H.H.J. Bloemen

Model-based predictive control for Hammerstein?Wiener systems

In this paper a model-based predictive control (MPC) algorithm is presented for Hammerstein?Wiener systems. This type of system consists of a linear dynamic block preceded and followed by a static non-linear block. These systems appear useful in modelling several non-linear processes encountered in industry. Directly using such a model in a MPC algorithm will in general lead to a non-linear optimization problem due to the static non-linearities. This can be avoided by exploiting the structure of these models. In this paper the non-linearities are transformed into polytopic descriptions. This procedure enables one to use robust linear MPC techniques for controlling these systems. In such a way a convex optimization problem is retained. For the presented MPC algorithm, which is stated as an optimization problem subject to linear matrix inequalities, nominal closed loop stability is proven. In two examples it is shown that by means of transforming the non-linearities into polytopic descriptions, as done in the presented MPC algorithm, a better tuning of the input?output behaviour of the plant is obtained, compared to removing the static non-linearities from the control problem by an inversion, a technique often used for these systems.

Wiener model identification and predictive control for dual composition control of a distillation column

The benefits of using the Wiener model based identification and control methodology presented in this paper, compared to linear techniques, are demonstrated for dual composition control of a moderate–high purity distillation column simulation model. An identification experiment design is presented which enables one to identify both the low and high gain directions of the distillation column, properties which are important for control and hard to identify in a conventional identification experiment setup as is demonstrated in the paper. Data from the proposed experiment design is used for indirect closed-loop identification of both a linear and a Wiener model, which shows the ability of the Wiener model to approximate the nonlinearity of the distillation column much closer than the linear model can. The identified Wiener model is used in a MPC algorithm in which the nonlinearity of the Wiener model is transformed into a polytopic description. In this way a convex optimisation problem is retained while the effect of the nonlinearity on the input–output behaviour of the plant is still taken into account. The performance of the proposed Wiener MPC is compared with linear MPC based on the identified linear models, and with a Wiener MPC in which the nonlinearity of the Wiener model is removed from the control problem via an inversion, a popular way to handle Wiener models in a MPC framework. The simulations demonstrate that the proposed Wiener MPC outperforms the other MPC algorithms.

Brief Optimizing the end-point state-weighting matrix in model-based predictive control

In this paper a linear model-based predictive control (MPC) algorithm is presented, for which nominal closed-loop stability is guaranteed. The input is obtained by minimizing a quadratic performance index over a finite horizon plus an end-point state (EPS) penalty, subject to input, state and output constraints. Under certain conditions, the weighting matrix in the EPS penalty enables one to specify an invariant ellipsoid in which the input, state and output constraints are satisfied. In existing MPC algorithms this weighting matrix is calculated off-line. The main contribution of this paper is to incorporate the calculation of the EPS-weighting matrix into the on-line optimization problem of the controller. The main advantage of this approach is that a natural and automatic trade-off between feasibility and optimality is obtained. This is demonstrated in a simulation example.

Model-based predictive control for Hammerstein systems

Hammerstein systems are a class of systems represented by a static nonlinearity at the input followed by a linear dynamic block. In the paper the static input nonlinearity is transformed into a polytopic description. The remaining uncertain linear model is used in a MPC algorithm of which the optimization problem involves minimization of a linear objective function subject to linear matrix inequalities (LMIs), which is a convex problem. A procedure is presented to remove a number of LMIs from the optimization problem, prior to solving it. By means of an iterative procedure the conservatism of the polytopic description can be reduced. Nominal closed loop stability of this Hammerstein MPC algorithm is guaranteed. A comparison is presented between the proposed algorithm and an algorithm which removes the nonlinearity from the control problem via an inversion.

An interpolation strategy for discrete-time bilinear MPC problems

Input-output (I-O) feedback linearization suffers from a number of restrictions which have limited its use in model-based predictive control. Some of these restrictions do not apply to the case of bilinear systems, but problems with input constraints and unstable zero dynamics persist. This paper overcomes these difficulties by means of an interpolation strategy. Involved in this interpolation is a feasible and stabilizing trajectory, which is computed through the use of invariant feasible sets, and a more aggressive trajectory, which can be chosen to be either the unconstrained optimal trajectory or any alternative one.

MPC for Wiener systems

Wiener systems are characterized by a linear dynamic block followed by a static nonlinearity. In the paper a model-based predictive control (MPC) strategy is proposed for this type of systems. In this MPC algorithm the static nonlinearity is transformed into a polytopic uncertainty description of the output mapping which enables the use of robust linear MPC techniques. The optimization problem is given by a linear objective function subject to linear matrix inequalities. Nominal closed loop stability of this Wiener MPC strategy can be guaranteed.

An optimization algorithm dedicated to a MPC problem for discrete time bilinear models

This paper describes an algorithm for solving the optimization problem which occurs in a model-based predictive control (MPC) algorithm for discrete time bilinear models. This optimization problem is nonlinear in general, because the model acts as a nonlinear equality constraint. Common approaches of performing such a nonlinear optimization problem boil down to (successively) approximating the nonlinear objective function, followed by performing a line search. In this paper it is demonstrated that the structural properties of the bilinear state space model enable to formulate the nonlinear optimization problem as a sequence of quadratic programming problems which exactly represent the original objective function, implying that no additional line search is needed. The proposed optimization algorithm is compared to one that is based on linearization around an input trajectory. To benefit from the advantages of both algorithms, a hybrid algorithm is proposed, which outperforms the other two in most cases.

Interpolation in MPC for discrete time bilinear systems

Feedback linearization suffers from a number of restrictions which have limited its use in model-based predictive control. Some of these restrictions do not apply to the case of bilinear systems, but problems with input constraints and unstable zero dynamics persist. This paper overcomes these difficulties by means of an interpolation strategy. Involved in this interpolation is a stabilizing trajectory which is computed through the use of invariant feasible sets (defined for the bilinear model) and a more aggressive trajectory which can be chosen to be either the unconstrained optimal trajectory or an alternative which guarantees that the state vector remains bounded and that the output converges to the origin.

Bilinear versus linear MPC: Application to a polymerization process

Abstract In this paper a comparison between a linear-model-based and a bilinear-model-based identification and predictive control methodology is presented. Input-output data from a nonlinear first-principles simulation model of the free-radical polymerization of methylmethacrylate are used for black-box identification of a linear and a bilinear model. These black-box models are used within a model-based predictive controller that controls the nonlinear white-box simulation model. The results demonstrate a better performance of the bilinear-model-based methodology compared to the linear-model-based methodology.

On the trade-off between feasibility and performance in bilinear and state-affine model-based predictive control

Closed-loop stabilizing model-based predictive control (MPC) algorithms for discrete-time bilinear and state-affine models are presented. Stability of the closed-loop is obtained through the use of an appropriate end-point weighting and end-point inequality constraint. In this way the infinite-horizon performance index is bounded from above by the objective function that is minimized in the MPC algorithm. This paper presents an algorithm that aims at obtaining a large feasibility region by maximizing off-line the region that is defined by the end-point inequality constraint. In order to improve the performance of the MPC algorithm, the conservatism of the upper bound on the infinite-horizon performance index is reduced in the on-line computations.