Development of LTV subspace system identification using basis functions approach to assessing the performance of control loops for nonlinear processes

A new procedure is proposed for the evaluation of the control loop performance assessment for nonlinear systems using the linear time-varying (LTV) subspace system identification approach. First, a unified LTV subspace system identification is developed. Using the basis function approach, the basis function can make the LTV subspace identification look mathematically the same as the linear time-invariant one. The subspace spanned by the columns of the extended observability matrix from the system input-output data is constructed. And the system matrices are determined directly by the extended observability matrix. To simplify the complicated model structure in LTV systems, two methods are proposed. One is the kernel based method that reduces the computations, and the other, multivariate orthogonal least squares that extracts the useful basis function. Then this work presents an LQG based performance assessment of the LTV system with the subspace framework, and the performance bounds at each time point are set up. They lead to simple monitoring charts, easy tracking of the progress in each operation point, and monitoring the occurrence of the observable upsets. To demonstrate the potential applications of the proposed strategies, a real industrial problem is used.