@article {Boeira:Bordignon:eckhard:Campestrini:2018, title = {Comparing MIMO Process Control Methods on a Pilot Plant}, journal = {Journal of Control, Automation and Electrical Systems}, volume = {29}, number = {4}, year = {2018}, note = {n/a}, month = {Aug}, pages = {411{\textendash}425}, abstract = {

This work presents a comparison among three different control strategies for multivariable processes. The techniques were implemented in a pilot plant with coupled control loops, where all steps used to design the controllers were described allowing to establish a trade-off between algorithm complexity, information needed from the process and achieved performance. Two data-driven control techniques are used: multivariable ultimate point method to design a decentralized PID controller and virtual reference feedback tuning to design a centralized PID controller. A mathematical model of the process is obtained and used to design a model-based generalized predictive controller. Experimental results allow us to evaluate the performance achieved for each method, as well as to infer on their advantages and disadvantages.

}, issn = {2195{\textendash}3899}, doi = {10.1007/s40313-018-0387-6}, author = {E. Boeira and Bordignon, V. and D. Eckhard and L. Campestrini} } @conference {Boeira:Eckhard:2018, title = {Multivariable Virtual Reference Feedback Tuning with Bayesian regularization}, booktitle = {XXII Congresso Brasileiro de Autom{\'a}tica}, year = {2018}, note = {n/a}, pages = {1{\textendash}8}, publisher = {{SBA} Sociedade Brasileira de Autom{\'a}tica}, organization = {{SBA} Sociedade Brasileira de Autom{\'a}tica}, address = {Jo{\~a}o Pessoa}, abstract = {

This paper proposes the use of regularization on the multivariable formulation of the Virtual Reference Feedback Tuning (VRFT). When the process to be controlled has a significant amount of noise, the standard VRFT approach, that uses the instrumental variable technique, provides estimates with very poor statistical properties. To cope with that, this paper considers the use of regularization on the estimation procedure, reducing the covariance error at the cost of inserting a small bias. Also, this paper explains different types of regularization matrices and presents the methodology to tune these matrices. In order to demonstrate the benefits of the proposed formulation, a numerical example is presented.

}, doi = {10.20906/CPS/CBA2018-1060}, author = {E. C. Boeira and D. Eckhard} } @article {Eckhard:Campestrini:Boeira:2018, title = {Virtual Disturbance Feedback Tuning}, journal = {IFAC Journal of Systems and Control}, volume = {3}, year = {2018}, note = {n/a}, pages = {23{\textendash}29}, abstract = {n/a}, issn = {2468{\textendash}6018}, doi = {https://doi.org/10.1016/j.ifacsc.2018.01.003}, author = {D. Eckhard and L. Campestrini and E. C. Boeira} } @article {Campestrini:Eckhard:Bazanella:Gevers:2017, title = {Data-driven model reference control design by prediction error identification}, journal = {Journal of the Franklin Institute}, volume = {354}, number = {6}, year = {2017}, note = {n/a}, month = {April}, pages = {2828{\textendash}2647}, abstract = {

Abstract This paper deals with Data-Driven (DD) control design in a Model Reference (MR) framework. We present a new \{DD\} method for tuning the parameters of a controller with a fixed structure. Because the method originates from embedding the control design problem in the Prediction Error identification of an optimal controller, it is baptized as Optimal Controller Identification (OCI). Incorporating different levels of prior information about the optimal controller leads to different design choices, which allows to shape the bias and variance errors in its estimation. It is shown that the limit case where all available prior information is incorporated is tantamount to model-based design. Thus, this methodology also provides a framework in which model-based design and \{DD\} design can be fairly and objectively compared. This comparison reveals that \{DD\} design essentially outperforms model-based design by providing better bias shaping, except in the full order controller case, in which there is no bias and model-based design provides smaller variance. The practical effectiveness of the design methodology is illustrated with experimental results.

}, issn = {0016{\textendash}0032}, doi = {10.1016/j.jfranklin.2016.08.006}, author = {L. Campestrini and D. Eckhard and A. S. Bazanella and M. Gevers} } @article {Eckhard:Bazanella:Rojas:Hjalmarsson:2017, title = {Cost function shaping of the output error criterion}, journal = {Automatica}, volume = {76}, year = {2017}, note = {

n/a

}, pages = {53{\textendash}60}, abstract = {

Abstract Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because in most cases both the corresponding objective function and the search space are nonconvex. The difficulty in solving the optimization problem depends mainly on the experimental conditions, more specifically on the spectra of the input/output data collected from the system. It is therefore possible to improve the convergence of the algorithms by properly choosing the data prefilters; in this paper we show how to perform this choice. We present the application of the proposed approach to case studies where the standard algorithms tend to fail to converge to the global minimum.

