Zhu Quanmin, Zhang Jianhua, Zhang Weicun
School of Engineering, University of the West of England, Coldharbour Lane, Bristol BS16 1QY, UK.
School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266525, China.
Entropy (Basel). 2023 Jul 17;25(7):1076. doi: 10.3390/e25071076.
This study presents a general framework for the control of unknown dynamic systems with unknown input delay. A concise output feedback control system is structured with tuning stabilization/dynamic response by an output feedback low gain, removing steady state error against step reference with a feedforward gain. A series of stability analyses are presented for the designed control systems, (1) a gain/phase margin theorem is proposed for stability analysis by regulating the feedback gain, and (2) a stability theorem based on rational function approximation of the time delay is presented for dealing with the transcendental polynomial characteristic equations, which is equivalent to the analysis from the algebraic polynomial characteristic equation. Both approaches give coherent results for stability analysis by regulating the feedback gain. The approaches are applicable to nonlinear systems, which are linearizable in the neighborhood of the operating points. The low complexity of the controllers does not require hard analytical derivation/numerical calculations to produce an acceptable control performance for the considered systems. Several representative simulation case studies provide demonstrations of computational experiments against those analytically derived and guidance for potential applications.
本研究提出了一种用于控制具有未知输入延迟的未知动态系统的通用框架。通过输出反馈低增益来调整稳定性/动态响应，并利用前馈增益消除针对阶跃参考的稳态误差，从而构建了一个简洁的输出反馈控制系统。针对所设计的控制系统进行了一系列稳定性分析：（1）提出了增益/相位裕度定理，用于通过调节反馈增益进行稳定性分析；（2）提出了基于时延有理函数逼近的稳定性定理，用于处理超越多项式特征方程，这等同于从代数多项式特征方程进行的分析。通过调节反馈增益，这两种方法在稳定性分析中给出了一致的结果。这些方法适用于在工作点邻域内可线性化的非线性系统。控制器的低复杂度不需要进行复杂的解析推导/数值计算就能为所考虑的系统产生可接受的控制性能。几个具有代表性的仿真案例研究展示了针对那些解析推导结果的计算实验，并为潜在应用提供了指导。
