Fractional Order (FO) Two Degree of Freedom (2-DOF) control of Linear Time Invariant (LTI) plants

The dynamics of Fractional Order (FO) System have recently attracted substantial attention in the field of control. Taking note of this, the Fractional Order (FO) controllers provides additional flexibility in the design by virtue of its non-integer orders. However, all the available control schemes in this domain are mostly featured in 1-DOF (Degree of Freedom) formation which compromises between response and loop goals. Differently, a 2-DOF (Degree of Freedom) topology allows one to shape the transient response ensuring at the same time satisfactory loop margins. It is thus anticipated here that the integration of 2-DOF (Degree of Freedom) control scheme with FO Compensator may accelerate successful attainment of system response and loop robustness. Hence, this paper addresses the development of 2-DOF (Degree of Freedom) FO control system design methodology for integer as well as non-integer order plants. The additional degree of freedom and the non-integer order of the controller together ensure desired output response as well as adequate loop robustness. Novel design procedures for the 2-DOF (Degree of Freedom) control scheme are presented in meticulous manner depending upon the nature of the plant under consideration. A unique approach for FO pre-filter is presented depending upon the nature of the loop compensators in case of non-commensurate order plants. It is observed here that the proposed 2-DOF (Degree of Freedom) scheme bestows an added DOF in addition to the auxiliary design parameter by the virtue of its non-integer orders. The closed loop system response manifests that the proposed approach show cases exclusively surpassing system response and robustness compared to its 1-DOF (Degree of Freedom) as well as integer order 2-DOF (Degree of Freedom) counterparts. The potency of the method put forward is established with MATLAB simulation as well as real-time experimentation. The proposed control schemes are implemented to two highly non-linear real time systems of TRMS system and Cart-Inverted Pendulum System. The experimental outcomes are demonstrated to endorse the benefits of the control scheme advocated.