Adaptive Neural Network Control for the Trajectory Tracking of the Furuta Pendulum

Abstract

The purpose of this paper is to introduce a novel adaptive neural network-based control scheme for the Furuta pendulum, which is a two degree-of-freedom underactuated system. Adaptation laws for the input and output weights are also provided. The proposed controller is able to guarantee tracking of a reference signal for the arm while the pendulum remains in the upright position. The key aspect of the derivation of the controller is the definition of an output function that depends on the position and velocity errors. The internal and external dynamics are rigorously analyzed, thereby proving the uniform ultimate boundedness of the error trajectories. By using real-time experiments, the new scheme is compared with other control methodologies, therein demonstrating the improved performance of the proposed adaptive algorithm.

Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

“…In this sense, (15) can be interpreted as an additional matching condition of algebraic nature, which is therefore always solvable and relates the disturbance estimatẽto Λ(q) by means of the coupling term M d M −1 . (18), where Λ(q) is defined according to (15), (16), (17) and̃is estimated according to (10). Then, q * is a strict minimum of V ′ d , all trajectories q(t), p(t) are bounded and the equilibrium (q, p) = (q * , 0) is asymptotically stable for some parameters , k v > 0.…”

“…In particular, introducing (15) the matching conditions (4), (5) and their respective solutions M d , V d remain unchanged. In this sense, (15) can be interpreted as an additional matching condition of algebraic nature, which is therefore always solvable and relates the disturbance estimatẽto Λ(q) by means of the coupling term M d M −1 .…”

“…Theorem 1. Consider system (6) under Assumptions 1 to 3 in closed loop with control (18), where Λ(q) is defined according to (15), (16), (17) and̃is estimated according to (10). Then, q * is a strict minimum of V ′ d , all trajectories q(t), p(t) are bounded and the equilibrium (q, p) = (q * , 0) is asymptotically stable for some parameters , k v > 0.…”

“…6 However, the practical importance of disturbances in real systems has recently been attracting increasing interest within the research community. Furthermore, an H-infinity control was proposed for the inertia-wheel pendulum with bounded disturbances in the work of Binh et al 14 and an adaptive neural network control was employed to compensate friction forces for the Furuta pendulum in the work of Moreno-Valenzuela et al 15 In summary, most research on nonlinear underactuated mechanical systems with disturbances has been focusing on friction, while the constant disturbance rejection problem has remained relatively unexplored. 7,8 In parallel, the effect of continuous and smooth physical dissipation within IDA-PBC was studied in the works Delgado and Kotyczka 9 and Gómez-Estern and Van der Schaft, 10 while Dahl friction on actuated joints was considered in the work of Sandoval et al 11 Recently, an IDA-PBC design with adaptive friction compensation was proposed in the work of Franco.…”

“…12 Besides IDA-PBC, a sliding-mode-control formulation was proposed in the work of Martinez et al 13 for underactuated mechanical systems with Coulomb friction of known amplitude. Furthermore, an H-infinity control was proposed for the inertia-wheel pendulum with bounded disturbances in the work of Binh et al 14 and an adaptive neural network control was employed to compensate friction forces for the Furuta pendulum in the work of Moreno-Valenzuela et al 15 In summary, most research on nonlinear underactuated mechanical systems with disturbances has been focusing on friction, while the constant disturbance rejection problem has remained relatively unexplored. Initial results in this FRANCO respect were presented in the works of Teo et al 16 and Ryalat et al, 17 where integral control was overlaid to IDA-PBC in order to compensate constant matched disturbances (ie, only affecting the actuated joints).…”