Robust fractional order controller for irrigation main canal pools with time-varying dynamical parameters

Abstract

A new method is proposed with which to design a class of robust fractional order controllers – which we denote as FPI controllers since they can be regarded as a generalization of standard PI controllers – for the effective control of water distribution in irrigation main canal pools characterized by time-varying dynamical parameters. The closed loop behavior of the nominal plant is defined by using frequency specifications, which are combined with an optimization procedure that minimizes the IAE ( Integral of Absolute Error) – a cost related to the closed loop time response specifications – in the whole range of plant parameter variations. Interest in such robust fractional order controllers is justified by the fact that dynamical parameters of irrigation main canal pools may change drastically according to their operational regimes. Equivalent FPI, PI and PID controllers – in the sense of their exhibiting the same closed loop dynamics for the nominal plant specifications – were simulated for several working conditions, and their behaviors were compared. Additional issues, such as noise rejection or robustness to unmodelled high frequency dynamics have also been considered.