In this paper a previously offered black-box filtered-error neural-approximation-based control method for singularly perturbed flexible-link arms (FLA) is extended to a serial-gray-box method that assumes only the friction torques as unknown functions. Unlike the former method the knowledge of the unknown part is not used in design implementation of the fast control component. Because the neural network weights are updated adaptively the gray-box friction compensation method is applicable even when the friction functions change with time. Moreover, due to incorporation of the available first-principles knowledge into the control law the method exhibits dimensional extrapolation property with respect to nonfrictional measurable parameters of the plant. The capability of the gray-box method in the presence of static friction unmodeled dynamics are examined. Simulation results show that the proposed gray-box-based method provides better control modeling performances with less number of integrators in comparison with the black-box-based method. A procedure for determination of the parameters of the distributed mass-spring model is offered closed-form exact solutions for the equivalent deflection angle the spring coefficient the slope of the flexible-mode friction characteristic are derived. The gray-box method also works better than a newly developed Lyapunov-type controller which can be regarded as a robust control schema.
Neuro-Adaptive Friction Compensation for Single-Link Flexible Robots Using Serial-Gray-Box Modeling Strategy
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Bazaei, A., and Majd, V. J. (April 27, 2005). "Neuro-Adaptive Friction Compensation for Single-Link Flexible Robots Using Serial-Gray-Box Modeling Strategy." ASME. J. Dyn. Sys., Meas., Control. June 2006; 128(2): 297–306. https://doi.org/10.1115/1.2192838
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