Gouvêa Josiel Alves, Raptopoulos Luciano Santos Constantin, Pinto Milena Faria, Díaz Elkin Yesid Veslin, Dutra Max Suell, Sousa Lucas Costa de, Batista Victor Manuel Oliveira, Zachi Alessandro Rosa Lopes
Department of Control Systems and Automation Engineering, Federal Center of Technological Education of Rio de Janeiro, Nova Iguaçu 26.041-271, Brazil.
Graduate Program in Electrical Engineering, Federal Center of Technological Education of Rio de Janeiro, Rio de Janeiro 20.271-110, Brazil.
Sensors (Basel). 2023 Jul 22;23(14):6602. doi: 10.3390/s23146602.
This work proposes a mathematical solution for the attitude control problem of an ornithopter wing. An ornithopter is an artificial bird or insect-like aerial vehicle whose flight and lift movements are produced and maintained by flapping wings. The aerodynamical drag forces responsible for the flying movements are generated by the wing attitude and torques applied to its joints. This mechanical system represents a challenging problem because its dynamics consist of MIMO nonlinear equations with couplings in the input variables. For dealing with such a mathematical model, an Active Disturbance Rejection Control-based (ADRC) method is considered. The cited control technique has been studied for almost two decades and its main characteristics are the use of an extended state observer to estimate the nonmeasurable signals of the plant and a state-feedback control law in standard form fed by that observer. However, even today, the application of the basic methodology requires the exact knowledge of the plant's control gain which is difficult to measure in the case of systems with uncertain parameters. In addition, most of the related works apply the ADRC strategy to Single Input Single Output (SISO) plants. For MIMO systems, the control gain is represented by a square matrix of general entries but most of the reported works consider the simplified case of uncoupled inputs, in which a diagonal matrix is assumed. In this paper, an extension of the ADRC SISO strategy for MIMO systems is proposed. By adopting such a control methodology, the resulting closed-loop scheme exhibits some key advantages: (i) it is robust to parametric uncertainties; (ii) it can compensate for external disturbances and unmodeled dynamics; (iii) even for nonlinear plants, mathematical analysis using Laplace's approach can be always used; and (iv) it can deal with system's coupled input variables. A complete mathematical model for the dynamics of the ornithopter wing system is presented. The efficiency of the proposed control is analyzed mathematically, discussed, and illustrated via simulation results of its application in the attitude control of ornithopter wings.
本文提出了一种针对扑翼飞行器机翼姿态控制问题的数学解决方案。扑翼飞行器是一种类似人工鸟类或昆虫的飞行器，其飞行和升力运动通过拍打翅膀产生并维持。负责飞行运动的空气动力阻力由机翼姿态和施加在其关节上的扭矩产生。这个机械系统代表了一个具有挑战性的问题，因为其动力学由输入变量中存在耦合的多输入多输出非线性方程组成。为了处理这样的数学模型，考虑了一种基于自抗扰控制（ADRC）的方法。所引用的控制技术已经研究了近二十年，其主要特点是使用扩展状态观测器来估计被控对象的不可测量信号，以及由该观测器提供的标准形式的状态反馈控制律。然而，即使在今天，基本方法的应用仍需要精确知道被控对象的控制增益，而在参数不确定的系统中这很难测量。此外，大多数相关工作将ADRC策略应用于单输入单输出（SISO）被控对象。对于多输入多输出系统，控制增益由一般元素的方阵表示，但大多数已报道的工作考虑的是输入不耦合的简化情况，即假设为对角矩阵。本文提出了一种将ADRC单输入单输出策略扩展到多输入多输出系统的方法。通过采用这种控制方法所得到的闭环方案具有一些关键优点：（i）对参数不确定性具有鲁棒性；（ii）能够补偿外部干扰和未建模动态；（iii）即使对于非线性被控对象，也总能使用拉普拉斯方法进行数学分析；（iv）能够处理系统的耦合输入变量。给出了扑翼飞行器机翼系统动力学的完整数学模型。通过在扑翼飞行器机翼姿态控制中的应用仿真结果，对所提出控制方法的有效性进行了数学分析、讨论和说明。
