Robust Higher-Order Sliding Mode Finite-Time Control of Aeroelastic Systems

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I N THE past, considerable effort has been made for the analysis of aeroelastic instabilities and development of control systems for the stabilization of aeroelastic systems [1]. The analysis of divergence, flutter, and limit-cycle oscillations (LCOs) of a transonic airfoil configuration [2] and supersonic wing section has been performed [3]. A review of the wide range of physical phenomena associated with unsteady transonic flow is provided by Mabey [4]. A boundary-element method for the prediction of performance of flapping foils with unsteady leading-edge separation has been developed by Pan et al. [5]. Authors have presented robust aeroservoelastic stability analysis using the μ method [6]. Several authors have designed control systems for the flutter suppression of the benchmark active control technology wind-tunnel model constructed at the NASA Langley Research Center [7–9]. Also, at the Texas A&M University, a two-degree-of-freedom experimental apparatus has been constructed for the study of the aeroelastic phenomena [10–13]. For this laboratory model, a variety of control systems have been designed using a single trailing-edge control surface as well as leading- and trailing-edge control surfaces [10,12–14]. A control law based on the state-dependent Riccati equation method has been proposed [15]. A robust global control law using output feedback [16] and a variable structure controller using partial state feedback have been designed [17]. Authors have developed several adaptive control systems for this aeroelastic system with uncertainties [13,18–27]. Control of aeroelastic systems using a neural network has also been considered [20,24]. A model reference output feedback adaptive variable structure control law including relays for this system has been also developed [25]. Recently, a non certainty-equivalent control law and L1 adaptive control systems have been designed for the suppression of LCOs [23,26,27]. The design of robust continuous control systems using parameter adaptation and robustifying signals has been considered [28,29]. An adaptive controller for a minimum-phase airfoil model under unsteady flow has been designed [30]. Researchers have investigated finite-time control of a class of nonlinear systems [31–33]. Also, for a class of uncertain nonlinear multivariable systems, a higher-order sliding-mode control law for the finite-time control has been developed [34], which has a simple structure compared to adaptive systems. In view of its simple structure, it is of interest to design a higher-order sliding-mode finite-time control system for the stabilization of aeroelastic systems. (A comparison of this controller with adaptive controllers designed for aeroelastic systems is provided in Sec. III.) The contribution of this technical Note lies in the design of a second-order sliding-mode control system for the finite-time stabilization of an aeroelastic system, using a leading- and a trailing edge control surface. The model includes parametric uncertainties as well as external disturbance force and moment. A robust control system is designed for the tracking of reference plunge and pitch angle trajectory. The control law includes a nominal finite-time stabilizing continuous control signal designed for the model without uncertainties and a discontinuous control signal for nullifying the effect of uncertain functions in the model. In the closed-loop system, finite-time control of the complete state vector of the aeroelastic model to the origin is accomplished. Simulation results are presented that show that the controller suppresses the oscillatory motion of the system, despite parameter uncertainties and gust loads.


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