems

by employing an integral fast TSM. It achieves

rejection for both system uncertainty and input

nonlinearity. The global reaching condition of the

sliding mode is guaranteed by the Lyapunov stability

theory. The new control law possesses faster

convergence than the linear sliding mode method,

and the singularity problem of TSM is avoided. Then,

the control law was extended for tracking control of a

dynamic model of spacecraft which was a multi-input

and multi-output (MIMO) system. Finally, the

simulation results confirmed the effectiveness of the

proposed control method.

Keywords: adaptive control, terminal sliding mode

control, input nonlinearity

1. INTRODUCTION

As a robust control technique, the sliding mode control

(SMC) has been developed for a wide range of linear and

nonlinear systems [1-3]. The early studies of SMC

concentrated on the linear sliding mode (LSM) which

featured asymptotical convergence. In recent years, the

terminal sliding mode (TSM) control has received much

attention. Its major advantage is the finite-time

convergence. The TSM control has been used in many

applications, such as robots [4], spacecraft [5], and

DC-DC buck converters [6-7].

It is well known that the TSM has faster convergence

than the LSM when the system states are near the origin.

However, the convergence of TSM is slower if the

system states are far away from the origin. So, fast TSM

(FTSM) was proposed to enhance its convergence by Yu

et al. in [8]. The other drawback of TSM is singularity

problem. As a negative fractional power item arises in

the derivative of TSM, it may lead to an infinite large

control signal. Due to the limitation of practical

implementations, this is hard to be accepted. Moreover,

this may deteriorate the system stability or damage the

devices. Considering this problem, Feng, Yu, and Liu et

al. contributed to propose new forms of TSM known as

nonsingular TSM (NTSM) in [9-11]. Although the

singularity is avoided, a stagnation problem of sliding

mode arises. It means that the derivative of Lyapunov

function for the sliding mode may remain zero before the

Lyapunov function converges to zero. If this occurs, the

motion of sliding mode stagnates at some nonzero points

in the reaching phase. As a result, the system trajectory

cannot converge to the origin or the reference signal, and

the control objective will not be achieved. Note that, it is

difficult to prove that this stagnation problem does not

occur in the case that the NTSM control is cooperated

with the adaptive technique. Therefore, the adaptive

technique was combined with the TSM and FTSM

controllers in [12-14]. Thus, the control singularity

problem still existed.

Most of the TSM control research focused on the

second-order systems. For higher order systems,

Mobayen and Wu et al. studied on the recursive TSM

control which was applied to non-holonomic systems

[15,16] and hypersonic flight vehicle [17,18]. Being

different from the conventional TSM control designed

for matched uncertainty, Yang et al. proposed a novel

NTSM control approach for mismatched disturbance in

[19]. The disturbance rejection was achieved by a new

sliding manifold with disturbance observer technique.

Besides the model uncertainties and disturbances, the

input nonlinearity also makes negative effects on the

system stability and control performance. In practice, the

common input nonlinearity includes dead-zone,

saturation, and sector nonlinearity. For the sector

nonlinearity, Hsu proposed a special LSM controller

form in [20]. With this controller form, a useful lemma

was introduced to transform the irreversible nonlinear

input function to some available control parameters.

Furthermore, dead-zone was considered in [21]. With

Hsu’s method, TSM control was developed for sector

nonlinearity by Yang and Aghababa et al. in [22-24]. For

the adaptive NTSM control in [22,23], the switching gain

was directly adjusted by adaptive technique. However, it

is difficult to prove that the stagnation problem does not

occur. So the switching gain was changed to constant

gain in the extreme case that the stagnation may occur.

In [25], Hu et al. proposed a LSM controller for

systems subjected to input saturation using Hsu’s method.

The effect of input saturation was estimated by adaptive

technique. Moreover, Chen et al. designed a TSM

controller for uncertain systems with unknown

Linjie Xin

, Qinglin Wang

, Yuan Li

, and Jinhua She

School of Automation, Beijing Institute of Technology, Zhongguancun Street, Haidian District, Beijing, 100081 China

E-mail: xinlinjie08@163.com; wangql@bit.edu.cn; liyuan@bit.edu.cn ()

School of Engineering, Tokyo University of Technology, 1404-1 Katakura, Hachioji, Tokyo, 192-0982 Japan

E-mail: she@stf.teu.ac.jp

Adaptive fast terminal sliding mode control for a class

of uncertain systems with input nonlinearity

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