This paper is concerned with the stabilisation problem of an Euler–Bernoulli beam with uncertain parameters and disturbances. To correctly represent the beam's behaviour, the partial differential equations model is utilised for the control design of the beam without missing any high-order mode information. Then the linear matrix inequalities (LMIs) method is applied to the robust adaptive neural network control design to cope with systematic uncertainties and stabilise the beam system with disturbance compensation. Through resolving LMIs, feasible sets of designed control parameters can be effectively obtained without model linearisation. Finally, numerical simulations are done to validate the effectiveness of the proposed control.

本文关注的是具有不确定参数和扰动的 Euler-Bernoulli 梁的镇定问题。为了正确表示光束的行为，偏微分方程模型用于光束的控制设计，而不会遗漏任何高阶模式信息。然后将线性矩阵不等式 (LMI) 方法应用于鲁棒自适应神经网络控制设计，以应对系统不确定性并通过扰动补偿稳定梁系统。通过求解 LMI，无需模型线性化即可有效地获得设计控制参数的可行集。最后，进行数值模拟以验证所提出的控制的有效性。