A Model-Free Design of the Youla Parameter on the Generalized Internal Model Control Structure with Stability Constraint

Abstract

In the design of the control system, the plant perturbations and the plant uncertainties could cause the performance degradation and/or destabilization of the control system. The H∞ control synthesis and the μ synthesis are well known as the suitable controller syntheses for the plant with the large plant perturbations and/or the plant uncertainties (Zhou & Doyle, 1998), and many successful applications are also reported in various fields. However, these controller syntheses provide the controller robustly stabilizing the closed-loop system for the worst-case and overestimated disturbances and uncertainties at the expense of the nominal control performance. It means that there exists a trade-off between the nominal control performance and the robustness in the design of the control system. Meanwhile from the view point of the control architecture, the Generalized Internal Model Control (GIMC) structure is proposed by Zhou using Youla parameterization (Vidyasagar, 1985) to resolve the above-mentioned trade-off (Campos-Delgado & Zhou, 2003; Zhou & Ren, 2001). The GIMC structure is interpreted as an extension of the Internal Model Control (IMC) (Morari & Zafiriou, 1997), which is only applicable to stable plants, to unstable plants by introducing coprime factorization. The GIMC structure consists of a conditional feedback structure and an outer-loop controller. The conditional feedback structure can detect model uncertainties and any disturbances, and they are compensated through the Youla parameter. It means that the robustness of the control system in the GIMC structure is specified by the Youla parameter. On the other hand, in case where there exist no plant uncertainties and no disturbances, the conditional feedback structure would detect nothing, and the feedback control systemwould be governed only by the outer-loop controller. Since the nominal control performance is independent of the Youla parameter, the outer-loop controller can be designed according to various controller design techniques, and the trade-off between the nominal control performance and the robustness is resolved. For the design of the Youla parameter, we proposed the design method using the dual Youla parameter which represents the plant perturbation and/or the plant uncertainties (Matsumoto et al., 1993; Yubai et al., 2007). The design procedure is as follows: The dual Youla parameter is identified by the Hansen scheme (Hansen et al., 1989) using appropriate identification techniques, and the Youla parameter is designed based on the robust controller A Model-Free Design of the Youla Parameter on the Generalized Internal Model Control Structure with Stability Constraint 17