Projection based MIMO control performance monitoring: I>covariance monitoring in state space

In this paper we propose a new control performance monitoring method based on subspace projections. We begin with a state space model of a generally non-square process and derive the minimum variance control (MVC) law and minimum achievable variance in a state feedback form. We derive a multivariate time delay (MTD) matrix for use with our extended state space formulation, which implicitly is equivalent to the interactor matrix. We show how the minimum variance output space can be considered an optimal subspace of the general closed-loop output space and propose a simple control performance calculation which uses orthogonal projection of filtered output data onto past closed-loop data. Finally, we propose a control performance monitoring technique based on the output covariance and diagnose the cause of suboptimal control performance using generalized eigenvector analysis. The proposed methods are demonstrated on a few simulated examples and an industrial wood waste burning power boiler.