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.