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
This paper deals with a state model identification of a gas turbine used for gas transport, using a subspace approach of the state space model. This method provides a reliable and robust state representation of the mo...This paper deals with a state model identification of a gas turbine used for gas transport, using a subspace approach of the state space model. This method provides a reliable and robust state representation of the model, taking advantage of its benefits in the control, monitoring, and supervision of this machine. The model for each variable is set so that the state matrices associated with the gas turbine model are determined from their real input/output data. The comparison of the obtained identification results with those of the actual turbine operation serves to validate the proposed model in this work. This numerical algorithm of the subspace identification method is full of information and more accurate in terms of residual modeling error, and expresses a very high level of confidence in the identified turbine system dynamics. Hence, the controllability and observability tests of turbine operation for different input/output variables allowed to validate the real-time operating stability of the turbine.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。
文摘This paper deals with a state model identification of a gas turbine used for gas transport, using a subspace approach of the state space model. This method provides a reliable and robust state representation of the model, taking advantage of its benefits in the control, monitoring, and supervision of this machine. The model for each variable is set so that the state matrices associated with the gas turbine model are determined from their real input/output data. The comparison of the obtained identification results with those of the actual turbine operation serves to validate the proposed model in this work. This numerical algorithm of the subspace identification method is full of information and more accurate in terms of residual modeling error, and expresses a very high level of confidence in the identified turbine system dynamics. Hence, the controllability and observability tests of turbine operation for different input/output variables allowed to validate the real-time operating stability of the turbine.
