Fuzzy neural network and observer-based fault-tolerant adaptive nonlinear control of uncertain 5-DOF upper-limb exoskeleton robot for passive rehabilitation

Neural Network Dynamic Surface Backstepping Control for the Speed and Tension System of Reversible Cold Strip Rolling Mill

“…Based on (19), (26), and (31), we know _ u i is easy to attain, while the matched uncertainty Δ i is complex and unknown. Based on (19), (26), and (31), we know _ u i is easy to attain, while the matched uncertainty Δ i is complex and unknown.…”

“…where e 31 ¼ F 3 À F Ã 3 , e 32 = V 3 À V 3d and e 33 = I 3 À I 3d are the error variables; F Ã 3 is the given value of the right coiler tension subsystem; V 3d and I 3d are the outputs of the low-pass filters; τ 32 and τ 33 are the time constants of the low-pass filters; k 31 , k 32 , k 33 ∈ R + are the controller parameters, _ u 3 is the certain control part. Based on (19), (26), and (31), we know _ u i is easy to attain, while the matched uncertainty Δ i is complex and unknown. Considering the neural network has better online learning ability, and is easy to be grasped and understood, thus the neural network adaptive method will be adopted to conduct approximation for the matched uncertainty Δ i in the next step.…”

“…The input vectors of the neural network are chosen as x 1 = [e 11 e 12 e 13 ] T , x 2 = [e 21 e 22 ] T , x 3 = [e 31 e 32 e 33 ] T , and then based on (19), (26), and (31)-(32), the neural network dynamic surface backstepping controllers for the speed and tension system (2) can be redesigned as…”

“…Furthermore, for the uncertainty item with relatively small value and change rate, a nonlinear disturbance observer (NDO) [12,13] can be adopted to conduct dynamic observation and compensation, because its structure is simple, calculation amount is small, and control parameters are easily set. On the other hand, for an uncertainty item with relatively large value and change rate, neural network control [14,15], fuzzy control [16,17], or fuzzy neural network control [18,19] can be adopted to conduct dynamic approximation and compensation, because they can approximate any continuous function online, which is helpful to improve the tracking control precision and the robust stability of the system. Therefore, in this paper, for the speed and tension system of reversible cold strip rolling mill with uncertainties, a control strategy is proposed based on nonlinear disturbance observers (NDOs), dynamic surface backstepping control, and neural network adaptive approximation.…”

“…Based on (10)-(11), (13)-(15), (18)-(19), (32)-(33) and (35), and take the time derivative of e 11 , e 12 and e 13 respectively, then we can get _ e 11 ¼ Àk 11 e 11 À…”