Enrique Baeyens

Design of PID-type controllers using multiobjective genetic algorithms

The design of a PID controller is a multiobjective problem. A plant and a set of specifications to be satisfied are given. The designer has to adjust the parameters of the PID controller such that the feedback interconnection of the plant and the controller satisfies the specifications. These specifications are usually competitive and any acceptable solution requires a tradeoff among them. An approach for adjusting the parameters of a PID controller based on multiobjective optimization and genetic algorithms is presented in this paper. The MRCD (multiobjective robust control design) genetic algorithm has been employed. The approach can be easily generalized to design multivariable coupled and decentralized PID loops and has been successfully validated for a large number of experimental cases.

Wind energy aggregation: A coalitional game approach

In this paper we explore the extent to which a group of N wind power producers can exploit the statistical benefits of aggregation and quantity risk sharing by forming a willing coalition to pool their variable power to jointly offer their aggregate power output as single entity into a forward energy market. We prove that wind power generators will always improve their expected profit when they aggregate their generated power and use tools from coalitional game theory to design fair sharing mechanisms to allocate the payoff among the coalition participants. We show that the corresponding coalitional game is super-additive and has a nonempty core. Hence, there always exists a mechanism for profit-sharing that makes the coalition stable. However, the game is not convex and the celebrated Shapley value may not belong to the core of the game. An allocation mechanism that minimizes the worst-case dissatisfaction is proposed.

Coalitional Aggregation of Wind Power

This paper explores scenarios in which independent wind power producers form willing coalitions to exploit the reduction in aggregate power output variability obtainable through geographic diversity. In the setting of a two settlement electricity market, we examine the advantage gained through optimal coalitional contract offering strategies for quantity risk reduction. We show that a group of independent wind power producers can always improve their expected profit by cooperatively offering their aggregated power. Using coalitional game theory we identify sharing mechanisms to fairly allocate the profits to coalition members. We show that the resulting coalitional game is balanced, guaranteeing that the core of the game is necessarily nonempty. In addition, we propose a profit sharing mechanism that minimizes the worst-case dissatisfaction to recover an imputation in the core. Finally, we illustrate our theoretical results with empirical studies using data from five representative wind farms in upstate New York.

Subspace-based Identification Algorithms for Hammerstein and Wiener Models

Subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented in this paper. The proposed algorithms consist basically of two steps. The first one is a standard subspace-based identification algorithm applied to an auxiliary multivariable linear system whose inputs (respectively outputs) are filtered versions of the original inputs (respectively outputs). The filters are the nonlinear functions describing the static nonlinearities for the Hammerstein case and its inverses for the Wiener case. The second step consists of a 2-norm minimization problem which is solved via Singular Value Decomposition. Consistency of the estimates can be guaranteed under weak assumptions. The performance of the proposed identification algorithms is illustrated through simulation examples.

MRCD: a genetic algorithm for multiobjective robust control design

Abstract A genetic algorithm (GA) for the class of multiobjective optimization problems that appears in the design of robust controllers is presented in this paper. The design of a robust controller is a trade-off problem among competitive objectives such as disturbance rejection, reference tracking, stability against unmodeled dynamics, moderate control effort and so on. However, general methodologies for solving this class of design problems are not easily encountered in the literature because of the complexity of the resultant multiobjective problems. In this paper, a recently developed class of GAs, multiobjective GAs, are used to solve robust control design problems. Here, a new algorithm, called multiobjective robust control design, has been proposed. The structure and operators of this algorithm have been specifically developed for control design problems. The performace of the algorithm is evaluated by solving several test cases and is also compared to the standard algorithms used for the multiobjective design of robust controllers.

Identification of multivariable Hammerstein systems using rational orthonormal bases

A non-iterative algorithm for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein systems is presented. The proposed algorithm is numerically robust, since it is based only on least squares estimation and singular value decomposition. Under weak assumptions on the persistency of excitation of the inputs, the algorithm provides consistent estimates even in the presence of coloured noise. Key in the derivation of the results is the use of rational orthonormal bases for the representation of the linear part of the system. An additional advantage of this is the possibility of incorporating prior information about the system in a typically black-box identification scheme.

Subspace Identification of Multivariable Hammerstein and Wiener Models

Abstract In this paper, subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented. The proposed algorithms consist basically of two steps. The first one is a standard (linear) subspace algorithm applied to an equivalent linear system whose inputs (respectively outputs) are filtered (by the nonlinear functions describing the static nonlinearities) versions of the original inputs (respectively outputs). The second step consists in a 2-norm minimization problem which is solved via a Singular Value Decomposition.

Analysis of changes in the beat-to-beat P-wave morphology using clustering techniques

Several pathologies related to the atrial electrical activity can be detected in the electrocardiogram P-wave. A study on the beat-to-beat P-wave morphology changes of 89 ECG signals is performed in this article. An algorithm based on the embedding space techniques has been used to extract the P-wave information of the ECG. The P-waves obtained in several of these ECGs exhibit intermittent morphology changes. The morphologies have been classified by using the K-means clustering algorithm. The mechanism behind different P-wave morphologies and its possible pathophysiological importance remains to be clarified.

Optimal sharing of quantity risk for a coalition of wind power producers facing nodal prices

It is widely accepted that aggregation of geographically diverse wind energy resources offers compelling potential to mitigate wind power variability, as wind speed at different geographic locations tends to decorrelate with increasing spatial separation. In this paper, we explore the extent to which a coalition of wind power producers can exploit the statistical benefits of aggregation to mitigate the risk of quantity shortfall with respect to forward contract offerings for energy. We propose a simple augmentation of the existing two-settlement market system with nodal pricing to permit quantity risk sharing among wind power producers by affording the group a recourse opportunity to utilize improved forecasts of their ensuing wind energy production to collectively modify their forward contracted positions so as to utilize the projected surplus in generation at certain buses to balance the projected shortfall in generation at complementary buses. Working within this framework, we show that the problem of optimally sizing a set of forward contracts for a group of wind power producers reduces to convex programming and derive closed form expressions for the set of optimal recourse policies. We also asses the willingness of individual wind power producers to form a coalition to cooperatively offer contracts for energy. We first show that the expected profit derived from coalitional contract offerings with recourse is greater than that achievable through independent contract offerings. And, using tools from coalitional game theory, we show that the core for our game is non-empty.

A cooperative game for the realized profit of an aggregation of renewable energy producers

The aggregation of renewable energy has significant potential to mitigate undesirable characteristics such as intermittency and variability and thereby facilitate grid integration. Using cooperative game theory, it has been shown that aggregation is also beneficial for renewable energy producers because they can increase their expected profit by making a coalition, bidding a joint contract that maximizes the expected profit and sharing the profit in a way that keeps the game stable. However, we show that the realized (as opposed to expected) profit of the coalition, using the contract that maximizes the expected profit, cannot be suitably distributed among its members. We propose an alternative coalition contract and prove that it allows for a satisfactory distribution of the realized profit among the coalition members keeping the game stable. We design a new payoff allocation that lies in the core of the game of the realized profit. Finally, we analyze the cost of stabilizing the game by evaluating the loss of expected profit that a coalition incurs by bidding the stabilizing contract.