}, keywords = {Model fitting}, issn = {0005{\textendash}1098}, doi = {http://dx.doi.org/10.1016/j.automatica.2016.10.015}, url = {//www.sciencedirect.com/science/article/pii/S0005109816304198}, author = {Diego Eckhard and Alexandre S. Bazanella and Cristian R. Rojas and Hakan Hjalmarsson} } @conference {Scheid:Eckhard:Goncalves:Campestrini:2016, title = {Application of Virtual Reference Feedback Tuning to a non-minimum phase pilot plant}, booktitle = {2016 IEEE Conference on Control Applications (CCA)}, year = {2016}, note = {n/a}, month = {Sept}, pages = {1318{\textendash}1323}, publisher = {IEEE}, organization = {IEEE}, address = {Buenos Aires}, abstract = {

Virtual Reference Feedback Tuning (VRFT) is a data-driven technique used to design controllers without the need of a process model, only input-output data is utilized. When the process has non-minimum phase (NMP) zeros, the original method usually presents poor performance, because scarcely the reference model has the same NMP zeros as the process. To overcome this problem, a flexible criterion has been proposed to the VRFT method, in a way that both the controller parameters and the NMP zeros of the process are estimated together. In this paper we present the application of the VRFT method with flexible criterion to the level control of a MIMO pilot plant. We show that a sequential controller design may incorporate NMP behavior to the process. We then use the VRFT method with flexible criterion to design the controller using only closed-loop data from the process.

}, keywords = {Adaptation models, closed loop systems, closed-loop data, control system synthesis, Data models, data-driven technique, feedback, level control, MIMO pilot plant, MIMO systems, nonminimum phase pilot plant, nonminimum phase zeros, Process control, sequential controller design, Standards, Transfer functions, Tuning, Valves, virtual reference feedback tuning, VRFT}, doi = {10.1109/CCA.2016.7587989}, author = {R. {Scheid Filho} and D. Eckhard and G. R. {Gon{\c c}alves da Silva} and L. Campestrini} } @conference {Salton:Eckhard:Flores:Fernandes:Azevedo:2016, title = {Disturbance observer and nonlinear damping control for fast tracking quadrotor vehicles}, booktitle = {2016 IEEE Conference on Control Applications (CCA)}, year = {2016}, note = {n/a}, month = {Sept}, pages = {705{\textendash}710}, publisher = {IEEE}, organization = {IEEE}, address = {Buenos Aires}, abstract = {

This paper considers the design and implementation of a discrete-time fast tracking controller for quadrotor vehicles subject to perturbations. The proposed controller consists of a model-based disturbance observer and a Composite Nonlinear Feedback (CNF) controller. The CNF control law introduces nonlinear damping to the system so that it possesses a fast rise time without overshoot. The least square identification method is applied to develop a model based disturbance observer, thus decoupling the problems of track following and disturbance rejection. Experimental results are provided in order to validate the proposed approach.

}, keywords = {CNF controller, composite nonlinear feedback controller, control system synthesis, Control systems, damping, discrete time systems, discrete-time fast tracking controller design, disturbance rejection, fast tracking quadrotor vehicles, feedback, helicopters, least square identification method, least squares approximations, Mathematical model, model-based disturbance observer, nonlinear control systems, nonlinear damping control, observers, perturbation techniques, perturbations, Sensors, track following problems, Vehicle dynamics, Vehicles}, doi = {10.1109/CCA.2016.7587901}, author = {A. T. Salton and D. Eckhard and J. V. Flores and G. Fernandes and G. Azevedo} } @conference {Flores:Eckhard:Salton:2016, title = {Modified {MIMO} Resonant Controller Robust to Period Variation and Parametric Uncertainty}, booktitle = {2016 {IEEE} Conference on Control Applications ({CCA})}, year = {2016}, note = {n/a}, month = {Sept}, pages = {1256{\textendash}1261}, publisher = {IEEE}, organization = {IEEE}, address = {Buenos Aires}, abstract = {

In this work a modified Resonant Controller is proposed to deal with the tracking/rejection problem of periodic signals robust to period variations and parametric uncertainties in the plant. The control strategy is based on a resonant structure in series with a notch filter, which will be responsible to improve the robustness to period variation. A robust state feedback controller is designed by solving a linear matrix inequality (LMI) optimization problem guaranteeing the robust stability of the closed loop system. A numerical example is presented to illustrate the method.

