BALANCED MODEL ORDER REDUCTION FOR LINEAR DYNAMIC SYSTEMS

Abstract

Fractional calculus is widely regarded as the calculus of the 21st century. It generalises the order of differential and integral operators to non-integer orders. Model order reduction and controller design are an integral part of systems and control engineering. This thesis deals with the formulation of modified balanced truncation approach and its application in the design of a fractional order two degree of freedom internal model controller (FO-TDF-IMC). A generalized FO-TDF-IMC technique is mathematically formulated in this thesis, in which the set-point tracking controller is an integer order and the disturbance rejection controller is of fractional order type. Further, the fractional order TDF-IMC controller is converted into classical feedback form, where the controller is expressed as PID controller in cascade with fractional order low pass filter. To validate the efficacy of the proposed FO-TDF-IMC scheme, an example of a boiler system is taken. An extensive comparative analysis is undertaken with existing internal model control based techniques in literature such as one and two degree of freedom integer order internal model control technique. Further, the robustness of the proposed scheme is validated via introduction of input, output step disturbance and random disturbance respectively. The performance of the proposed approach is also scrutinized with respect to the key performance indices. The simulation results are a testimony to the effectiveness and superiority of the proposed technique.