Finite horizon MPC for systems in innovation form

System identification and model predictive control have largely developed as two separate disciplines. Nevertheless, the major part of industrial MPC commissioning is generation of data and identification of models. In this contribution we attempt to bridge this gap by contributing some of the missing links. Input-output models (FIR, ARX, ARMAX, Box-Jenkins) as well as subspace models can be represented as state space models in innovation form. These models have correlated process and measurement noise. The correct LQG control law for systems with correlated process and measurement noise is not well known. We provide the correct finite-horizon LQG controller for this system and use this to develop a state space representation of the closed-loop system. This representation is used for closed-loop frequency and covariance analysis. These measures are used in tuning of the unconstrained and constrained MPC. We demonstrate our results on a simulated industrial furnace.

[1]  Stephen P. Boyd,et al.  Receding Horizon Control , 2011, IEEE Control Systems.

[2]  Marko Bacic,et al.  Model predictive control , 2003 .

[3]  Per Hagander,et al.  Discrete-Time LQG with Cross-Terms in the Loss Function and the Noise Description , 1991 .

[4]  Lennart Ljung,et al.  System identification (2nd ed.): theory for the user , 1999 .

[5]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[6]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[7]  Yucai Zhu,et al.  Multivariable System Identification For Process Control , 2001 .

[8]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[9]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[10]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[11]  B. Datta.  Numerical methods for linear control systems : design and analysis , 2004 .

[12]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[13]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[14]  Graham C. Goodwin,et al.  Digital control and estimation : a unified approach , 1990 .

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

[16]  George E. P. Box,et al.  Time Series Analysis: Box/Time Series Analysis , 2008 .

[17]  E. Mosca.  Optimal, Predictive and Adaptive Control , 1994 .

[18]  M. Gevers,et al.  A personal view of the development of system identification: A 30-year journey through an exciting field , 2006, IEEE Control Systems.

[19]  Karl Johan Åström,et al.  Computer Aided Design of Control Systems , 1984 .

[20]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[21]  Jay H. Lee,et al.  Model predictive control: past, present and future , 1999 .

[22]  Håkan Hjalmarsson,et al.  From experiment design to closed-loop control , 2005, Autom..

[23]  片山 徹.  Subspace methods for system identification , 2005 .

[24]  B. Moor,et al.  Subspace identification for linear systems , 1996 .

[25]  E. Mosca.  MODEL-BASED PREDICTIVE CONTROL , 2006 .

[26]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[27]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[28]  Graham C. Goodwin,et al.  Constrained Control and Estimation: an Optimization Approach , 2004, IEEE Transactions on Automatic Control.

[29]  Michel Gevers,et al.  Identification for Control: Achievements and Open Problems 1 , 2004 .

[30]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[31]  Daniel E. Rivera,et al.  Beyond Step Testing and Process Reaction Curves: Introducing Meaningful System Identification Concepts in the Undergraduate Chemical Engineering Curriculum , 2000 .

[32]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[33]  Graham C. Goodwin,et al.  Lagrangian duality between constrained estimation and control , 2005, Autom..

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

[35]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[36]  George A. Perdikaris.  Computer Controlled Systems , 1991 .

[37]  C.C. White,et al.  Dynamic programming and stochastic control , 1978, Proceedings of the IEEE.

[38]  Graham C. Goodwin,et al.  Constrained Control and Estimation , 2005 .

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

[40]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[41]  Michel Gevers,et al.  Identification for Control: Achievements and Open Problems 1 , 2004 .

[42]  Daniel Boley,et al.  Numerical Methods for Linear Control Systems , 1994 .

[43]  David R. Cox,et al.  Time Series Analysis , 2012 .

[44]  D.G. Dudley,et al.  Dynamic system identification experiment design and data analysis , 1979, Proceedings of the IEEE.

[45]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[46]  Kenneth R. Muske,et al.  Disturbance modeling for offset-free linear model predictive control , 2002 .

[47]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[48]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[49]  R. H. Kwong.  On the linear quadratic Guassian problem with correlated noise and its relation to minimum variance control , 1991 .

[50]  B. Anderson,et al.  Digital control of dynamic systems , 1981, IEEE Transactions on Acoustics, Speech, and Signal Processing.