ADAPTIVE POLE-PLACEMENT CONTROL OF MIMO STOCHASTIC SYSTEMS: USING DNLMS ALGORITHM

• Main Authors: Hung-Ming Huang, 黃弘明
• Other Authors: Wen-Shyong Yu
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/22796276294233492015

碩士 === 大同工學院 === 電機工程研究所 === 87 === In this thesis, the adaptive pole-placement control using delayed normalized least mean squares (DNLMS) algorithm with decreasing step size is proposed for controlling the multi-input multi-output (MIMO) stochastic systems. The DNLMS algorithm is used to estimate the system parameters such that the control parameters can be adaptively adjusted simultaneously. With the assumptions of the mixing input condition and the law of large numbers, we will prove the DNLMS algorithm with decreasing step size has the almost sure convergence property in the nonhomogeneous case. Then, we will prove the sample convergence of the weight matrix. The feature of the DNLMS is that when the error is large in the beginning, a big step size is used to estimate the parameters; later, as the error converges and is small, a small step size for getting good precision is used. Although the convergence property of the algorithm is proved for the nonhomogeneous case, it is also suitable for the homogeneous case. Moreover, the algorithm used in the homogeneous case gives better performance than that used in the nonhomogeneous case because the estimates can converge to the true values; nevertheless, the estimates will only converge to the optimal value in the nonhomogeneous case. By using the DNLMS to adaptively tune the parameters of the model, an adaptive pole-placement control law is derived for stabilizing the MIMO stochastic controlled system in the mean squares sense. We also prove that the system have self-tuning results under the adaptive pole-placement control law. If the estimate parameters occur pole-zero cancellation, we may apply the perturbation scheme to guarantee that the adaptive pole-placement control schemes are stabilizing. A series of simulations are performed to demonstrate the effectiveness of the proposed scheme. The results show that the proposed scheme is fairly robust to the control systems with uncertainties as well as improved performance characteristics.