Robust proportional-integral-derivative design for processes with interval parametric uncertainty

A novel method for designing proportional-integral-derivative controllers for processes containing interval parametric uncertainty is presented. The control design problem is posed as an optimisation problem where performance is maximised subject to some stability margins over a family of transfer functions. The resulting problem falls within the category of robust optimisation (RO) problems. The authors derive conditions that allow to obtain a solution to the RO problem by solving a nominal optimisation problem (in some cases at the expense of introducing some conservatism). This simplification is made by introducing an instrumental fractional-order plant that characterises the uncertain (interval) process and stating certain conditions over the fractional-order loop transfer function. The design approach is also applied to a Smith-predictor-based dead-time compensator. Some examples are given throughout this study to illustrate the proposed design method.