Economic performance assessment with optimized LQG benchmarking in MIMO systems

The objective of an economic performance assessment strategy is to quantitatively measure the effectiveness of a process in an economic framework. Such procedures typically involve the comparison of current operation with an appropriate benchmark to determine potential improvement through improved process control. In this work, a linear quadratic Gaussian (LQG) controller is used as a benchmark under conditions of uncertainty. By relating key process variables to a function describing the profitability of a process, the current and potential (with LQG control) modes of operation can be assessed in an economic framework. This work provides an approach to such an assessment for a MIMO system through economic optimization of an LQG controller weighting matrix, and illustrates results in the form of a case studies. I. NOTATION K steady state gain matrix cu economic performance coefficient vector of process inputs cy economic performance coefficient vector of process outputs nu number of process inputs ny number of process outputs P profitability of operation ū mean process input vector ui i th process input variable umin process input lower limits umax process input upper limits ȳ mean process output vector yi i th process output variable ymin process output lower limits ymax process output upper limits zαu z-coefficient corresponding to input constraint violation of with probability 1− α zαy z-coefficient corresponding to output constraint violation of with probability 1− α αu probability of an acceptable input αy probability of an acceptable output λ LQG weighting vector [λu λy] λmin minimum LQG weight λmax maximum LQG weight This work was supported by NORPAC Controls Ltd. R.B. Gopaluni and D.J. Marshman are with the Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC, Canada [email protected], [email protected] G.A. Dumont is with the Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada [email protected] T. Chmelyk and M.S. Sidhu are with NORPAC Controls Ltd., 7500 Winston Street, Burnaby, BC, Canada [email protected], [email protected] λu LQG input weighting vectors λu,i LQG weighting parameter for i input λy LQG output weighting vectors λy,i LQG weighting parameter for i output ∆λ incremental testing resolution of λ σu input standard deviations σy output standard deviations