Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time

Abstract

Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes.

Design of two-layered fractional order fuzzy logic controllers applied to robotic manipulator with variable payload

“…A comparative study for the different design structures of the fractional order fuzzy PID (FOFPID) controller for the oscillatory fractional order systems with dead ti""me. The performance of different controllers were obtained for the set-point tracking, control effort and disturbance rejection was also investigated [17]. Sharma et al presented the FOFPID controller for the two-link planar robotic manipulator for the trajectory tracking task, and found it to be superior to other conventional controllers for the trajectory tracking, disturbance rejection, parameter variations and noise suppression [18].…”

A Hybrid Fuzzy Logic FOPID Position Controller for DC Motor Driving Tracking Systems System

“…These equations are plugged by substantial requirements for computation and the theory underlying their solution is incomplete. The dynamic equations of the telescope are given by Equations (1) and (2) [1] and - [14].…”

“…The extension of differentiation and integration order from integer to non-integer numbers provides a more flexible tuning strategy and therefore an easier achieving of control requirements with respect to classical controllers. The fraction order controller form is given by the following equation [14][15]:…”

“…And KP, KI, and KD are the initial values of the conventional PID. In this paper, the fuzzy logic controller is used for PID parameter adaptation and is different than that used in [14] which use the fuzzy controller like PD controller. Figure 6.…”

Stochastic Resonance Control by Coupling Two Fractional Bistable Systems

“…In recent years, fractional calculus are widely used in fluid mechanics, image processing, seismic analysis, fractional PID controllers [5][6][7][8], compared to the integer order, it has global relevance characteristic, and can well describe the history-dependent system functions process. For fractional order system fewer parameters are required but can be obtained very good results.…”