Discrete Time Sliding-Mode Control Design with Grey Predictor

combined residual modification with artificial neural network sign estimation to improve the prediction accuracy. Yao, et al [3] added an adaptive value in the grey differential equation to improve system performance. Su, Lin, and Hsu [4] proposed a Markov-Fourier grey model, in which Fourier series is used to fit residuals and Markov matrices is employed to encode possible global information generated by residuals. In addition, some investigators [11], [12] have paid their attentions to the optimization of the background value of the GM(1,1) model in order to improve the its prediction accuracy. Actually, these modified versions only improve the prediction accuracy on a small scale, especially for a non-monotone data sequence. In practice, these above methods are very complex and hard to implement on microprocessors. To overcome this issue, a novel grey predictor combined with a Lagrange polynomial, called as an advanced GM(1,1) model, is brought up not only aiming at a more precise estimation but also giving a reasonable computation time for on-line control. The addition of the Lagrange polynomial maintains the simplicity of grey prediction and decreases the original prediction error obviously. This paper presents an advanced GM(1,1) model which can improve the accuracy of the conventional grey prediction and applies it to discrete sliding-mode control (DSMC). Using a Lagrange polynomial to take as a compensator and combining it with the original GM(1,1) model, the proposed prediction method can decrease the prediction error and easily implement in microprocessors with less computing time and memories. Then we employ this technique in DSMC to detect the system unknown perturbation. Comparing with the conventional DSMC, the proposed algorithm can reduce the switching gain and result in that the system state is bounded in a smaller region. Numeric simulation results of a DC motor are given to illustrate the feasibility and successfulness of the proposed design.