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Neural Network Approximation Of Piecewise Continuous Functions: Application To Friction Compensation
, 2000
"... One of the most important properties of neural nets (NN) for control purposes is the universal approximation property. Unfortunately, this property is generally proven for continuous functions. In most real industrial control systems there are nonsmooth functions (e.g. piecewise continuous) for whic ..."
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Cited by 9 (2 self)
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One of the most important properties of neural nets (NN) for control purposes is the universal approximation property. Unfortunately, this property is generally proven for continuous functions. In most real industrial control systems there are nonsmooth functions (e.g. piecewise continuous) for which approximation results in the literature are sparse. Examples include friction, deadzone, backlash, and so on. It is found that attempts to approximate piecewise continuous functions using smooth activation functions require many NN nodes and many training iterations, and still do not yield very good results. Therefore, a novel neural network structure is given for approximation of piecewise continuous functions of the sort that appear in friction, deadzone, backlash and other motion control actuator nonlinearities. The novel NN consists of neurons having standard sigmoid activation functions, plus some additional neurons having a special class of nonsmooth activation functions termed 'jum...
Backlash Compensation In Nonlinear Systems Using Dynamic Inversion By Neural Networks
, 1999
"... A dynamic inversion compensation scheme is presented for backlash. The compensator uses the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. The technique provides a general procedure for using NN to determine the dynamic preinverse of ..."
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Cited by 7 (4 self)
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A dynamic inversion compensation scheme is presented for backlash. The compensator uses the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. The technique provides a general procedure for using NN to determine the dynamic preinverse of an invertible dynamical system. A tuning algorithm is presented for the NN backlash compensator which yields a stable closedloop system. 1 INTRODUCTION A general class of industrial motion control systems has the structure of a nonlinear dynamical system preceded by some nonlinearities in the actuator, either deadzone, backlash, saturation, etc. This includes xypositioning tables [19], robot manipulators [14], overhead crane mechanisms, and more. The problems are particularly exacerbated when the required accuracy is high, as in micropositioning devices. Due to the nonanalytic nature of the actuator nonlinearities and the fact that their exact nonlinear functions are unknown, such systems...
Neural Net Backlash Compensation With Hebbian Tuning By Dynamic Inversion
"... Neural network compensation scheme is presented for the class of nonlinear systems with backlash nonlinearity. The compensator uses the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. Instead of a derivative, which cannot be implement ..."
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Cited by 2 (0 self)
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Neural network compensation scheme is presented for the class of nonlinear systems with backlash nonlinearity. The compensator uses the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. Instead of a derivative, which cannot be implemented, a filtered derivative is used. Full rigorous stability proofs are given using filtered derivative. Compared with adaptive backstepping control schemes, we do not require the unknown parameters to be linear parametrizable. No regression matrices are needed. The technique provides a general procedure for using NN to determine the dynamic preinverse of an invertible dynamical system. A modified Hebbian algorithm is presented for NN tuning which yields a stable closedloop system. Using this method yields a relatively simple adaptation structure and offers computational advantages over gradient descent based algorithms. 1 Introduction Recently, in seminal work several rigorously derived ad...