Single-variable Systems

The internal model control (IMC) is a powerful framework for control system design and implementation (Morari and Zafiriou, 1989), and it has sound theoretical foundation. Its stability analysis is extremely easy to carry out and the design trade-off between performance and robustness is clearly understood. It has attracted the attention of industrial users because there is only one user-defined tuning parameter, which is directly related to the closed-loop time constant or equivalently, the closed-loop bandwidth. On the other hand, the vast majority of controllers being used in industry are of the PID type due to its simplicity and popularity (Astrom and Hagglund, 1995). Recently, great efforts have been made to develop PID tuning strategies for more general processes (Barnes et al., 1993; Sung and Lee, 1996; Sung et al., 1996; Datta et al., 2000). Each method was derived for its particular optimization objectives and plant model assumptions, and therefore performs well only for its own class. It is common that practising control engineers may not be certain which tuning method should be chosen to provide good control in a given process.It would hence be desirable to develop a design method that works universally with high performance for general stable linear processes, and is capable of producing a high-order controller when the PID controller is no longer adequate.