D.R. Ramirez

Real-Time Implementation of a Constrained MPC for Efficient Airflow Control in a PEM Fuel Cell

Fuel cells represent an area of great industrial interest due to the possibility to generate clean energy for stationary and automotive applications. It is clear that the proper performance of these devices is closely related to the kind of control that is used; therefore, a study of improved control alternatives is fully justified. The air-supply control is widely used to guarantee safety and to achieve a high performance. This paper deals with this control loop, proposing and comparing two control objectives aimed at satisfying the oxygen starvation avoidance criterion and the maximum efficiency criterion, respectively. The control architecture is based on a constrained explicit model predictive control (MPC) law suitable for real-time implementation due to its low computational demands. The proposed controller is implemented and evaluated on a 1.2-kW polymer electrolyte membrane or proton exchange membrane fuel-cell test bench, thus obtaining real data which show that the maximum efficiency criterion does not conflict with the starvation avoidance criterion and allows system performance improvements of up to 3.46%. Moreover, experimental results utilizing the explicit MPC approach also show improved transient responses compared to those of the manufacturers control law.

Model Predictive Control techniques for Hybrid Systems

Abstract This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.

Randomized methods for design of uncertain systems

In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the binomial distribution and related tail inequalities, and compute the sample complexity. This contribution significantly improves the existing results by reducing the number of required samples in the randomized algorithm. These results are then applied to the analysis of worst-case performance and design with robust optimization. The second contribution of the paper is to introduce a general class of sequential algorithms, denoted as Sequential Probabilistic Validation (SPV). In these sequential algorithms, at each iteration, a candidate solution is probabilistically validated, and corrected if necessary, to meet the required specifications. The results we derive provide the sample complexity which guarantees that the solutions obtained with SPV algorithms meet some pre-specified probabilistic accuracy and confidence. The performance of these algorithms is illustrated and compared with other existing methods using a numerical example dealing with robust system identification.

Constrained explicit predictive control strategies for PEM fuel cell systems

This paper presents the development of an explicit predictive control strategy for a stand-alone PEM (polymer electrolyte membrane) fuel cell. This fuel cell can be considered as a good benchmark since it is representative of the state of the art of PEM technology and is used by many research groups. The experiments are performed on a detailed nonlinear simulator of a fuel cell which has been validated experimentally. In order to achieve real-time implementation of the control strategy, the predictive control algorithm must be computed in a explicit way because of the sampling time of this system, which is in the order of milliseconds. The work shows the development and simulation results of the constrained explicit predictive controller that reduces the computational effort needed.

Min-max predictive control of a heat exchanger using a neural network solver

Min-max model predictive controllers (MMMPC) have been proposed for the control of linear plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the numerical optimization problem that has to be solved at every sampling time. This fact severely limits the class of processes in which this control is suitable. In this brief, the use of a neural network (NN) to approximate the solution of the min-max problem is proposed. The number of inputs of the NN is determined by the order and time delay of the model together with the control horizon. For large time delays the number of inputs can be prohibitive. A modification to the basic formulation is proposed in order to avoid this latter problem. Simulation and experimental results are given using a heat exchanger.

Implementation of min–max MPC using hinging hyperplanes. Application to a heat exchanger ☆

Abstract Min–max model predictive control (MMMPC) is one of the few control techniques able to cope with modelling errors or uncertainties in an explicit manner. The implementation of MMMPC suffers a large computational burden due to the numerical min–max problem that has to be solved at every sampling time. This fact severely limits the range of processes to which this control structure can be applied. An implementation scheme based on hinging hyperplanes that overcome these problems is presented here. Experimental results obtained when applying the controller to the heat exchanger of a pilot plant are given.

On the piecewise linear nature of min-max model predictive control with bounded uncertainties

This paper shows how a min-max model predictive control with bounded additives uncertainties and a quadratic cost function results in a piecewise linear control law. Proofs based on properties of the cost function and the optimization problem are given. The results are illustrated by a simulation example.

Explicit solution of min–max MPC with additive uncertainties and quadratic criterion

Abstract Min–max model predictive control (MMMPC) is one of the strategies proposed to control plants subject to bounded uncertainties. This technique is very difficult to implement in real time because of the computation time required. Recently, the piecewise affine nature of this control law has been proved for unconstrained linear systems with quadratic performance criterion. However, no algorithm to compute the explicit form of the control law was given. This paper shows how to obtain this explicit form by means of a constructive algorithm. An approximation to MMMPC in the presence of constraints is presented based on this algorithm.

Brief paper: Min-max MPC using a tractable QP problem

Min-Max MPC (MMMPC) controllers [5] suffer from a great computational burden that is often circumvented by using upper bounds of the worst possible case of a performance index. These upper bounds are usually computed by means of linear matrix inequalities (LMI) techniques. In this paper a more efficient approach is shown. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min-max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min-max problem and the resulting control is shown to have guaranteed stability. Simulation examples are given in the paper.

Efficient implementation of constrained min-max model predictive control with bounded uncertainties

Min-max model predictive control (MMMPC) is one of the strategies used to control plants subject to bounded additive uncertainties. The implementation of MMMPC suffers a large computational burden, especially when hard constraints are taken into account, due to the complex numerical optimization problem that has to be solved at every sampling time. The paper shows how to overcome this by transforming the original problem into a reduced min-max problem whose solution is much simpler. In this way, the range of processes to which MMMPC can be applied is considerably broadened. Proofs based on the properties of the cost function and a simulation example are given in the paper.