In this paper, the data-driven control performance monitoring framework [J. Yu, S.J. Qin, Statistical MIMO controller performance monitoring. Part I: data driven covariance benchmark, J. Proc. Cont., in press] is extended to the performance diagnosis aspect with focus on variable identification. To identify the control loops or controlled variables responsible for performance degradation or improvement, two types of multivariate contribution methods are proposed. One of the diagnostic methods is a loading based contribution chart to evaluate the significance of contribution of the corresponding loop/variable. The bootstrap resampling procedure is conducted to estimate the probability distribution and statistics of the relevant eigenvector loadings. Then confidence intervals are derived for the loadings. The other approach is to examine the angle between each individual loop/variable and the worse/better performance subspace. The cosine of the angle is defined as the contribution index and shown to be the canonical correlation coefficient between a unit vector and the worse/better performance subspace. The asymptotic statistics of canonical correlation is then utilized to derive the confidence limits for the angle based contributions. Two simulated examples (a multiloop control and a multivariable MPC system) are provided to illustrate the effectiveness of the proposed performance diagnosis approaches. An industrial example from a power boiler unit is further used to show the validity of the methods. The performance diagnosis results and the numerical features of these two approaches are compared and discussed. © 2007 Elsevier Ltd. All rights reserved.
Bibliographical noteFinancial support for this work from the National Science Foundation under DMI-0432433 and Weyerhaeuser Company through sponsorship of the Texas-Wisconsin Modeling and Control Consortium is gratefully acknowledged.
- Angle based contribution
- Loading based contribution
- MIMO control performance monitoring
- Performance diagnosis