This paper describes a technique for modeling and identifying a class of nonlinear servomechanism systems with stick-slip friction. The physics of the stick-slip friction is considered in modeling the process. Identification of the system parameters is formulated as a nonlinear optimization problem. A modified simplex algorithm is proposed as the optimization procedure. The difficulties encountered in choosing identification algorithm and input signals for the problem are discussed. A simulation example of a servomotor system is provided.
This paper presents an adaptive momentum algorithm which can update the momentum coefficient automatically in every iteration step. The basic idea comes !rom the optimal gradient method used in the standard backpropagation algorithm. Because of the very complex nonlinear structure in the multi-layer feedforward neural network, it is very dimcult to obtain the optimal gradient vector by analytical methods, but it can be proven that the optimal gradient vectors in two successive iteration steps are orthogonal. Based on this property one can use the Gram-Schmidt orthogonalization method to ensure the orthogonality of the successive gradient vectors. The result of this process is equivalent to adding a momentum term to the standard backpropagation algorithm and the momentum coefficient is updated automatically in every iteration. Numerical simulations show that the adaptive momentum algorithm not only can eliminate possible divergent oscillations during the initial training, but can also accelerate the learning process and result in a lower error when the final convergence is reached.
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