}, keywords = {Aerospace electronics, closed loop system, closed loop systems, control strategy, control system synthesis, feedback, Frequency control, Harmonic analysis, linear matrix inequalities, linear matrix inequality, LMI, MIMO, MIMO resonant controller robust, MIMO systems, parametric uncertainty, period variation, periodic signals robust, rejection problem, Resonant frequency, robust control, robust stability, robust state feedback controller designed, Robustness, tracking problem, Uncertainty}, doi = {10.1109/CCA.2016.7587979}, author = {J. V. Flores and D. Eckhard and A. T. Salton} } @conference {Tesch:Eckhard:Bazanella:2016, title = {Iterative feedback tuning for cascade systems}, booktitle = {2016 European Control Conference (ECC)}, year = {2016}, note = {n/a}, month = {June}, pages = {495{\textendash}500}, address = {Aalborg}, abstract = {

Iterative Feedback Tuning (IFT) is a data-driven method used to tune parameters of feedback controllers minimising an H2 criterion. The method uses data from experiments to estimate the gradient of the criterion, and uses iterative quasinewton algorithms to adjust the controllers. When the method is used in cascade systems, usually the inner loop is firstly adjusted, and after the outer loop. In this article we describe an extension to the IFT method that adjusts both inner and outer loop at the same time using only data from closed-loop experiments at each iteration.

}, keywords = {Cost function, Electronic mail, Iterative methods, Mathematical model, Transfer functions, Tuning}, doi = {10.1109/ECC.2016.7810333}, author = {D. Tesch and D. Eckhard and A. S. Bazanella} } @article {Campestrini:Eckhard:Chia:Boeira:2016, title = {Unbiased MIMO VRFT with application to process control}, journal = {Journal of Process Control}, volume = {39}, year = {2016}, note = {

n/a

}, pages = {35{\textendash}49}, abstract = {

Abstract Continuous process industries usually have hundreds to thousands of control loops, most of which are coupled, i.e. one control loop affects the behavior of another control loop. In order to properly design the controllers and reduce the interactions between loops it is necessary to consider the multivariable structure of the process. Usually {MIMO} (multiple-input, multiple-output) controllers are designed using {MIMO} models of the process, but obtaining these models is a task very demanding and time consuming. Virtual Reference Feedback Tuning ({VRFT}) is a data-driven technique to design controllers which do not use a model of the process; all the needed information is collected from input/output data from an experiment. The method is well established for {SISO} (single-input, single-output) systems and there are some extensions to {MIMO} process which assume that all the outputs should have the same closed-loop performance. In this paper we develop a complete framework to {MIMO} {VRFT} which provides unbiased estimates to the optimal {MIMO} controller (when it is possible) even when the closed-loop performances are distinct to each loop. When it is not possible to obtain the optimal controller because the controller class is too restrictive (for example {PID} controllers) then we propose the use of a filter to reduce the bias on the estimates. Also, when the data is corrupted by noise, the use of instrumental variables to eliminate the bias on the estimate should be considered. The article presents simulation examples and a practical experiment on a tree tank system where the goal is to control the level of two tanks.

}, issn = {0959{\textendash}1524}, doi = {http://dx.doi.org/10.1016/j.jprocont.2015.12.010}, author = {L. Campestrini and D. Eckhard and L. A. Ch{\'\i}a and E. Boeira} } @conference {Silva:Brusamarello:Eckhard:Pereira:Netto:Muller:2016, title = {Contactless Battery Charger Controller for Wireless Sensor Node}, booktitle = {Symposium on Instrumentation Systems, Circuits and Transducers (INSCIT)}, year = {2016}, note = {n/a}, address = {Belo Horizonte}, abstract = {n/a}, author = {R. W. P. da Silva and V. Brusamarello and D. Eckhard and C. E. Pereira and J. C. Netto and I. M{\"u}ller} } @conference {Haselein:Poleto:Konrad:Eckhard:2016, title = {Identifica{\c c}{\~a}o de par{\^a}metros de um modelo din{\^a}mico para biorretores anaer{\'o}bicos}, booktitle = {7a Confer{\^e}ncia Internacional de Materiais e Processos para Energias Renov{\'a}veis}, year = {2016}, note = {n/a}, pages = {1{\textendash}7}, address = {Porto Alegre}, abstract = {n/a}, author = {W. Haselein and C. Poleto and O. Konrad and D. Eckhard} } @conference {Tesch:Eckhard:Guarienti:2016, title = {Pitch and Roll control of a Quadcopter using Cascade Iterative Feedback Tuning}, booktitle = {4th {IFAC} Symposium on Telematics Applications}, year = {2016}, note = {n/a}, pages = {30{\textendash}35}, publisher = {IFAC}, organization = {IFAC}, address = {Porto Alegre}, abstract = {

