Optimal back-off point determination and controller weight selection for multivariate systems under finite-horizon control

• Methodology to trade-off variances of different process variables for optimal plant operation.
• Calculation of weights for finite horizon controller for minimal backed-off operating point.
• Approximate piecewise linear programming approach to solve the non-convex constrained optimization problem in multivariate controller design.
• Simulation case studies on multivariate systems demonstrate the advantages of proposed approach.

Plant economic performance is most often related to the operating point, specifically the mean values of the process variables; meanwhile, most existing performance assessment techniques involve examining the variances or covariances of the controlled variables. A combined approach is to determine the appropriate trade-off between variances of different process variables in order to operate the plant at the point that provides maximum economic benefit while satisfying the operating constraints. This problem is referred to as the minimum backed-off operating point selection, and previous works have formulated it as a non-convex constrained optimization problem. In the current work, a new technique is introduced that can provide the optimal plant operating point. Additionally, this method provides the weights for a finite horizon controller that results in the optimal trade-off in process variable variances that will allow satisfaction of the operating constraints at the optimal operating point. In this method, the plant and disturbance models for the given process are used to generate data representing possible trade-offs between process variable standard deviations. Employing a piecewise linear regression to describe the sample points of this standard deviations data allows for the operating point selection problem to be solved as a small number of linear programs. The advantages of this approach are demonstrated through the use of mathematical and simulation case studies.