It is well known that linear time-invariant controllers fail to provide desired robustness margins (e.g. gain margin, phase margin) for plants with non-minimum phase zeros. Attempts have been made in literature to alleviate this problem using high-frequency periodic controllers. But because of high frequency in nature, real-time implementation of these controllers is very challenging. In fact, no practical applications of such controllers for multivariable plants have been reported in literature till date. This article considers a laboratory-based, two-input–two-output, quadruple-tank process with a non-minimum phase zero for real-time implementation of the above periodic controller. To design the controller, first, a minimal pre-compensator is used to decouple the plant in open loop. Then the resulting single-input–single-output units are compensated using periodic controllers. It is shown through simulations and real-time experiments that owing to arbitrary loop-zero placement capability of periodic controllers, the above decoupled periodic control scheme provides much improved robustness against multi-channel output gain variations as compared to its linear time-invariant counterpart. It is also shown that in spite of this improved robustness, the nominal performances such as tracking and disturbance attenuation remain almost the same. A comparison with ${\mathcal{H}}_{\infty }$-linear time-invariant controllers is also carried out to show superiority of the proposed scheme.

众所周知，线性时不变控制器无法为具有非最小相位零点的设备提供所需的鲁棒性裕度（例如增益裕度、相位裕度）。文献中已经尝试使用高频周期控制器来缓解这个问题。但由于本质上是高频，这些控制器的实时实现非常具有挑战性。事实上，迄今为止，文献中还没有报道这种控制器在多变量设备中的实际应用。本文考虑了一个基于实验室的、两输入两输出、具有非最小零相位的四槽过程，用于实时实现上述周期控制器。为了设计控制器，首先，使用最小的预补偿器在开环中去耦设备。然后使用周期性控制器补偿由此产生的单输入单输出单元。通过仿真和实时实验表明，由于周期性控制器的任意回路零放置能力，上述解耦周期性控制方案与其线性时不变对应方案相比，提供了针对多通道输出增益变化的大大提高的鲁棒性。还表明，尽管鲁棒性有所提高，但跟踪和干扰衰减等标称性能几乎保持不变。与 与线性时不变对应方案相比，上述解耦周期控制方案针对多通道输出增益变化提供了大大提高的鲁棒性。还表明，尽管鲁棒性有所提高，但跟踪和干扰衰减等标称性能几乎保持不变。与 与线性时不变对应方案相比，上述解耦周期控制方案针对多通道输出增益变化提供了大大提高的鲁棒性。还表明，尽管鲁棒性有所提高，但跟踪和干扰衰减等标称性能几乎保持不变。与${\mathcal{H}}_{\infty }$还进行了线性时不变控制器以显示所提出方案的优越性。