Quadcopter is a type of Unmanned Aerial Vehicle which is lifted and propelled by four rotors. The vehicle has a complex non-linear dynamic which makes the tuning of the roll and pitch controllers difficult. Usually the control design is based on a mathematical model which is strongly related to physical components of vehicle: mass, moment of inertia and aerodynamic. When a tool is attached to the vehicle, a new model must be computed to redesign the controllers. In this article we will adjust the controllers of a real experimental quadcopter using the Cascade Iterative Feedback Tuning method. The method is data-driven, so it does not uses a model for the vehicle; all it uses is input-output data collect from the closed-loop system. The method minimizes the \{H2\} error between the desired response and the actual response of the vehicle angle using the Newton-Raphson algorithm. The method achieves the desired performance without the need of the vehicle model, with low cost and low complexity.

}, issn = {2405{\textendash}8963}, doi = {10.1016/j.ifacol.2016.11.118}, author = {D. A. Tesch and D. Eckhard and W. C. Guarienti} } @conference {sartori:eckhard:2016, title = {Tratamento do fator de decaimento exponencial para o Modelo {Diebold-Li} no ajuste da {ETTJ} brasileira}, booktitle = {Congresso Nacional de Matem{\'a}tica Aplicada e Computacional}, year = {2016}, note = {n/a}, address = {Gramado}, abstract = {n/a}, doi = {10.5540/03.2017.005.01.0122}, author = {L. D. Sartori and D. Eckhard} } @conference {Silva:Eckhard:Muller:Winter:Pereira:Netto:2016, title = {{PI}-based Transmission Power Control for {WirelessHART} Field Devices}, booktitle = {4th {IFAC} Symposium on Telematics Applications}, year = {2016}, note = {n/a}, pages = {343{\textendash}348}, publisher = {IFAC}, organization = {IFAC}, address = {Porto Alegre}, abstract = {

Wireless networks are gaining space in industrial environments due to the low installation costs and low maintenance. Robustness is also one of the main requirements for these systems to be adopted, and, in this context, WirelessHART (WH), ISA SP100.11a, and WIA-PA protocols met these characteristics. In order to provide low maintenance, these protocols must provide reliable radio links while keeping low power consumption to allow battery powered devices. Unfortunately, the standards of these protocols do not impose any RF power modulation technique, which is a form to increase even more the battery endurance of a wireless field device. Instead, RF power levels are fixed and selected by commissioning, and must allow the longest link per device. In this case, devices in closer ranges waste energy during transmissions, as they could save energy by modulating the RF power. This paper presents a RF power modulation technique that employs a proportional-integral controller and allows reduction of energy consumption while keeping the robustness of RF links. A proof of concept of the power modulation technique is implemented and verified showing good results and proving that the proposed controller is feasible. The proposal has the advantage to be fully compatible with the standard.

}, issn = {2405{\textendash}8963}, doi = {10.1016/j.ifacol.2016.11.159}, author = {R. P. da Silva and D. Eckhard and I. M{\"u}ller and J. M. Winter and C. E. Pereira and J. C. Netto} } @conference {Eckhard:Campestrini:2015, title = {An{\'a}lise do uso de modelos discretizados para identifica\c{a}{\~a}o de modelos de biorreatores anaer{\'o}bicos}, booktitle = {Proceeding Series of the Brazilian Society of Applied and Computational Mathematics}, year = {2015}, note = {n/a}, pages = {10059-1 {\textendash} 10059-7}, address = {Natal}, abstract = {n/a}, doi = {10.5540/03.2016.004.01.0059}, author = {D. Eckhard and L. Campestrini} } @conference {Eckhard:Mattos:Tesch:2015, title = {Aplica{\c c}{\~a}o do m{\'e}todo {VRFT} no projeto de controle de quadric{\'o}pteros}, booktitle = {Proceeding Series of the Brazilian Society of Applied and Computational Mathematics}, year = {2015}, note = {n/a}, pages = {10092-1 {\textendash} 10092-7}, address = {Natal}, abstract = {n/a}, doi = {10.5540/03.2016.004.01.0092}, author = {D. Eckhard and A. A. D. de Mattos and D. Tesch} } @conference {Garcia:Eckhard:Netto:Pereira:Muller:2015, title = {Bluetooth Enabled Data Collector for Wireless Sensor Networks}, booktitle = {2015 Brazilian Symposium on Computing Systems Engineering (SBESC)}, year = {2015}, note = {n/a}, pages = {54{\textendash}57}, publisher = {IEEE}, organization = {IEEE}, address = {Foz do Igua{\c c}u}, abstract = {

