PID tracking control design for electrical DC motors with experimental validation H2 norm

Tracking control for electrical DC motors refers to the use of control systems to ensure that the motor's output, in terms of speed and position, accurately follows a desired trajectory or command over time. The present paper studies the H2 tracking control problem of a class of nonlinear systems modelled by DC nonlinear models. In contrast to other approaches in the literature, firstly, this paper considers the H2 performance constraints in a unified way to solve the tracking control problem for the speed of DC nonlinear models and motor position. Secondly, it provides an inequality covering the well–known H2 rational matrix, which is a recently proposed state–space representation of H2. Thirdly, the authors also studied the performance of an error system based on the Lyapunov–Krasovskii functional used in this paper, for stability. The control parameters are obtained through the solution of each of the presented LMIs. At the end of this paper, it is also demonstrated that nonlinear controllers with other schemas like PID controller are suitable for almost all simulated and practical applications.

直流电机（DC motor）跟踪控制，指通过控制系统确保电机的转速与位置输出能够随时间精确跟踪期望轨迹或指令。本文针对一类基于直流非线性模型建模的非线性系统，研究其H₂跟踪控制问题。与现有文献中的其他方法不同，本文首先以统一方式处理H₂性能约束，以求解直流非线性模型的转速与电机位置跟踪控制问题；其次，本文给出了一类覆盖经典H₂有理矩阵的不等式，该有理矩阵是近期提出的H₂状态空间表示形式；第三，本文基于所采用的李雅普诺夫-克拉索夫斯基泛函（Lyapunov-Krasovskii functional），对误差系统的稳定性性能展开研究。控制参数可通过求解本文所提出的各线性矩阵不等式（LMIs）得到。最后，本文还验证了诸如PID控制器这类其他架构的非线性控制器，几乎可适用于所有仿真与实际应用场景。