Design of adaptive optimal robust control for two-flexible-link manipulators in the presence of matched uncertainties

Abstract

This study uses a comprehensive control approach to deal with the trajectory tracking problem of a two-flexible-link manipulator subjected to model uncertainties. Because the control inputs of two-flexible-link manipulators are less than their state variables, the proposed controller should be able to tackle the stated challenge. Practically speaking, there is only a single control signal for each joint, which can be used to suppress link deflections and control joint trajectories. To achieve this objective, a novel optimal robust control scheme, with an updated gain under the adaptive law, has been developed in this work for the first time. In this regard, a nonsingular terminal sliding mode control approach is used as the robust controller and a control Lyapunov function is used as the optimal control law, to benefit from the advantages of both methods. To systematically deal with system uncertainties, an adaptive law is used to update the gain of nonsingular terminal sliding mode control. The advantage of this approach over the existing methods is that it not only can robustly and stably control an uncertain nonlinear system against external disturbances but also can optimally solve a quadratic cost function (e.g. minimization of control effort). The Lyapunov stability theory has been applied to verify the stability of the proposed approach. Moreover, to show the superiority of this method, the computer simulation results of the proposed method have been compared with those of an adaptive sliding mode control scheme. This comparison shows that the presented approach is capable of optimizing the control inputs while achieving the stability of the examined two-flexible-link manipulator in the presence of model uncertainties and external disturbances.

Hybrid Force and Motion Control of a Three-Dimensional Flexible Robot Considering Measurement Noises

“…Xu [21] Planar TL FM; MC; utilizing joint variables in control design; singular perturbation method. Shafei, Bahrami and Talebi [22] MC. Kilicaslan, Ider, and Ozgoren [23] MC.…”

“…The control law was developed by using joint space variables for the MC of a planar TL FM. Shafei, Bahrami and Talebi [22] designed a sliding mode control and a Lyapunov function considering planar TL FM and spatial TL FM. Kilicaslan, Ider, and Ozgoren [23] have proposed a task space MC law for a spatial three-link FM.…”

Adaptive vibration control for constrained moving vehicle-mounted nonlinear 3D rigid-flexible manipulator system subject to actuator failures

“…Flexible parts gradually replace some rigid parts in mechanical systems to improve performance. Several researchers have studied the modeling and control problem of the flexible mechanical system (FMS), such as flexible manipulators Shafei et al (2021), flexible wings He et al (2022), flexible spacecraft Liu et al (2019a), flexible riser systems Zhao et al (2019), and flexible aerial refueling hose Liu et al (2017).…”

A composite controller for manipulator with flexible joint and link under uncertainties and disturbances

“…In the last years, the controller design for the flexible link or flexible joint manipulator has been extensively studied. Many advanced technologies have been applied in the flexible link, such as sliding mode control (Xu et al, 2000; Mujumdar et al, 2015), boundary control (Jiang et al, 2018; Mamani et al, 2012), neural network (NN) control (Gao et al, 2019; Hu et al, 2020a, 2020b; Xu, 2018), fuzzy control (Jnifene and Andrews, 2005; Lin and Lewis, 2003; Tinkir et al, 2010), robust control (Lee and Lee, 2002; Shafei et al, 2020), and singular perturbation (SP) approach (El-Badawy et al, 2010; Siciliano and Book, 1988). In Choi and Cheon (2004), a sliding mode controller was already reported.…”