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In this paper, a compensation method of nonlinear friction using on-line input estimation (IE) method is developed. To illustrate the validity and performance of the proposed algorithm applied to positioning system, comparisons with the results using the Gomonwattanapanich method and robustness analysis are performed. The simulation result shows that the estimated friction torque does not need any assumption in the pattern of friction model in advance, the proposed algorithm has consistent robustness to diverse friction characteristics, and the method can significantly improve the performance of a control system.

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This study presents an input estimation method combined with the finite-element scheme for solving two-dimensional, hollow-cylinder, inverse heat conduction problems (IHCPs). The finite-element scheme is employed to discretize the problem in space, allowing multidimensional problems of various geometries to be treated. With the input estimation method, comprising the Kalman filtering technique and a recursive least-squares estimator, Kalman filtering estimates the interior temperature of the hollow cylinder using a system involving noise measurement and modeling error. A recursive least-squares estimator is derived that uses the residual innovation sequence to compute the magnitude of the unknown heat flux at the inner surface. The proposed method's superiority is demonstrated using several typical heat flux cases involving a hollow-cylinder inner surface that varies with time t and axial location z. The results show that this method has stability and good accuracy.