After several years of efforts, constrained model predictive control (MPC), the de facto standard algorithm for advanced control in process industries, has finally succumbed to rigorous analysis. Yet successful practical implementations of MPC were already in place almost two decades before a rigorous stability proof for constrained MPC was published. What is then the importance of recent theoretical results for practical MPC applications? In this publication we present a pedagogical overview of some of the most important recent developments in MPC theory, and discuss their implications for the future of MPC theory and practice. 1 (713) 743 4309, fax: (713) 743 4323, email: nikolaou@uh.edu. -- 2 -- TABLE OF CONTENTS 1 INTRODUCTION 3 2 WHAT IS MPC? 3 2.1 A TRADITIONAL MPC FORMULATION 6 2.2 EXPANDING THE TRADITIONAL MPC FORMULATION 7 2.3 MPC WITHOUT INEQUALITY CONSTRAINTS 8 3 STABILITY 10 3.1 WHAT IS STABILITY? 10 3.1.1 Stability with respect to initial conditions 11 3.1.2 Input...

. This paper presents analysis of a scheme for iterated identification and control design. The approach is based on least squares identification in closed loop and pole placement design. It has previously been shown that the criteria for control and identification are the same provided that the data filters are chosen properly. The iterated scheme may be viewed as a recursion in model parameters. Each step consists of system identification and control design. Interesting questions are then: What are the fix points? Are the fix points stable? These questions are investigated for some simple examples. Relations to other problems like model reduction and adaptive control are also discussed. Keywords. Adaptive Control, Control Design, Identification, Least Squares Estimation, Model reduction, Pole Placement Control, Prediction Error Methods. 1. INTRODUCTION A sensible formulation of an identification problem should consider the ultimate use of the model. In control system design we are in...

Using the dual Youla parametrizations of controller based coprime factor plant perturbations and plant based coprime factor controller perturbations, we provide a computational procedure for computing an optimal infinite horizon Linear Quadratic Gaussian (LQG) controller from any stabilizing controller. The method allows us to calculate a new optimal LQG controller from a previous one when the plant has slightly changed, and to quantify the change in the controller as a function of the change in the plant. In addition, we compute the degradation in the achieved LQG cost when the LQG controller is computed on the basis of a plant model that is "close to" the real plant, where the closeness is measured by some norm of the perturbation. 1 Introduction Consider that you have some initial plant, P0 , and some controller, C0 , that stabilizes P0 . Using stable proper coprime factor descriptions of P0 and C0 , and the Youla parametrizations, one can then characterize both the set C of all ...

We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. For three different control design criteria (minimum variance, LQG and model reference control) we show that, under those conditions, a better performance is achieved by closing the loop during the identification. The measure of performance is the variance of the error between the output of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from the identified model). 1 Introduction Consider that a linear time invariant system, perturbed by noise, is to be controlled and that a control design criterion has been selected. The control design criteria that we study in this paper can be a Minimum Variance (MV) control design, or a Linear Quadratric Gaussian (LQG) design, or a Model Reference (MR) design. If ...

In this work, we formulate a new approach to simultaneous constrained Model Predictive Control and Identification (MPCI). The proposed approach relies on the development of a persistent excitation (PE) criterion for processes described by DARX models. That PE criterion is used as an additional constraint in the standard on-line optimization of MPC. The resulting on-line optimization problem of MPCI is handled by successively solving a series of semi-definite programming problems. Advantages of MPCI in comparison to other closed-loop identification methods are (a) Constraints on process inputs and outputs are handled explicitly, (b) Deterioration of output regulation is kept to a minimum, while closed-loop identification is performed. The applicability of the method is illustrated by a number of simulation studies. Theoretical and computational issues for further investigation are suggested. * Author to whom all correspondence should be addressed. Current address: Chemical Engineering...

Model predictive control (MPC) is currently the most widely implemented advanced process control technology for petroleum refineries and chemical plants. Based on the present state of the art in theory and practice, MPC works well for processes operating over a narrow range of conditions. However, processes frequently have to operate over a wide range of conditions, for reasons such as varying feedstocks, fluctuating markets for products and raw materials, large process disturbances, and equipment wear. Unsatisfactory MPC performance over widely ranging operating conditions may result in process downtime, environmental and safety risks, and waste of resources, with substantial economic losses. Therefore, there is a need for flexible MPC systems that perform well over a wide range of process operating conditions. While the inner complexity of such (next-generation) MPC systems may be high (to realize the sought improvements in control performance), the complexity of the design, operation, and maintenance of such systems by process engineers and operators should be low. The development and implementation of flexible MPC systems will almost certainly be facilitated by the future availability of predictably ever more powerful computers and communication hardware. 1.

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