The wireless sensor networks (WSN) are gradually gaining attention because it is a key technology for the Internet of Things. For most of these networks, the data is usually collected in a manual way, by removing a memory unit or connecting the collector node to a personal computer. This is a constraint, because it demands the manipulation of the collector radio by the operator, which consists in a problem in practical applications. The main goal of this work is to present a non-invasive alternative way to collect the data by means of Bluetooth technology. The approach allows the development of hermetic devices, which is a desirable feature for practical deployment of the sensor nodes.

}, doi = {10.1109/SBESC.2015.17}, author = {C. S. Garcia and D. Eckard and J. C. Netto and C. E. Pereira and I. M{\"u}ller} } @conference {Eckhard:Campestrini:Boeira:GomesdaSilva:2014, title = {Aplica{\c c}{\~a}o de m{\'e}todos de controle baseado em dados em um sistema de controle de n{\'\i}vel industrial}, booktitle = {XVI Congreso Latinoamericano de Control Autom{\'a}tico}, year = {2014}, note = {n/a}, pages = {1410{\textendash}1415}, publisher = {AMCA}, organization = {AMCA}, address = {Canc{\'u}n}, abstract = {

Os m{\'e}todos de projeto de controladores baseado em dados s{\~a}o um conjunto de t{\'e}cnicas utilizadas para ajustar os ganhos de controladores, que n{\~a}o utilizam um modelo matem{\'a}tico do processo na sintonia dos par{\^a}metros. Alguns destes m{\'e}todos s{\~a}o o Iterative Feedback Tuning (IFT), Correlation based Tuning (CbT), Virtual Reference Feedback Tuning (VRFT) e Optimal Controller Identification (OCI). Apesar de algumas destas t{ {\'e}cnicas existirem por mais de uma d{\'e}cada, s{\~a}o encontrados poucos trabalhos na literatura que demonstram a aplicabilidade dos m{\'e}todos em sistemas industriais. Neste trabalho duas t{\'e}cnicas de projeto de controladores baseado em dados n{\~a}o-iterativas (VRFT e OCI) s{\~a}o aplicadas em em um sistema de controle de n{\'\i}vel industrial, que utiliza uma rede Foundation Fieldbus H1. O trabalho demostra que as t{\'e}cnicas apresentadas podem ser aplicadas com facilidade em sistemas industriais gerando repostas din{\^a}micas satisfat{\'o}rias.

}, author = {D. Eckhard and L. Campestrini and E. Boeira and J. M. {Gomes da Silva Jr.}} } @conference {Muller:Winter:Pereira:Netto:Eckhard:2014, title = {Automatic {RF} power adjustment for {WirelessHART} field devices}, booktitle = {2014 IEEE International Conference on Industrial Technology}, year = {2014}, note = {n/a}, pages = {749{\textendash}753}, publisher = {IEEE}, organization = {IEEE}, address = {Busan}, abstract = {

Industrial wireless networks are gradually being adopted in industry, especially due to the low installation costs and low maintenance provided by these systems. For the use in harsh environments, the communication system should provide reliable radio links and low power to allow battery powered devices. In this context, WirelessHART, ISA SP100.11a and WIA-PA protocols were developed to meet these requirements. The standards of these protocols define a minimum number of RF fixed power and selectable only by commissioning. Within this scenario, it is important to adapt RF power modulation, a procedure already used in several communication protocols to minimize the energy consumption of transceivers while maintaining link quality. In this paper, three ways to modulate RF power are analyzed within WirelessHART field devices. A specific approach that works in a decentralized way is developed and the results show it can save 50\% of energy in certain cases. The proposal has the extra advantage to be compatible with the standard.

