T.J.J. van den Boom

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.

MPC for continuous piecewise-affine systems

Abstract A large class of hybrid systems can be described by a max–min-plus-scaling (MMPS) model (i.e., using the operations maximization, minimization, addition and scalar multiplication). First, we show that continuous piecewise-affine systems are equivalent to MMPS systems. Next, we consider model predictive control (MPC) for these systems. In general, this leads to nonlinear, nonconvex optimization problems. We present a new MPC method for MMPS systems that is based on canonical forms for MMPS functions. In case the MPC constraints are linear constraints in the inputs only, this results in a sequence of linear optimization problems such that the MPC control can often be computed in a much more efficient way than by just applying nonlinear optimization as was done in previous work.

Optimal coordination of ramp metering and variable speed control-an MPC approach

We present a model predictive control (MPC) approach to optimally coordinate variable speed limits and ramp metering for highway traffic. The basic idea is that speed limits can increase the range in which ramp metering is useful. The control objective is to minimize the total time that vehicles spend in the network. For the prediction of the evolution of the traffic flows in the network we use an adapted version of the METANET model that takes the variable speed limits into account. The coordinated control results in a network with less congestion, a higher outflow, and a lower total time spent. In addition, the receding horizon approach of MPC results in an adaptive, online control strategy that automatically takes changes in the system parameters into account.

Robust stability constraints for fuzzy model predictive control

This paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the Takagi-Sugeno (T-S) type, resulting in a stable closed-loop control system. Conditions are given that guarantee closed-loop robust asymptotic stability for open-loop bounded-input-bounded-output (BIBO) stable processes with an additive l/sub 1/-norm bounded model uncertainty. The idea is closely related to (small-gain-based) l/sub 1/-control theory, but due to the time-varying approach, the resulting robust stability constraints are less conservative. Therefore the fuzzy model is viewed as a linear time-varying system rather than a nonlinear one. The goal is to obtain constraints on the control signal and its increment that guarantee robust stability. Robust global asymptotic stability and offset-free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances.

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.

Model predictive control for perturbed max-plus-linear systems

Abstract Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Recently, we have extended MPC to a class of discrete event systems that can be described by a model that is “linear” in the (max,+) algebra. In our previous work, we have only considered MPC for the deterministic noise-free case without modeling errors. In this paper, we extend our previous results on MPC for max-plus-linear systems to cases with noise and/or modeling errors. We show that under quite general conditions the resulting optimization problems can be solved very efficiently.

Model predictive control for max-plus-linear systems

Model predictive control (MPC) is a very popular controller design method in the process industry. An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. In this paper we extend MPC to a class of discrete event systems, i.e. we present an MPC framework for max-plus-linear systems. In general the resulting optimization problem is nonlinear and nonconvex. However, if the control objective and the constraints depend monotonically on the outputs of the system, the MPC problem can be recast as problem with a convex feasible set. If in addition the objective function is convex, this leads to a convex optimization problem, which can be solved very efficiently.Model predictive control (MPC) is a very popular controller design method in the process industry. An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. In this paper we extend MPC to a class of discrete event systems, i.e. we present an MPC framework for max-plus-linear systems. In general the resulting optimization problem is nonlinear and nonconvex. However, if the control objective and the constraints depend monotonically on the outputs of the system, the MPC problem can be recast as problem with a convex feasible set. If in addition the objective function is convex, this leads to a convex optimization problem, which can be solved very efficiently.

Model Predictive Control Approach for Recovery from Delays in Railway Systems

The model predictive control (MPC) framework, a very popular controller design method in the process industry, is extended to transfer coordination in railway systems. In fact, the proposed approach can also be used for other systems with both hard and soft synchronization constraints, such as logistic operations. The main aim of the control is to optimally recover from delays by breaking connections (at a cost). In general, the MPC control design problem for railway systems leads to a nonlinear, nonconvex optimization problem. Computing an optimal MPC strategy using an extended linear complementarity problem is demonstrated. Also presented is an extension with an extra degree of freedom to recover from delays by letting some trains run faster than usual (again at a cost). The resulting extended MPC railway problem can also be solved using an extended linear complementarity problem.

Fault-tolerant control using dynamic inversion and model-predictive control applied to an aerospace benchmark ⋆

This paper features the combination of model-based predictive control and dynamic inversion into a constrained and globally valid control method for fault-tolerant flight-control purposes. The fact that the approach is both constrained and model-based creates the possibility to incorporate additional constraints, or even a new model, in case of a failure. Both of these properties lead to the fault-tolerant qualities of the method. Efficient distribution of the desired control moves over the control effectors creates the possibility to separate the input allocation problem from the inversion loop when redundant actuators are available. An important part of this paper consists of the application of the proposed theory to an aerospace benchmark of high complexity. It is shown through an example that the theory is well-suited to the task, provided that fault-detection and isolation information is available continuously.