Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization - A Guide for Parameters Computation Based on Robustness

[EN] A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and are intended as a tool for designers who seek to implement LADRC by considering the load disturbance response of processes whose behavior is approximated by a general first-order system with delay. The validation of the proposed tuning rules is done through illustrative examples and the control of a nonlinear thermal process. Compared to classical PID (Proportional-Integral-Derivative) and other LADRC tuning methods, the derived functions offer an improvement in either disturbance rejection, robustness or both design objectives.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades, Spain, under Grant RTI2018-096904-B-I00.Martínez, BV.; Sanchís Saez, J.; Garcia-Nieto, S.; Martínez Iranzo, MA. (2021). Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization - A Guide for Parameters Computation Based on Robustness. Mathematics. 9(5):1-34. https://doi.org/10.3390/math90505171349

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

[EN] In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature (ArchiveUpdateP(Q,epsilon)D(xy), Archive_nevMOGA, and targetSelect) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades (Spain) (grant number RTI2018-096904-B-I00), by the Generalitat Valenciana regional government through project AICO/2019/055 and by the Universitat Politecnica de Valencia (grant number SP20200109).Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Martínez Iranzo, MA. (2021). A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization. Mathematics. 9(9):1-28. https://doi.org/10.3390/math9090999S1289

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

[EN] New challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented - a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem. (c) 2008 Elsevier Inc. All rights reserved.Partially supported by MEC (Spanish Government) and FEDER funds: Projects DPI2005-07835, DPI2004-8383-C03-02 and GVA-026.Blasco, X.; Herrero Durá, JM.; Sanchís Saez, J.; Martínez Iranzo, MA. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences. 178(20):3908-3928. https://doi.org/10.1016/j.ins.2008.06.010S390839281782

WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy

[EN] Several approaches have been presented to identify Wiener-Hammerstein models, most of them starting from a linear dynamic model whose poles and zeros are distributed around the static non- linearity. To achieve good precision in the estimation, the Best Linear Approximation (BLA) has usually been used to represent the linear dynamics, while static non-linearity has been arbitrarily parameterised without considering model complexity. In this paper, identification of Wiener, Hammerstein or Wiener-Hammerstein models is stated as a multiobjective optimisation problem (MOP), with a trade-off between accuracy and model complexity. Precision is quantified with the Mean-Absolute-Error (MAE) between the real and estimated output, while complexity is based on the number of poles, zeros and points of the static non- linearity. To solve the MOP, WH-MOEA, a new multiobjective evolutionary algorithm (MOEA) is proposed. From a linear structure, WH-MOEA will generate a set of optimal models considering a static non-linearity with a variable number of points. Using WH-MOEA, a procedure is also proposed to analyse various linear structures with different numbers of poles and zeros (known as design concepts). A comparison of the Pareto fronts of each design concept allows a more in-depth analysis to select the most appropriate model according to the user¿s needs. Finally, a complex numerical example and a real thermal process based on a Peltier cell are identified, showing the procedure¿s goodness. The results show that it can be useful to consider the simultaneously precision and complexity of a block-oriented model (Wiener, Hammerstein or Wiener- Hammerstein) in a non-linear process identification.This work was supported in part by the Ministerio de Ciencia, Innovación y Universidades, Spain, under Grant RTI2018-096904-B-I00-AR, and in part by the Salesian Polytechnic University of Ecuador through a Ph.D. scholarships granted to J. Zambrano.Zambrano, J.; Sanchís Saez, J.; Herrero Durá, JM.; Martínez Iranzo, MA. (2020). WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy. IEEE Access. 8:228655-228674. https://doi.org/10.1109/ACCESS.2020.3046352228655228674

Preference driven multi-objective optimization design procedure for industrial controller tuning

