Adaptive Radial Basis Function Neural Network Based Hierarchical Sliding Mode Controller for 2-Dimensional Double Pendulum Overhead Crane
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Date
2024-01
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Addis Ababa University
Abstract
Several control methods for an overhead crane modeled as a double pendulum with
constant cable length have been published in various studies. Most of the proposed
control methods were open-loop and linear control methods or nonlinear control methods
that fully depended on the system model.However, the dynamic of an overhead
crane is a complex nonlinear function of uncertain or unknown parameters, which
reduces the performance of such control methods. In this thesis, an adaptive radial
basis function neural network-based hierarchical sliding mode controller (ARBFNNHSMC)
is designed to control a 2-dimensional overhead modeled as a double pendulum
system with variable cable length using the Lagrange equation of motion.
To reduce the chattering effect of the sliding mode controller as well as increase its
robustness, ARBFNN is designed to estimate unknown or uncertain nonlinear functions
in the system. The overall control law, which contains only some parts of the
crane model, is designed, and the adaptation law is derived from the Lyapunov stability
condition to update the weight of the network based on observed errors. The
proposed control strategy and derived model are verified using MATLAB/Simulink
software.For the same controller parameters,500% changes in model parameters are
taken, and trolley displacement settling time and rising time for HSMC are 12.3
seconds and 6.95 seconds, respectively. On the other hand, the maximum hook’s
and payload’s swing angles are around 1.34 deg and 1.9 deg for HSMC, and it is
around 1.04 deg and 1.64 deg for ARBFNN-HSMC. The residual hook’s and payload’s
swing angles are 0.0137 deg and -0.0319 deg, respectively, in the case of HSMC
and -0.0011 deg and -0.0022 deg for ARBFNN-HSMC. This numerical result shows
that ARBFNN-HSMC has better performance than HSMC for large parameter variations.
In addition, the controller output of ARBFNN-HSMC is smoother than that
of HSMC, as evidenced by the result.
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Keywords
RBFNN, HSMC, 2D overhead crane, Double pendulum, Adaptive law