The paper presents a generalized composite noncertainty-equivalence adaptive control system for the control of a prototypical aeroelastic wing section using a single trailing-edge control surface. The plunge–pitch (two-degree-of-freedom) dynamics of this aeroelastic system include torsional pitch-axis nonlinearity. The open-loop system exhibits limit cycle oscillations beyond a critical free-stream velocity. It is assumed that parameters of the model are not known. The objective is to suppress the oscillatory responses of the system. Based on the immersion and invariance approach, a generalized composite noncertainty-equivalence adaptive (NCEA) control system for regulation of the pitch angle is designed. The control system consists of a control module and a composite parameter identifier—designed independently. The composite integral parameter estimation law is based on (1) the immersion and invariance (I&I) theory, (2) gradient-based adaptation algorithm, and (3) classical certainty-equivalence adaptive (CEA) update rule. Besides the composite integral component, the full parameter estimate also includes a judiciously chosen nonlinear algebraic function. This composite identifier inherits stronger stability properties. Using the Lyapunov analysis, asymptotic suppression of the limit cycle oscillations and the boundedness of system trajectories are established. Interestingly, in the closed-loop system including the composite update rule, there exist two attractive manifolds to which the system’s trajectories converge. Simulation results are presented which show the suppression of the oscillatory plunge displacement and pitch angle responses despite uncertainties in the model parameters. Furthermore, the performance and stability properties of this composite NCEA control system—including the gradient-based adaptation and the update rule of the CEA system—are better than the simple NCEA system.

本文提出了一种通用复合不确定性等价自适应控制系统，该控制系统使用单个后缘控制面控制典型的航空弹性机翼截面。该气动弹性系统的俯仰-俯仰（两自由度）动力学包括扭转俯仰轴非线性。开环系统表现出超过临界自由流速度的极限循环振荡。假定模型的参数未知。目的是抑制系统的振荡响应。基于沉浸和不变性方法，设计了一种用于调节俯仰角的通用复合不确定度自适应（NCEA）控制系统。该控制系统由一个控制模块和一个独立设计的复合参数标识符组成。复合积分参数估计法则基于（1）沉浸和不变性（I＆I）理论，（2）基于梯度的自适应算法和（3）经典确定性等价自适应（CEA）更新规则。除了复合积分分量外，全参数估计还包括明智选择的非线性代数函数。该复合标识符继承了更强的稳定性。使用李雅普诺夫分析，建立了极限环振荡的渐近抑制和系统轨迹的有界性。有趣的是，在包含复合更新规则的闭环系统中，存在两个有吸引力的流形，系统的轨迹收敛于该流形。给出了仿真结果，该仿真结果显示了尽管模型参数存在不确定性，但也抑制了振荡插入位移和俯仰角响应。此外，此复合NCEA控制系统的性能和稳定性（包括基于梯度的自适应和CEA系统的更新规则）比简单的NCEA系统要好。