Adaptive fractional-order control of electrical flexible-joint robots: Theory and experiment

Abstract

Real-time fractional-order control of electrically driven flexible-joint robots has been addressed in this article. An important contribution of this article is that the control law is designed based on the Fourier series that eliminates the need for computation of regressor matrix. Moreover, the nonlinear effects of actuator saturation are considered in the control law. The lumped uncertainty can be approximated using Fourier series with unknown coefficients. Then, the unknown coefficients are estimated using the adaptation law obtained in the stability analysis. The overall closed-loop system is proven to be robust and bounded-input bounded-output stable. In addition, it has been shown that the joint-position errors are uniformly bounded based on Lyapunov’s stability concept. The satisfactory performance of the proposed control scheme is verified by experimental results. To highlight the superiority of the proposed method, experimental results of two voltage-based controllers are also presented.

Polynomial-Based Robust Adaptive Impedance Control of Electrically Driven Robots

“…Here, the control objective is to design a control input u(t) to realize the perfect motor current vector in (22) with the aim of reducing the error signal e I as small as possible. It returns to this fact that, a constant-bounded disturbance will not destroy the stability result under robust control I d which is a result of uniform ultimate boundedness of the tracking error using the Lyapunov-based theory of guaranteed stability of uncertain systems [34].…”

“…To solve the aforementioned problems, some robust and adaptive approaches based on uncertainty estimation have been proposed. As pointed out in the paper, 10 function approximation methods such as neuro-fuzzy systems, [11][12][13] Szasz-Mirakyan Operator, 14 differential equations, 15,16 Fourier series expansion and Bernstein polynomials [17][18][19][20][21][22][23][24][25] have been utilized in robust adaptive control of many nonlinear systems. The Stone-Weierstrass theorem, from the classical real analysis' point of view, can be used to guarantee that these mathematical tools possess the universal approximation property.…”

Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator

“…To cope with these problems, function approximation techniques (FATs) have been proposed whereas; FAT‐based estimators have simpler structures and fewer tuning parameters. Some robust adaptive controllers for robots using the Fourier series and Legendre Polynomials as universal approximator have been proposed in Reference . A third order Taylor series‐based uncertainty estimator for electrically driven robots in the presence of nonlinearities associated with actuator input constraint has been presented in Reference .…”

Adaptive control realization for canonic Caputo fractional-order systems with actuator nonlinearity: application to mechatronic devices

“…The research [20] investigated the existence of actuator saturation in linear fractional processes, and some applicable hypotheses were obtained using the conventional Lyapunov theorems. In [21], an adaptive fractional-order control algorithm was developed for control of robotic manipulators with actuator saturation. However, the convergence to zero was not guaranteed in mathematical synthesis of that research, and the outputs of the system might involve steady state errors.…”