}, doi = {10.1109/ICIT.2014.6895025}, author = {I. M{\"u}ller and J. M. Winter and C. E. Pereira and J. C. Netto and D. Eckhard} } @article {Campestrini:Eckhard:Rui:Bazanella:2014, title = {Identifiability Analysis and Prediction Error Identification of Anaerobic Batch Bioreactors}, journal = {Journal of Control, Automation and Electrical Systems}, volume = {25}, number = {4}, year = {2014}, note = {n/a}, pages = {438{\textendash}447}, abstract = {

This paper presents the identifiability analysis of a nonlinear model for a batch bioreactor and the estimation of the identifiable parameters within the prediction error framework. The output data of the experiment are the measurements of the methane gas generated by the process, during 37 days, and knowledge of the initial conditions is limited to the initial quantity of chemical oxygen demand. It is shown by the identifiability analysis that only three out of the eight model parameters can be identified with the available measurements and that identification of the remaining parameters would require further knowledge of the initial conditions. A prediction error algorithm is implemented for the estimation of the identifiable parameters. This algorithm is iterative, relies on the gradient of the prediction error, whose calculation is implemented recursively, and consists of a combination of two classic optimization methods: the conjugated gradient method and the Gauss?Newton method.

}, issn = {2195{\textendash}3880}, doi = {10.1007/s40313-014-0129-3}, author = {L. Campestrini and D. Eckhard and R. Rui and A. S. Bazanella} } @article {GomesdaSilva:Castelan:Corso:Eckhard:2013, title = {Dynamic output feedback stabilization for systems with sector-bounded nonlinearities and saturating actuators}, journal = {Journal of the Franklin Institute}, volume = {350}, number = {3}, year = {2013}, note = {n/a}, pages = {464{\textendash}484}, abstract = {

In the present work a systematic methodology for computing dynamic output stabilizing feedback control laws for nonlinear systems subject to saturating inputs is presented. In particular, the class of Lur{\textquoteright}e type nonlinear systems is considered. Based on absolute stability tools and a modified sector condition to take into account input saturation effects, an \{LMI\} framework is proposed to design the controller. Asymptotic as well as input-to-state and input-to-output (in a L2 sense) stabilization problems are addressed both in regional (local) and global contexts. The controller structure is composed of a linear part, an anti-windup loop and a term associated to the output of the dynamic nonlinearity. Convex optimization problems are proposed to compute the controller considering different optimization criteria. A numerical example illustrates the potentialities of the methodology.

}, issn = {0016{\textendash}0032}, doi = {10.1016/j.jfranklin.2012.12.009}, author = {J. M. {Gomes da Silva Jr.} and E. B. Castelan and J. Corso and D. Eckhard} } @article {Eckhard:Bazanella:Rojas:Hjalmarsson:2013, title = {Input design as a tool to improve the convergence of {PEM}}, journal = {Automatica}, volume = {49}, number = {11}, year = {2013}, note = {n/a}, pages = {3282{\textendash}3291}, abstract = {

The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The shape of the cost function, and hence the difficulty in solving the optimization problem, depends directly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. Therefore, it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input; in this paper, we address this problem. We present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design. We present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima.

}, issn = {0005-1098}, doi = {10.1016/j.automatica.2013.08.027}, author = {D. Eckhard and A. S. Bazanella and C. R. Rojas and H. Hjalmarsson} } @book {Bazanella:Campestrini:Eckhard:2012, title = {Data-driven Controller Design: The ${H}_2$ Approach}, year = {2012}, note = {n/a}, publisher = {Springer}, organization = {Springer}, address = {Netherlands}, abstract = {

Data-driven methodologies have recently emerged as an important paradigm alternative to model-based controller design and several such methodologies are formulated as an H2 performance optimization. This book presents a comprehensive theoretical treatment of the H2 approach to data-driven control design. The fundamental properties implied by the H2 problem formulation are analyzed in detail, so that common features to all solutions are identified. Direct methods (VRFT) and iterative methods (IFT, DFT, CbT) are put under a common theoretical framework. The choice of the reference model, the experimental conditions, the optimization method to be used, and several other designer?s choices are crucial to the quality of the final outcome, and firm guidelines for all these choices are derived from the theoretical analysis presented. The practical application of the concepts in the book is illustrated with a large number of practical designs performed for different classes of processes: thermal, fluid processing and electromechanical.