Multi-objective optimization design procedures have shown to be a valuable tool for con- trol engineers. These procedures could be used by designers when (1) it is difficult to find a reasonable trade-off for a controller tuning fulfilling several requirements; and (2) if it is worthwhile to analyze design objectives exchange among design alternatives. Despite the usefulness of such methods for describing trade-offs among design alterna- tives (tuning proposals) with the so called Pareto front, for some control problems finding a pertinent set of solutions could be a challenge. That is, some control problems are com- plex in the sense of finding the required trade-off among design objectives. In order to improve the performance of MOOD procedures for such situations, preference handling mechanisms could be used to improve pertinency of solutions in the approximated Pareto front. In this paper an overall MOOD procedure focusing in controller tuning applications using designer s preferences is proposed. In order to validate such procedure, a bench- mark control problem is used and reformulated into a multi-objective problem statement, where different preference handling mechanisms in the optimization process are evalu- ated and compared. The obtained results validate the overall proposal as a potential tool for industrial controller tuning.This work was partially supported by projects TIN2011-28082, ENE2011-25900 from the Spanish Ministry of Economy and Competitiveness. First author gratefully acknowledges the partial support provided by the postdoctoral fellowship BJT-304804/2014-2 from the National Council of Scientific and Technologic Development of Brazil (CNPq) for the development of this work.Reynoso Meza, G.; Sanchís Saez, J.; Blasco Ferragud, FX.; Martínez Iranzo, MA. (2016). Preference driven multi-objective optimization design procedure for industrial controller tuning. Information Sciences. 339:108-131. doi:10.1016/j.ins.2015.12.002S10813133

Nonlinear Robust Identification using Evolutionary Algorithms. Application to a Biomedical Process

[EN] This work describes a new methodology for robust identification (RI), meaning the identification of the parameters of a model and the characterization of uncertainties. The alternative proposed handles non-linear models and can take into account the different properties demanded by the model. The indicator that leads the identification process is the identification error (IE), that is, the difference between experimental data and model response. In particular, the methodology obtains the feasible parameter set (FPS, set of parameter values which satisfy a bounded IE) and a nominal model in a non-linear identification problem. To impose different properties on the model, several norms of the IE are used and bounded simultaneously. This improves the model quality, but increases the problem complexity. The methodology proposes that the RI problem is transformed into a multimodal optimization problem with an infinite number of global minima which constitute the FPS. For the optimization task, a special genetic algorithm (epsilon-GA), inspired by Multiobjective Evolutionary Algorithms, is presented. This algorithm characterizes the FPS by means of a discrete set of models well distributed along the FPS. Finally, an application for a biomedical model which shows the blockage that a given drug produces on the ionic currents of a cardiac cell is presented to illustrate the methodology. (C) 2008 Elsevier Ltd. All rights reserved.Partially supported by MEC (Spanish government) and FEDER funds: Projects DP12005-07835, DP12004-8383-CO3-02 and Generalitat Valenciana (Spain) Project GVA-026.Herrero Durá, JM.; Blasco, X.; Martínez Iranzo, MA.; Ramos Fernández, C.; Sanchís Saez, J. (2008). Nonlinear Robust Identification using Evolutionary Algorithms. Application to a Biomedical Process. Engineering Applications of Artificial Intelligence. 21(8):1397-1408. https://doi.org/10.1016/j.engappai.2008.05.001S1397140821

Model-based predictive control of greenhouse climate for reducing energy and water consumption

