Backstepping funnel control for prescribed performance of robotic manipulators with unknown dead zone

Abstract

In this paper, a backstepping funnel control (BFC) is proposed to achieve a prescribed tracking performance for robotic manipulator systems with unknown input dead zone. According to the differential mean value theorem, the dead zone inverse compensation approach is avoided by representing the dead zone as a linear time-varying system. Without constructing the complex barrier Lyapunov function, a new constraint variable is employed and the tracking error will be forced to fall into prescribe boundaries. A simple sigmoid neural network is utilized to approximate the system uncertainties and the calculation of derivative terms generated by the recursive steps of traditional backstepping control can be avoided. With the proposed scheme, no prior knowledge is required on the bound of input dead zone, and the convergence of the position tracking error is guaranteed via the Lyapunov synthesis. Comparative simulation examples are given to illustrate the effectiveness of the proposed method.

Adaptive sliding mode disturbance observer–based funnel trajectory tracking control of quadrotor with external disturbances

“…In another line, funnel control can also be utilized to improve the transition performance of control systems, and as comparison made in [31], funnel control is simpler and more effective than PPC. Several applications based on this method have been developed in [32][33][34][35][36]. To address the problem of unknown dead zone in robotic manipulator systems while guaranteeing the transient behaviour of tracking error, a backstepping funnel control is proposed in [32], where the dead zone is represented as a linear time-varying system and the bound of input dead zone is not required.…”

“…Several applications based on this method have been developed in [32][33][34][35][36]. To address the problem of unknown dead zone in robotic manipulator systems while guaranteeing the transient behaviour of tracking error, a backstepping funnel control is proposed in [32], where the dead zone is represented as a linear time-varying system and the bound of input dead zone is not required. Different from [32], the neural network-based funnel controller is proposed in [33], in which neural network is utilized to estimate the non-linear dead zone.…”

“…To address the problem of unknown dead zone in robotic manipulator systems while guaranteeing the transient behaviour of tracking error, a backstepping funnel control is proposed in [32], where the dead zone is represented as a linear time‐varying system and the bound of input dead zone is not required. Different from [32], the neural network–based funnel controller is proposed in [33], in which neural network is utilized to estimate the non‐linear dead zone. In [34], funnel control is applied to ensure the transient and steady‐state performance of velocity and altitude tracking for air‐breathing hypersonic vehicles.…”