This paper proposes a convex-optimization-based relatively optimal controller (ROC) for the attitude regulation of 3 degree of freedom (DOF) tandem helicopter utilizing feedback linearization (FBL). The constant velocity in the pseudo-active axis achieved by regulating two active axes results in the motion of the helicopter in a circular path at a specified altitude. The FBL helps in transforming the system model into two decoupled subsystems in Brunovsky’s canonical form to reduce the computational complexities. Minimum control effort and constraint satisfaction are guaranteed by ROC while regulating the attitude of the 3-DOF tandem helicopter from a nominal initial condition. The Lyapunov stability theorem is employed for illustrating the stability of the closed-loop system. The robustness analysis gives a measure of perturbation that the designed controller can accommodate. Simulation results demonstrate the superiority over an FBL-based linear quadratic regulator controller. The efficacy of the proposed strategy is substantiated by experimental results.

本文提出了一种基于凸优化的相对最优控制器 (ROC)，用于利用反馈线性化 (FBL) 进行 3 自由度 (DOF) 串联直升机的姿态调节。通过调节两个主动轴实现的伪主动轴上的恒定速度导致直升机在指定高度沿圆形路径运动。FBL 有助于将系统模型转换为布鲁诺夫斯基规范形式的两个解耦子系统，以降低计算复杂性。ROC 在从标称初始条件调节 3 自由度串联直升机的姿态的同时，保证了最小的控制努力和约束满足。李雅普诺夫稳定性定理用于说明闭环系统的稳定性。稳健性分析给出了设计的控制器可以容纳的扰动量度。仿真结果表明优于基于 FBL 的线性二次调节器控制器。实验结果证实了所提出策略的有效性。