Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network

Abstract

In this paper, nonlinear dynamical equations of the flexible manipulator with a lumped payload at the free end are derived from Hamilton's principle. The obtained model consists of both distributed parameters and lumped parameters, namely, partial differential equations (PDEs) governing the flexible motion of links and boundary conditions in the form of ordinary differential equations (ODEs). Considering the great nonlinear approximation ability of the radial basis function (RBF) neural network, we propose a combined control algorithm that includes two parts: one is a boundary controller to track the desired joint positions and suppress the vibration of flexible links; another is a RBF neural network designed to compensate for the parametric uncertainties. The iteration criterion of the RBF neural network weight matrix is derived from the extended Lyapunov function. Stabilization analysis is further carried out theoretically via LaSalle’s invariance principle. Finally, the results of the numerical simulation verify that the proposed control law can realize the asymptotic convergence of tracking error and suppression of the elastic vibration as well.

The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

“…The PDE dynamic model can reflect the dynamic characteristics of the micro-deformed structure more accurately than the ODE dynamic model [ 5 , 9 ]. The Hamilton method was used to derive the PDE dynamic equation of the micro-deformable manipulator system [ 5 , 7 , 9 , 12 ]; moreover, the corresponding boundary conditions of the system were obtained. This process did not require complex force analysis of the micro-deformable manipulator system.…”

“…Based on the partial differential equation (PDE) dynamic model of the flexible manipulator system, some researchers used the adaptive boundary control method [ 5 , 6 , 7 ] to control the manipulator, while others used the neural network control method [ 8 ]. Several researchers have combined the adaptive boundary control method with the approximation or compensation results of radial basis function (RBF) neural network [ 9 , 10 , 11 , 12 , 13 ] to optimize the control performance of flexible systems. Additionally, the RBF neural network proportional differential (PD) control method of the flexible manipulator was studied in [ 14 ].…”

“…These lead to overflow and instability; moreover, change of the system space state cannot be described accurately [ 18 , 19 , 26 ]. The overflow problems were considered in a few PDE modeling papers [ 5 , 7 , 9 , 12 ] and RBF neural network was used to estimate interference of one end, but the other end was ignored [ 9 ]. Due to the partial interference being neglected, the established model was not accurate enough.…”

Fast luffing control of flexible boom of mobile elevated work platform with uncertain control input gain

“…There are also many model-free controllers used for the control of flexible manipulators, such as PID and improved PID, [28][29][30] model free predictive control, 31,32 neural network, [33][34][35] ADRC, 36,37 etc. Among those control methods, the ADRC proposed by Han 38 has simple structure and excellent disturbance rejection performance, forming a new paradigm for feedback control systems.…”