[EN] This work focuses on development of control algorithms by incorporating energy and water consumption to maintain climatic conditions in greenhouse. Advanced control algorithms can supply solutions to modern exploitations. The new developments usually require accurate models (probably multivariable and non-linear ones) and control methodologies capable of using these models. As an additional requirement it is important for the final application to be easy to use, so advanced control will not mean an increase in complexity of the manipulation of the installation. This article shows an alternative to classical climate control. It is based on two fundamental elements: an accurate non-linear model and a model-based predictive control (MBPC) that incorporate energy and water consumption. Genetic algorithms (GAs) play a key role in these two elements because functions to solve are non-convex and with local minima. First of all GAs supply a way to adjust the non-linear model parameters obtained from first principles, and finally GAs open the possibility of using non-linear model in the MBPC and of establishing a flexible cost index to minimize energy and water consumption. The results on a plastic greenhouse with arch-shaped roofs and for Mediterranean area are presented, important reduction in energy and water used in the cooling system (nebulization) is obtained. (c) 2006 Elsevier B.V. All rights reserved.Partially supported by MEC (Spanish government) and FEDER funds: projects DPI2004-8383-C03-02 and DPI2005-07835.Blasco, X.; Martínez Iranzo, MA.; Herrero Durá, JM.; Ramos Fernández, C.; Sanchís Saez, J. (2007). Model-based predictive control of greenhouse climate for reducing energy and water consumption. Computers and Electronics in Agriculture. 55(1):49-70. https://doi.org/10.1016/j.compag.2006.12.001S497055

T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws

[EN] This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi-Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum *-norm (upper bound of the 1-norm) for the T-S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.This work has been funded by Ministerio de Economia y Competitividad, Spain (research project RTI2018-096904-B-I00) and Conselleria de Educacion, Cultura y Deporte-Generalitat Valenciana, Spain (research project AICO/2019/055).Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2020). T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws. International Journal of Applied Mathematics and Computer Science (Online). 30(3):529-550. https://doi.org/10.34768/amcs-2020-0039S52955030

Robust identification of non-linear greenhouse model using evolutionary algorithms

[EN] This paper presents the non-linear modelling, based oil first principle equations, for a climatic model of a greenhouse and the estimation of the feasible parameter set (FPS) when the identification error is bounded simultaneously by several norms. The robust identification problem is transformed into a multimodal optimization problem with an infinite number of global minima that constitute the FPS. For the optimization task, a special evolutionary algorithm (epsilon-GA) is presented, which characterizes the FPS by means of a discrete set of models that are well distributed along the FPS. A procedure for determining the norm bounds, such that FPS not equal 0, is (c) 2007 Elsevier Ltd. All rights reserved.Partially supported by MEC (Spanish government) and FEDER funds: projects DPI2005-07835 and DPI2004- 8383-C03-02.Herrero Durá, JM.; Blasco, X.; Martínez Iranzo, MA.; Ramos Fernández, C.; Sanchís Saez, J. (2008). Robust identification of non-linear greenhouse model using evolutionary algorithms. Control Engineering Practice. 16(5):515-530. https://doi.org/10.1016/j.conengprac.2007.06.001S51553016

Applied Pareto multi-objective optimization by stochastic solvers

[EN] It is well known that many engineering design problems with different objectives, some of which can be opposed to one another, can be formulated as multi-objective functions and resolved with the construction of a Pareto front that helps to select the desired solution. Obtaining a correct Pareto front is not a trivial question, because it depends on the complexity of the objective functions to be optimized, the constraints to keep within and, in particular, the optimizer type selected to carry out the calculations. This paper presents new methods for Pareto front construction based on stochastic search algorithms (genetic algorithms, GAs and multi-objective genetic algorithms, MOGAs) that enable a very good determination of the Pareto front and fulfill some interesting specifications. The advantages of these applied methods will be proven by the optimization of well-known benchmarks for metallic supported I-beam and gearbox design. (C) 2008 Elsevier Ltd. All rights reserved.This research has been partially financed by GV06-026 Generalitat Valenciana and DPI2005-07835, MEC (Spain)-FEDER.Martínez Iranzo, MA.; Herrero Durá, JM.; Sanchís Saez, J.; Blasco, X.; García-Nieto, S. (2009). Applied Pareto multi-objective optimization by stochastic solvers. Engineering Applications of Artificial Intelligence. 22(3):455-465. https://doi.org/10.1016/j.engappai.2008.10.018S45546522