In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model ...In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.展开更多
针对现有MOESP(multiple-input multiple-output output-error state space model identification)和N4SID(numerical algorithm for subspace state space systemidentification)算法在计算状态空间模型系统矩阵(A、B、C、D)时的不足,...针对现有MOESP(multiple-input multiple-output output-error state space model identification)和N4SID(numerical algorithm for subspace state space systemidentification)算法在计算状态空间模型系统矩阵(A、B、C、D)时的不足,提出1种改进的子空间辨识方法。该方法利用MOESP算法可以根据系统观测矩阵直接计算出系统矩阵A和输出矩阵C的优点,先计算矩阵A和C,然后采用N4SID算法计算输入矩阵B和前馈矩阵D。该方法既能够避免MOESP算法在计算矩阵B和D时需要构建大矩阵的缺点,又能避免N4SID算法在计算矩阵A和C时需要求解线性最小二乘的问题,降低了算法的复杂性。将该算法应用于某天然气电站和Alstom气化炉模型的辨识中,通过考核算法的CPU运算时间、CPU浮点数运算次数(floating-pointoperations,FLOPS)和相对误差等指标,将该算法与原有MOESP和N4SID算法进行了比较。计算结果表明,改进的子空间辨识算法能够在保证较好辨识精度的前提下,提高原有算法的计算效率,特别是在大容量数据样本条件下,能够有效降低CPU运算时间和FLOPS。展开更多
基金supported by the Ministry of Higher Education and Scientific Research of Tunisia
文摘In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.
文摘针对现有MOESP(multiple-input multiple-output output-error state space model identification)和N4SID(numerical algorithm for subspace state space systemidentification)算法在计算状态空间模型系统矩阵(A、B、C、D)时的不足,提出1种改进的子空间辨识方法。该方法利用MOESP算法可以根据系统观测矩阵直接计算出系统矩阵A和输出矩阵C的优点,先计算矩阵A和C,然后采用N4SID算法计算输入矩阵B和前馈矩阵D。该方法既能够避免MOESP算法在计算矩阵B和D时需要构建大矩阵的缺点,又能避免N4SID算法在计算矩阵A和C时需要求解线性最小二乘的问题,降低了算法的复杂性。将该算法应用于某天然气电站和Alstom气化炉模型的辨识中,通过考核算法的CPU运算时间、CPU浮点数运算次数(floating-pointoperations,FLOPS)和相对误差等指标,将该算法与原有MOESP和N4SID算法进行了比较。计算结果表明,改进的子空间辨识算法能够在保证较好辨识精度的前提下,提高原有算法的计算效率,特别是在大容量数据样本条件下,能够有效降低CPU运算时间和FLOPS。
