系统辨识与自适应控制实验报告

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1、系统辨识与自适应控制实验报告一、实验目的1.了解最小二乘算法的实现；2.使用最小二乘法一次完成算法、递推最小二乘法以及广义最小二乘法对系统进行辨识。二、实验内容设单输入-单输出系统的差分方程为y（k）=-取真实值=[1.6420.7150.390.35]，输入数据如下表所列。ku(k)ku(k)ku(k)11.14711-0.958210.48520.201120.810221.6333-0.78713-0.044230.0434-1.589140.947241.3265-1.05215-1.474251.70660.86616-0.71926-0.34071

2、.15217-0.086270.89081.15718-1.099281.14490.626191.450291.177100.433201.15130-0.390用的真实值利用查分方程求出作为测量值，为均值为0，方差为0.1，0.5的不相关随机序列。（1）用最小二乘法估计参数（2）用递推最小二乘法估计参数θ。（3）用辅助变量法估计参数θ。（4）设，用广义最小二乘法估计参数θ。（5）用增广矩阵法估计参数θ详细分析和比较所获得的参数辨识结果，并说明上述参数辨识方法的优点。一、实验设备Matlab软件，PC机一台。四、实验原理4.1最小二乘一次完成算法4.1.1公

3、式辨识参数上式中4.1.2程序流程图图1最小二乘一次完成程序流程图4.2递推最小二乘算法4.2.1递推公式公式为其中，4.2.2算法流程图图2递推最小二乘法实现程序框图4.3增广最小二乘递推算法4.3.1递推公式公式为：其中，4.3.2算法流程图图3增广最小二乘法算法流程图五、实验结果5.1最小二乘法一次完成实验结果XL=00000000000.20101.1470-0.47980-0.78700.20101.0245-0.4798-1.5890-0.7870-0.44391.0245-1.0520-1.58900.9629-0.44390.8660-1.05

4、20-1.23320.96291.15200.86600.5840-1.23321.57301.1520-1.09390.58400.62601.57300.5840-1.09390.43300.6260-0.56470.5840-0.95800.43300.7317-0.56470.8100-0.9580-0.77840.7317-0.04400.81000.4885-0.77840.9470-0.0440-0.59960.4885-1.47400.94700.8786-0.5996-0.7190-1.4740-0.21770.8786-0.0860-0.7

5、1900.0144-0.2177-1.0990-0.08600.59070.01441.4500-1.0990-1.16110.59071.15101.45000.5277-1.16110.48501.1510-0.62840.52771.63300.4850-0.1521-0.62840.04301.63300.1108-0.15211.32600.0430-0.60530.11081.70601.3260-0.2147-0.6053-0.34001.70600.3208-0.21470.8900-0.3400-0.60140.32081.14400.890

6、00.0005-0.60141.17701.1440yL=000.4798-1.02450.4439-0.96291.2332-0.58401.0939-0.58400.5647-0.73170.7784-0.48850.5996-0.87860.2177-0.0144-0.59071.1611-0.52770.62840.1521-0.11080.60530.2147-0.32080.6014-0.00050.4302辨识参数矩阵c=1.64200.71500.39000.3500a1=1.6420；a2=0.7150；b1=0.3900；b2=0.3500

7、下图为输入、输出矩阵的根径图图4最小二乘法一次实现输入输出根径图5.2递推最小二乘法算法辨识结果系统输出矩阵：y=Columns1through13000.4798-1.02450.4439-0.96291.2332-0.58401.0939-0.58400.5647-0.73170.7784Columns14through26-0.48850.5996-0.87860.2177-0.0144-0.59071.1611-0.52770.62840.1521-0.11080.60530.2147Columns27through30-0.32080.6014-0.

8、00050.4302辨识参数矩阵（辨识