Multi-objective performance optimisation for model predictive control by goal attainment

This article proposes an approach for performance tuning of model predictive control (MPC) using goal-attainment optimisation of the cost function weighting matrices. The approach is developed for three formulations of the control problem: (i) minimal and (ii) non-minimal design based on the same cost function and (iii) a non-minimal MPC approach with an explicit integral-of-error state variable and modified cost function. This approach is based on earlier research into multi-objective optimisation for proportional-integral-plus control systems. Simulation experiments for a 3-input, 3-output Shell heavy oil fractionator model illustrate the feasibility of MPC goal attainment for multivariable decoupling and attainment of a specific output response. For this example, the integral-of-error state variable offers improved design flexibility and hence, when it is combined with the proposed tuning method, yields an improved closed-loop response in comparison to minimal MPC.

[1]  Willy Wojsznis,et al.  Multi-objective optimization for model predictive control. , 2007, ISA transactions.

[2]  E. M. Shaban,et al.  Multivariable proportional-integral-plus (PIP) control of the ALSTOM nonlinear gasifier simulation , 2006 .

[3]  James B. Rawlings,et al.  Model predictive control with linear models , 1993 .

[4]  Wang,et al.  Auto-tuning of TITO decoupling controllers from step tests , 2000, ISA transactions.

[5]  Andrew Plummer,et al.  Decoupling pole-placement control, with application to a multi-channel electro-hydraulic servosystem , 1997 .

[6]  Peter C. Young,et al.  Design and application of PIP controllers: robust control of the IFAC93 benchmark , 2001 .

[7]  Peter C. Young,et al.  Computer aided control system design of PIP controllers for systems described by delta operator and backward shift models. , 1994 .

[8]  Peter C. Young,et al.  Direct digital and adaptive control by input-output state variable feedback pole assignment , 1987 .

[9]  Peter J. Fleming,et al.  Application of multi-objective optimisation to compensator design for SISO control systems , 1986 .

[10]  Roger M. Goodall,et al.  LQG and GA solutions for active steering of railway vehicles , 2000 .

[11]  M. Kothare,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  P. Young.  AN INSTRUMENTAL VARIABLE APPROACH TO ARMA MODEL IDENTIFICATION AND ESTIMATION , 2006 .

[13]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[14]  Min-Sen Chiu,et al.  Decoupling internal model control for multivariable systems with multiple time delays , 2002 .

[15]  Barry Lennox,et al.  Algorithms for industrial model predictive control , 2000 .

[16]  Diego J. Pedregal,et al.  Environmental time series analysis and forecasting with the Captain toolbox , 2007, Environ. Model. Softw..

[17]  Vasileios Exadaktylos,et al.  Non-minimal model predive control with an integral-of-error state variable. , 2006 .

[18]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[19]  Darci Odloak,et al.  Infinite horizon MPC with non-minimal state space feedback , 2009 .

[20]  P. Young,et al.  An improved structure for model predictive control using non-minimal state space realisation , 2006 .

[21]  Kent Robertson Van Horn,et al.  Design and application , 1967 .

[22]  Wei Zhang,et al.  Analytical design of two degree-of-freedom decoupling control scheme for two-by-two systems with integrator(s) , 2007 .

[23]  P. Young,et al.  Proportional-integral-plus (PIP) design for delta (delta) operator systems Part 2. MIMO systems , 1998 .

[24]  Furong Gao,et al.  Analytical decoupling control strategy using a unity feedback control structure for MIMO processes with time delays , 2007 .

[25]  Peter J. Fleming,et al.  Evolutionary algorithms in control systems engineering: a survey , 2002 .

[26]  Gabriele Pannocchia,et al.  Disturbance models for offset‐free model‐predictive control , 2003 .

[27]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[28]  K. Natarajan,et al.  Tuning of PI controllers with one-way decoupling in 2×2 MIMO systems based on finite frequency response data , 2003 .

[29]  Sirish L. Shah,et al.  Performance Evaluation of two Industrial MPC Controllers , 2003 .

[30]  P. Young,et al.  State space control system design based on non-minimal state-variable feedback: Further generalization and unification results , 2000 .

[31]  J. B. Gomm,et al.  Solution to the Shell standard control problem using genetically tuned PID controllers , 2002 .

[32]  Alberto Bemporad,et al.  An algorithm for multi-parametric quadratic programming and explicit MPC solutions , 2003, Autom..