Adaptive quantized sliding mode attitude tracking control for flexible spacecraft with input dead-zone via Takagi-Sugeno fuzzy approach

Highlights

• Flexible spacecraft Takagi-Sugeno fuzzy attitude control system is studied.

• The signal quantization is considered.

• The external disturbance and actuator input dead-zone are considered.

• A quantized adaptive fuzzy integral sliding mode control strategy is presented.

Abstract

This paper addresses the sliding mode control design problem for the flexible spacecraft attitude tracking control system with Takagi-Sugeno fuzzy model based method. In this design, the external disturbance and actuator input dead-zone are considered simultaneously, and the signals between sensors and controller are quantized before transmission over digital communication channels. A quantized adaptive integral sliding mode control law is proposed to ensure that the sliding motion is globally asymptotically stable, and the effects of unknown external disturbances, actuator nonlinearity and quantization errors are compensated via the online adaptive mechanism simultaneously. Moreover, under the proposed digital control law the finite-time reachability of the designed sliding surface can be guaranteed strictly. Finally, simulation results are presented to illustrate the feasibility and effectiveness of the developed quantized spacecraft attitude control method.

Introduction

In 1957, the first manmade spacecraft called “Sputnik” was launched [1] and the space exploration of human beings started. Since then, more and more studies have been devoted to the aerospace field [2], [3], [4], [5]. As a vital part of the successful completion of related tasks, spacecraft attitude control has attracted numerous attention from researchers [6], [7], [8], [9]. In particular, to assist communication and saving energy, recently elastic appendages such as antenna and solar arrays which possesses natural elastic characteristics are gradually attached to the main body of a spacecraft [10], [11], [12]. Since there exists strong coupling between the main body and elastic appendages, the dynamics of this kind of flexible spacecraft always contain high nonlinearity which makes it be more difficult to achieve a high-accuracy attitude tracking control performance [13].

Over the past few years, much research effort has been paid to the nonlinear attitude control problems for single or multiple spacecrafts. To mention a few, an observer-based control strategy is proposed in [14] for the flexible spacecraft attitude control system; with consideration of signal quantization, a digital adaptive fuzzy backstepping control method is introduced in [15]; In [16], the authors considered the event-triggered attitude consensus of multiple rigid-body systems via the gnomonic projection and Riemannian gradient descent approach, and two novel event-triggered attitude consensus protocols are designed under the absolute attitude and relative attitude measurement, respectively. It is worth pointing out that, among these existing design methods, the fuzzy logic method has been recognized as one of the most popular ways to cope with nonlinear problems. Its applications ranging from Petri net-based fuzzy control [17], predictive fuzzy control [18] to fuzzy-based model-free control [19], fuzzy-based sliding mode control [20], etc. In particular, the T-S fuzzy model based technique [21], which can approximate to the nonlinear systems with high accuracy, has been introduced into the aerospace field very recently for flexible spacecraft control [22], [23], [24], [25]. With this scheme, the difficulty and the complexity for the control synthesis work can be largely reduced [26], [27], [28], [29].

In practical space tasks, nonlinearity phenomenon such as saturation, degradation, and dead-zone does always occur in spacecraft control systems including both attitude actuators (for instance, reaction wheels) and orbit actuators (for instance, thrusters), which will inevitably weaken the capability of the spacecraft to perform complex space mission [31], [30], [32], [33]. In particular, the effect of the actuator dead-zone seriously degrade spacecraft control systems performance, and thus the constraint of actuator dead-zone should be taken into account in the design of attitude control system synthesis. In the past few years, a few researchers have devoted their efforts to this study, and fruitful design results have been available in the existing literature, see, for instance [34], [35], [36], etc. However, how to cope with and compensate the actuator dead-zone behaviour still refers to a significant problem in achieving satisfied performance in spacecraft attitude control system design.

On the other hand, with the rapid development of wireless micro satellites such as CubeSats and modular satellites [37], [38], [39], [40], communication networks have achieved comprehensive application in practical spacecraft systems. Since one characterization in communication networks is that the data in feedback control loops is transmitted via a signal quantization mechanism, recently some novel results on quantized feedback stabilization for single and multiple spacecraft formation have been reported [41], [42], [43]. It should be pointed out that, however, conventional spacecraft attitude control techniques cannot be directly applied to networked spacecraft setting, since the presupposition that system measurements and input data is executed with infinite precision cannot be ensured in the wireless communication environment. In addition, if the effects of high nonlinearity dynamics of flexible spacecraft, signal quantization and actuator dead-zone are taken into account simultaneously, the corresponding control system synthesis work will be more difficult and challenging, since the proposed control law is required to be constructed to tolerate and compensate these unexpected phenomenon in a unified framework. As a result, new effective design methods are desirable to be developed to solve this difficult research issue which emerges in modern advanced spacecraft application, which motivates our current investigation of this paper.

In this paper, the digital attitude tracking control problem is investigated for complex flexible spacecraft with actuator dead-zone over wireless digital communication channels. First, the T-S fuzzy model based methodology is employed to approximate the unknown nonlinear dynamics of flexible spacecraft. Second, with the simultaneous consideration of the external disturbance, actuator input dead-zone and state quantization, a quantized integral-type sliding mode control strategy is developed for the attitude control systems where adaptive feedback gains are set for compensation objective. Under the designed digital adaptive sliding mode control law, the sliding motion can be guaranteed to be globally asymptotically stable, and the state trajectory can arrive on the proposed sliding surface in finite time strictly. Finally, a numerical simulation is given to demonstrate the effectiveness of the presented digital attitude control approach of flexible spacecraft.

The paper is organized as follows. In Section II, the T-S fuzzy-based flexible spacecraft attitude tracking control model and the dynamic logarithmic quantizer are introduced. A fuzzy integral sliding surface and a digital adaptive fuzzy integral sliding mode controller are designed in Section III. In Section IV, simulation results for the closed-loop T-S fuzzy flexible spacecraft attitude tracking control system studied in Sections II-III and its comparison with other control strategies are presented. Section VI concludes the paper.

Following notations will be used throughout the paper. ${\mathbb{R}}^{m\times n}$ stands for the $m\times n$-dimensional Euclidean space; $I_n$ denotes an identity matrix of order $n\text{;}\Vert \ast \Vert$ represents the Euclidean 2-norm of a vector $\ast$; for a given vector or matrix $\mathrm{\Gamma },{\mathrm{\Gamma }}^{-1}$ refers to the inverse matrix of $\mathrm{\Gamma }$, and ${\mathrm{\Gamma }}^T$ represents the transpose matrix of $\mathrm{\Gamma }\text{;}\mathrm{\Gamma }>0$ (or $\mathrm{\Gamma }<0$) implies that $\mathrm{\Gamma }$ is positive (or negative) definite.