MIMO control performance monitoring based on subspace projections
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Control performance assessment has been the subject of intense scrutiny over the past 10 years and there are now numerous industrial examples of its value. The terms assessment and monitoring are used almost interchangeably in the literature and this has led to some confusion and debate over the interpretation of the minimum variance performance index.This research aligns the separate tasks of control performance assessment, monitoring and diagnosis under a unified state space framework. In this work, minimum variance control is formulated in state space without requiring Ricatti equations or spectral factorization.This results in a unique geometric interpretation of minimum variance control; the output of a process under minimum variance control occupies an optimal subspace of the general closed-loop process output.In this novel framework, control performance can be assessed for both feedback and feedforward-feedback control structures through a common subspace projection, making the technique suitable for monitoring model predictive control.A QR decomposition of the augmented data matrix enhances the procedure and allows for correlated disturbances.Typically, controller assessment provides only scalar indices.In this work, the actual and optimal output covariance matrices are displayed graphically as a diagnostic aid.Principal component analysis is used to isolate the dominant directions of sub-optimality.The impact of sensor and actuator faults on minimum variance control performance indices is rigorously analyzed.Finally, a new procedure is introduced which isolates sensor faults by applying known open-loop fault directions to the control invariant subspace of normal closed-loop process data.Several simulated and industrial examples are included to illustrate and support the developed theory.