}, doi = {10.1007/978-94-007-2300-9}, author = {A. S. Bazanella and L. Campestrini and D. Eckhard} } @mastersthesis {Eckhard:2012, title = {Ferramentas para melhoria da converg{\^e}ncia dos m{\'e}todos de identifica{\c c}{\~a}o por erro de predi{\c c}{\~a}o}, year = {2012}, note = {n/a}, school = {Universidade Federal do Rio Grande do Sul}, type = {phd}, address = {Porto Alegre}, abstract = {

The Prediction Error Method is related to a non-convex optimization problem. It is usual to apply iterative algorithms to solve this optimization problem. However, iterative algorithms can get stuck at a local minimum of the cost function or converge to the border of the searching space. An analysis of the cost function and sufficient conditions to ensure the convergence of the iterative algorithms to the global minimum are presented in this work. It is observed that this conditions depend on the spectrum of the input signal used in the experiment. This work presents tools to improve the convergence of the algorithms to the global minimum, which are based on the manipulation of the input spectrum.

}, url = {http://hdl.handle.net/10183/75872}, author = {D. Eckhard} } @conference {Campestrini:Eckhard:Konrad:Bazanella:2012, title = {Identifica{\c c}{\~a}o n{\~a}o-linear de um biorreator atrav{\'e}s da minimiza{\c c}{\~a}o do erro de predi{\c c}{\~a}o}, booktitle = {XIX Congresso Brasileiro de Autom{\'a}tica}, year = {2012}, note = {n/a}, pages = {3066{\textendash}3072}, publisher = {SBA}, organization = {SBA}, address = {Campina Grande}, abstract = {

This work presents a non-linear identification of a bioreactor through the minimization of the prediction error, where the output data are the measurements of the methane gas generated by the process, during 37 days. Since the chosen model is non-linear, an iterative method is used to obtain the model parameters. This method depends on the cost function?s gradient, whose calculus is implemented recursively, since it does not have a closed form. The algorithm used in the minimization of the cost function is a combination of two methods: the gradient method and the Newton-Raphson method. The model obtained is validated with output data from the process and it reproduces the behavior of the bioreactor with good precision.

}, author = {L. Campestrini and D. Eckhard and O. Konrad and A. S. Bazanella} } @conference {Eckhard:Hjalmarsson:Rojas:Gevers:2012, title = {Mean-Squared Error Experiment Design for Linear Regression Models}, booktitle = {16th {IFAC} Symposium on System Identification}, year = {2012}, note = {n/a}, pages = {1629{\textendash}1634}, publisher = {IFAC}, organization = {IFAC}, address = {Brussels}, abstract = {

This work solves an experiment design problem for a linear regression problem using a reduced order model. The quality of the model is assessed using a mean square error measure that depends linearly on the parameters. The designed input signal ensures a predefined quality of the model while minimizing the input energy.

}, doi = {10.3182/20120711-3-BE-2027.00339}, author = {D. Eckhard and H. Hjalmarsson and C. Rojas and M. Gevers} } @conference {Campestrini:Eckhard:Bazanella:Gevers:2012, title = {Model Reference Control Design by Prediction Error Identification}, booktitle = {16th {IFAC} Symposium on System Identification}, year = {2012}, note = {n/a}, pages = {1478{\textendash}1483}, publisher = {IFAC}, organization = {IFAC}, address = {Brussels}, abstract = {

This paper studies a one-shot (non-iterative) data-based method for Model Reference (MR) control design. It shows that the optimal controller can be obtained as the solution of a Prediction Error (PE) identification problem that directly estimates the controller parameters through a reparametrization of the input-output model. The standard tools of PE Identification can thus be used to analyze the statistical properties (bias and variance) of the estimated controller. It also shows that, for MR control design, direct and indirect data-based methods are essentially equivalent.

}, doi = {10.3182/20120711-3-BE-2027.00190}, author = {L. Campestrini and D. Eckhard and A. S. Bazanella and M. Gevers} } @conference {Eckhard:Bazanella:Rojas:Hjalmarsson:2012, title = {On the Convergence of the Prediction Error Method to Its Global Minimum}, booktitle = {16th {IFAC} Symposium on System Identification}, year = {2012}, note = {n/a}, pages = {698{\textendash}703}, publisher = {IFAC}, organization = {IFAC}, address = {Brussels}, abstract = {

The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The existence of local minima, and hence the difficulty in solving the optimization, depends mainly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. It is therefore possible to avoid the existence of local minima by properly choosing the spectrum of the input; in this paper we show how to perform this choice. We present sufficient conditions for the convergence of PEM to the global minimum and from these conditions we derive two approaches to avoid the existence of nonglobal minima. We present the application of one of these two approaches to a case study where standard identification toolboxes tend to get trapped in nonglobal minima.

