In this paper the performance monitoring method based on subspace projections from Part I [J. Proc. Cont. 13 (2003) 739] is extended to include measured disturbances and setpoint changes. It was shown in [J. Proc. Cont. 13 (2003) 739] that the minimum variance output space is an optimal subspace of the general closed-loop output space and that orthogonal projections of filtered output data onto past closed-loop output data can be used to assess the performance of feedback controllers. This paper demonstrates that the same framework is directly applicable to systems with measured disturbances by augmenting the data matrix with those measured disturbances. Furthermore, it provides a means of separating suboptimal control performance between that arising from unmeasured disturbances and that due to measured disturbances. The effect of setpoint changes on control performance can be calculated as special feedforward variables. The controller is generally time-varying to include the case of model predictive control. A simulation example and an industrial boiler process are used to demonstrate the effectiveness of the proposed method. © 2004 Elsevier Ltd. All rights reserved.
Bibliographical noteFinancial support for this work from the National Science Foundation under CTS-9985074 and Weyerhaeuser Company through sponsorship of the Texas–Wisconsin Modeling and Control Consortium is gratefully acknowledged.
- Covariance monitoring
- Feedforward control
- MIMO control performance monitoring
- Minimum variance
- Model predictive control