A Simple modification to the Smith Predictor Structure for dealing with high-order delayed processes considering one unstable pole

The traditional Smith Predictor (SP) is restricted to dealing with stable plants. In this paper, a slight modification of the SP is proposed in order to control unstable plants: systems of any order but with one unstable pole are tackled. In fact, many modifications to the SP can be found in the literature dealing with this kind of system, but none, to our best knowledge, have the simplicity of the structure here proposed. Only one or two gains are added to the traditional SP structure to achieve the stabilization of this kind of unstable system. A simple relation states the necessary and sufficient condition guaranteeing the existence of stabilizing gains, in terms of the location of the unstable pole and the size of the delay term. The range of values for the gains solving the problem is characterized. In addition, the tracking of setpoints and disturbance rejections are analysed. Some numerical examples are presented to illustrate the effectiveness of the proposed strategy, as well as one real-time example.