A digital control approach for unstable-first-order- plus-dead-time systems with P and PI controllers

Many dynamical systems can be modeled by unstable-first-order-plus-dead-time (UFOPDT) transfer functions. However, analysis and synthesis of UFOPDT systems are much more challenging due to the general difficulties of infinite dimensionality and the instability of the plant. Considering the control of such systems, explicit tuning formulae were derived for proportional (P) and proportional-integral (PI) controllers, based on the digitized open loop systems. Stability range was also discussed for the feedback systems with delays. Compared with existing results, the presented method significantly improved the accuracy and sufficiency, and simplified the tuning process. Numerical example about an isothermal chemical reactor control problem was given to illustrate this algorithm, and several relevant methods were also compared.