Multivariate statistical methods for control loop performance assessment

Performance assessment of univariate control loops is carried out by comparing the actual output variance with the minimum variance. The latter term is estimated by simple time series analysis of routine closed-loop operating data. This thesis extends these univariate performance assessment concepts to the multivariate case and develops new multivariate performance assessment techniques.; A key to performance assessment of multivariate processes using minimum variance control as a benchmark, is to estimate the benchmark performance from routine operating data with a priori knowledge of time-delays/interactor-matrices, An algorithm for estimation of the interactor matrix from closed-loop data is developed in this thesis. The expression for the feedback controller-invariant (minimum variance) term is then derived by using the unitary, weighted unitary and generalized unitary interactor matrices. It is shown that this term can be estimated from routine operating data. The same idea is extended to performance assessment of systems with non-invertible zeros and to performance assessment of multivariate feedback plus feedforward controllers. Although these methods are originally developed for stochastic systems, it is shown that the same methods can also be applied to deterministic systems by appropriate re-formulation of the initial problem. Thus, a unified approach for control loop performance assessment is proposed. Efficient algorithms for performance assessment are developed and evaluated by simulations as well as applications on real industrial processes.; Minimum variance characterizes the most fundamental performance limitation of a system due to existence of time-delays/infinite-zeros. Practically there are many limitations on the achievable control loop performance. For example, a feedback controller that indicates poor performance relative to minimum variance control is not necessarily a poor controller. Further analysis of other performance limitations with more realistic benchmarks is usually required. Performance assessment in a more practical context such as a user-defined benchmark or control action constraints is therefore proposed and evaluated by applications in this thesis. Practical performance assessment generally requires complete knowledge of a plant model. An identification effort is usually required. As a complement to existing identification methods, a two-step closed-loop identification method is proposed and tested by simulated and experimental data from a computer-interfaced pilot-scale process.