Practical implementation of gain scheduling strategies with FOPID controllers: A bumpless LPV approach

In this paper we propose a methodology to implement gain scheduling strategies for fractional-order proportional–integral–derivative controllers. In particular, we use a finite-dimensional approximation of the fractional operators and we implement it as a linear parameter varying system. Then, we provide a solution to the initialization problem that emerges when the parameters of the FOPID controller change discontinuously so that the control action is continuous, thereby avoiding any bump. Experimental results show that this method can be used in practice and has industrial relevance.