ABSTRACT
The tune up of fractional order (FO)-PIλDµ controllers is largely advocated in available literature which mostly requires evolutionary optimization techniques or solution of complex non-linear equations thereby leading to lack of practical solutions in terms of selecting the controller parameters. It may be quite feasible if one can consider PID control in the form of cascaded PI-PD control with which the task of attainment of the control objectives can be accomplished methodically. In extension to this, studies related to FO PIλ-PDµ controller are not too exhaustive. Generally, graphical methods are adopted to compute the controller parameters. There is still paucity of comprehensive design algorithms for these controllers to which end this work comes up with a novel and simple specification driven design methodology of the cascaded structures of FO PIλ-PDµ and [PI]λ-[PD]µ controllers following the classical control theory Keeping away from the complex and implicit design strategies they assist with an exact and unique solution to design these FO controllers in frequency domain with satisfactory dynamic performance in time domain which may not be possible with the FO-PIλDµ controllers. Illustrative examples and experimental validations aid to substantiate the reliability of the proposed method.
ABSTRACT
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.
ABSTRACT
This work proposes a novel design method for generalized order lead/lag compensators. With respect to the traditional lead/lag compensator, it introduces a new parameter, ß, which is a non-integer number. A new design method of the compensator is introduced in order to quantify its design parameters. Compared to its integer order counterpart, the generalized order lead compensator facilitates with the unique solution of desired design specifications with maximum phase at the desired gain cross-over frequency to achieve reshaping of the loop frequency domain characteristics. On the other hand, generalized order lag compensator is designed so as to allow minimum phase lag at the new gain crossover frequency. Examples with simulation and real-time results are presented to validate the efficacy of the proposed approach.
