Impact of MPC Embedded Performance Index on Control Quality

Abstract

Model Predictive Control (MPC) is a well established advanced process control technology. There are many successful implementations of different predictive strategies in process industry. There may be found various modifications of the MPC, however, one aspect remains fixed. MPC performance index is in quadratic form. Nonetheless, statistical analysis frequently points out that the quadratic regression formulation has some drawbacks. It is sensitive against the outliers. This work analyzes alternative and robust formulations of the MPC embedded performance index. It is shown that the quadratic formulation is not an optimal one, while the linear 1 weight improves control. Classical 2 norm together with robust Cauchy and Dynamic Covariance Scaling gives worse results. INDEX TERMS MPC, performance index, robust regression, 1 norm, Dynamic Covariance Scaling.

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

“…To penalise significant changes of the manipulated variable and to obtain good numerical properties, the second part of the cost function is the same as in the MPC-L 2 formulation [23].…”

“…In the the MPC-L algorithm, the sum of absolute values of the predicted control errors over the prediction horizon are taken into account rather than the sum of squared errors. Hence, the minimised cost function is: To penalise significant changes of the manipulated variable and to obtain good numerical properties, the second part of the cost function is the same as in the MPC-L formulation [ 23 ].…”

“…Secondly, the absolute value function is not differentiable, which means that the classical gradient-based optimisation method cannot be used. In spite of the second of the mentioned computational difficulties, in the literature, is it possible to find applications of gradient-based nonlinear optimisation methods to solve the MPC-L optimisation task ( 5 ) [ 23 , 24 , 28 ]. The objective of this work is to derive a much more computationally simple approach to the MPC-L problem in which nonlinear optimisation is not used.…”

“…The use of the sum of absolute values of the predicted control errors (the MPC-L algorithm) is much less popular. However, it may be easily verified that the second approach leads to better control quality [ 22 , 23 , 24 , 25 ]; the result is independent of the indicator used [ 23 ]. Furthermore, the classical L cost function is not always suitable from the point of stability, as pointed out in [ 26 ].…”

“…In such a case, a nonlinear optimisation problem with constraints must be solved at each sampling instant on-line, which may be computationally too demanding or completely impossible. Examples of nonlinear MPC-L algorithms in which the Sequential Quadratic Programming algorithm is used are described in [ 23 , 24 ]. A trust-region sequential quadratic programming method is used in [ 28 ].…”