$L_1$ Adaptive Fractional Control Optimized by Genetic Algorithms with Application to Polyarticulated Robotic Systems

Abstract

Recently, an adaptive control approach has been proposed. This approach, named L 1 adaptive control, involves the insertion of a low-pass filter at the input of the Model Reference Adaptive Control (MRAC). This controller has been designed to overcome several limitations of classical adaptive controllers such as (i) the initialization of estimated parameters, (ii) the stability problems with high adaptation gains, and (iii) the appropriate parameter excitation. In this paper, a new design of the filter is presented, used for L 1 adaptive control, for which the desired performances are guaranteed (appropriate values of the control during start-up, a high filtering of noises, a reduced time lag, and a reduced energy consumption). Parameters of the new proposed filter have been optimised by genetic algorithms. The proposed L 1 adaptive fractional control is applied to a polyarticulated robotic system. Simulation results show the efficiency of the proposed control approach with respect to the classical L 1 adaptive control in the nominal case and in the presence of a multiplicative noise.

A Robust Fuzzy Fractional Order PID Design Based On Multi-Objective Optimization For Rehabilitation Device Control

“…The variable masses of the thigh and the shank of the kid's lower limb, are presented in Table I depending on the age. The mean values of the masses are taken at seven years old and the others are calculated with analogy [90]. The fuzzy logic rules define the relationship between the input variables (the age of the patient) and the output variables (the adequate torque generated for the robot).…”

Adaptive Fractional‐Order Super‐Twisting Sliding Mode Controller for Lower Limb Rehabilitation Exoskeleton in Constraint Circumstances Based on the Grey Wolf Optimization Algorithm

“…In the last three decades, fractional-order (FO) calculus (which is a process of developing a general form of integerorder integration and diferentiation to noninteger-order one) has become an important issue adopted by mathematicians, engineers, and scientists [27,28]. Tanks to the benefts of using a fractional calculus represented by providing more fexibility for improving the control performance, adding an extra degree of freedom to the controller's structure, diferent FO controllers were formulated to enhance the control performance of nonlinear systems, such as fractional PID controllers [29], FO neural network controllers [30], and FO adaptive controllers [31,32].…”

“…Remark 2. Te diference between the structures of the three controllers developed above can be explained here: for the frst controller referred to as FSTSM and expressed in ( 29)- (31), the values of upper bound constants b 0 , b 1 , and b 2 are assumed to be known in advance and the tuning of controller parameters Λ 1 , Λ 2 , μ, k 1 , and k 2 can be found by the user using the trial-and-error strategy. In the case of the second controller referred to as OFSTSM and illustrated in (44), the controller parameters have been replaced by Λ 1 ′ , Λ 2 ′ , μ ′ , k 1 ′ , and k 2 ′ which can been obtained using GWO.…”