Minimum Variance Benchmark for Performance Assessment of Decentralized Controllers

Abstract

The available minimum variance (MV) benchmarks do not take the controller structure into account and thus can lead to incorrect conclusions regarding the performance of decentralized controllers. In this paper, we present a method for computing a lower bound on the least output variance achievable using decentralized controllers, where the nonconvexity of the optimization problem is handled using sums of squares programming. Though tight, the computation of this lower bound requires that the process model be known. As a more practical approach, we derive an MV benchmark for performance assessment of decentralized controllers on a loop by loop basis. The MV benchmark for loop by loop analysis can be estimated from the closed loop operating data with the knowledge of time delays between all the inputs and outputs. The usefulness of the proposed benchmarks is demonstrated using simulation examples.

Control of a Multivariable System Using Optimal Control Pairs: A Quadruple-Tank Process

“…see (17), i.e., the eventual optimal control pairs determined via the RNGA are y 1 -u 2 , y 2 -u 1 .…”

“…Decentralized control design represents one of possible framework approaches to control the MIMO plants [14]- [17]. By using decentralized control, independent feedback controllers are used to control a subset of input-output pairs [18].…”

“…A crucial step in the design of decentralized control systems is to determine input-output loop pairings (also called the control configuration selection) that have minimum crossinteractions among individual loops [17], [22]- [24]. A good closed-loop performance may not be achieved when an improper input-output pairing is selected, even in the case of advanced and well-tuned controllers [25].…”

Dynamic Data Reconciliation for Enhancing Performance of Minimum Variance Control in Univariate and Multivariate Systems

“…They also investigated the minimum variance performance based PID controller in the single loop case and developed an iterative solution for the calculation of the best achievable (minimum variance) PID control performance later . In recent years, MVC has been also developed for time-variant process systems, , model predictive controllers, , PCA-based minimum variance performance, decentralized controllers, adaptive optics systems, stochastic and deterministic control performance of batch processes, and nonlinear multivariate systems. , Shardt et al gave a good review of the current techniques for performance assessment …”

Achievable performance of decentralized control systems

“…There is work that attempts to evaluate the best achievable decentralized control performance via parameterizing all decentralized stabilizing controllers which results in an infinite dimensional optimization problem [20]. However, most of the existing results try to characterize the upper or lower bounds on the performance of decentralized control [13], [9], [24], [12], [11], [19]. Most of these results, however, are based on MVC benchmark, which is not desirable in many practical applications since it is characterized by excessive control moves and has poor robustness [7].…”