More than 15 years after Model Predictive Control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the on-line optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for nonlinear systems but for practical applications many questions remain, including the reliability and efficiency of the on-line computation scheme. To deal with model uncertainty "rigorously" an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, nonlinear state estimation, and batch system control. Many practical problems like control objective prior...

. This paper provides an overview of nonlinear model predictive control (NMPC) applications in industry, focusing primarily on recent applications reported by NMPC vendors. A brief summary of NMPC theory is presented to highlight issues pertinent to NMPC applications. Five industrial NMPC implementations are then discussed with reference to modeling, control, optimization, and implementation issues. Results from several industrial applications are presented to illustrate the benefits possible with NMPC technology. A discussion of future needs in NMPC theory and practice is provided to conclude the paper. 1. Introduction The term Model Predictive Control (MPC) describes a class of computer control algorithms that control the future behavior of a plant through the use of an explicit process model. At each control interval the MPC algorithm computes an open-loop sequence of manipulated variable adjustments in order to optimize future plant behavior. The first input in the optima...

We present a structured interior-point method for the e cient solution of the optimal control problem in model predictive control (MPC). The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We use a discrete-time Riccati recursion to solve the linear equations e ciently at each iteration of the interior-point method, and show that this recursion is numerically stable. We demonstrate the e ectiveness of the approach by applying it to three process control problems. 1

A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than 5), and short time horizons. In this paper we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 time steps (which entails solving a quadratic program with 450 variables and 1260 constraints) in around 5msec, allowing MPC to be carried out at 200Hz. 1

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March, 2003I hereby certify that the work embodied in this thesis is the result of original research and has not been submitted for a higher degree to any other University or Institution. Adrian WillsAcknowledgements I would like to thank my supervisor Dr. Will Heath for his exceptional patience, his willingness to sacrifice, his genuine and pragmatic approach to research and for his friendship which I hope continues. I am indebted to Will for more than I can recall and I am truly grateful for all of his help and support. Thanks. A special thanks to Dr. Liuping Wang, who helped establish my scholarship and the industrial partnership. A further special thanks to Professors Graham Goodwin and Rick Middleton for their technical and financial support. Thanks to Dr. Charlie Chessari and Jay Selahewa who established my scholarship through

Since 1984 there has been a concentrated e ort to develop e cient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interior-point methods (beyond their e ciency for LP): they extend gracefully to nonlinear convex optimization problems. New interior-point algorithms for problem classes such as semide nite programming (SDP) or second-order cone programming (SOCP) are now approaching the extreme e ciency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to e ciently solve nonlinear convex optimization problems opens up new applications. In the rst example we show how SOCP can be used to solve robust open-loop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the set-point and feedback gains for a controller, and compare this method with the more standard approach. Our nal application concerns analysis and synthesis via linear matrix inequalities and SDP. Submitted to a special issue of Journal of Process Control, edited by Y. Arkun & S. Shah, for papers presented at the 1997 IFAC Conference onAdvanced Process Control, June 1997, Ban. This and related papers available via anonymous FTP at

This is a Swedish Licentiate’s Thesis. Swedish postgraduate education leads to a Doctor’s degree and/or a Licentiate’s degree. A Doctor’s Degree comprises 160 credits (4 years of full-time studies). A Licentiate’s degree comprises 80 credits, of which at least 40 credits constitute a Licentiate’s thesis.

This article addresses the real-time implementation issues of a model predictive control based walking pattern generation for a humanoid robot. We approximate the multibody dynamic model with a linear discrete time system, and at each step solve a quadratic program in order to keep the output within a predefined set of constraints. The focus is on creating an efficient framework for forming and solving the underlying optimization problem. For that purpose we develop: a) a reliable guess for the active constraints at optimality; b) a fast way of generating an initial feasible point with respect to the set of constraints for each preview interval; c) a variable discretization sampling time. A simple implementation of a standard primal active set algorithm which exploits a “hot start” is used to demonstrate the advantages of the first point, while the latter one is verified using an existing dual solver.

Abstract: In this paper we present and discuss all aspects of controlling a realworld delay-time system application, the pulp bleaching process at Irving Paper Ltd. The bleaching process was thoroughly studied and modelled. A delay-time estimator was designed to tackle the problem of the long variable delay time, which was considered the biggest challenge in this project. The model predictive control (MPC) strategy was chosen to control the bleaching process taking into account its constraints, which were handled by incorporating a state of the art optimization method, i.e., an interior point method, in the controller. The designed MPC controller was implemented in the Irving Paper mill, in order to test and demonstrate its performance and stability.