In real-world applications, it is often desired that the design of a closed-loop system must attain not only high performance but also robustness. This paper presents a novel robustness-based formulation for control for discrete time minimum and non-minimum phase systems using the Virtual Reference Feedback Tuning (VRFT) framework. The proposed idea is to design robust lower and higher order Proportional Integral and Derivative (PID) controller using Maximum Sensitivity (${\mathrm{M}}_{\mathrm{s}}$) based closed-loop reference model by minimization of the VRFT objective function (J${}_{\mathrm{VR}}$) The efficacy of the approach is verified on various systems in simulation and also demonstrated on the Temperature Control Process and Level Control Process experimental setups. The proposed VRFT approach provides improved performance and robustness for set point tracking and disturbance rejection. Also, the proposed approach ensures stability and specific robustness of the closed-loop system. Further, the fragility of the controller is investigated for perturbations in the controller parameters.

在实际应用中，通常希望闭环系统的设计不仅要达到高性能，还要达到鲁棒性。本文提出了一种新的基于鲁棒性的公式，用于使用虚拟参考反馈调整 (VRFT) 框架控制离散时间最小和非最小相位系统。所提出的想法是使用最大灵敏度设计稳健的低阶和高阶比例积分和微分 (PID) 控制器 (${\mathrm{米}}_{\mathrm{秒}}$) 基于闭环参考模型的最小化 VRFT 目标函数 (J${}_{\mathrm{虚拟现实}}$) 该方法的有效性在各种模拟系统上得到验证，也在温度控制过程和液位控制过程实验设置上得到证明。所提出的 VRFT 方法为设定点跟踪和干扰抑制提供了改进的性能和鲁棒性。此外，所提出的方法确保了闭环系统的稳定性和特定的鲁棒性。此外，还针对控制器参数的扰动研究了控制器的脆弱性。