}, doi = {10.3182/20120711-3-BE-2027.00371}, author = {D. Eckhard and A. S. Bazanella and C. Rojas and H. Hjalmarsson} } @article {Eckhard:Bazanella:2012b, title = {Optimizing the convergence of data-based controller tuning}, journal = {Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering}, volume = {226}, number = {4}, year = {2012}, note = {n/a}, pages = {563{\textendash}574}, abstract = {

Data-based control design methods most often consist of iterative adjustment of the controller?s parameters towards the parameter values which minimize an Formula performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization algorithm ? no process model is used. Two topics are important regarding this algorithm: the convergence rate and the convergence to the global minimum. This paper discusses these issues and provides a method for choosing the step size to ensure convergence with high convergence rate, as well as a test to verify at each step whether or not the algorithm is converging to the global minimum.

}, issn = {0959{\textendash}6518}, doi = {10.1177/0959651811426062}, author = {D. Eckhard and A. S. Bazanella} } @article {Eckhard:Bazanella:2012, title = {Robust convergence of the steepest descent method for data-based control}, journal = {International Journal of Systems Science}, volume = {43}, number = {10}, year = {2012}, note = {n/a}, pages = {1969{\textendash}1975}, abstract = {

Iterative data-based controller tuning consists of iterative adjustment of the controller parameters towards the parameter values which minimise an {H2} performance criterion. The convergence to the global minimum of the performance criterion depends on the initial controller parameters and on the step size of each iteration. This article presents convergence properties of iterative algorithms when they are affected by disturbances.

}, issn = {0020{\textendash}7721}, doi = {10.1080/00207721.2011.563874}, author = {D. Eckhard and A. S. Bazanella} } @conference {Eckhard:Bazanella:2011, title = {On the global convergence of identification of output error models}, booktitle = {18th {IFAC} World congress}, year = {2011}, note = {n/a}, pages = {9058{\textendash}9063}, publisher = {IFAC}, organization = {IFAC}, address = {Milan}, abstract = {

The Output Error Method is related to an optimization problem based on a multi-modal criterion. Iterative algorithms like the steepest descent are usually used to look for the global minimum of the criterion. This algorithms can get stuck at a local minimum. This paper presents sufficient conditions about the convergence of the steepest descent algorithm to the global minimum of the cost function. Moreover, it presents constraints to the input spectrum which ensure that the convergence conditions are satisfied. This constraints are convex and can easily be included in an experiment design approach to ensure the convergence of the iterative algorithms to the global minimum of the criterion.

}, doi = {10.3182/20110828-6-IT-1002.03566}, author = {D. Eckhard and A. S. Bazanella} } @article {Campestrini:Eckhard:Gevers:Bazanella:2011, title = {Virtual Reference Feedback Tuning for non-minimum phase plants}, journal = {Automatica}, volume = {47}, number = {8}, year = {2011}, note = {n/a}, pages = {1778{\textendash}1784}, abstract = {

Model reference control design methods fail when the plant has one or more non-minimum phase zeros that are not included in the reference model, leading possibly to an unstable closed loop. This is a very serious problem for data-based control design methods, where the plant is typically unknown. In this paper, we extend the Virtual Reference Feedback Tuning method to non-minimum phase plants. This extension is based on the idea proposed in Lecchini and Gevers (2002) for Iterative Feedback Tuning. We present a simple two-step procedure that can cope with the situation where the unknown plant may or may not have non-minimum phase zeros.

}, issn = {0005{\textendash}1098}, doi = {10.1016/j.automatica.2011.04.002}, author = {L. Campestrini and D. Eckhard and M. Gevers and A. S. Bazanella} } @conference {Eckhard:Bergel:Bazanella:2010, title = {An{\'a}lise comparativa dos m{\'e}todos de ajuste de controladores baseados em dados}, booktitle = {XVIII Congresso Brasileiro de Autom{\'a}tica}, year = {2010}, note = {n/a}, pages = {1620{\textendash}1626}, publisher = {SBA}, organization = {SBA}, address = {Bonito}, abstract = {

This work addresses data-based control design. The properties inherent to data-based design are discussed under a common theoretical framework. The computational cost is estimated with relation to memory space and number of elementar operations. Simulations present a comparision between the studied methods.

}, author = {D. Eckhard and M. E. Bergel and A. S. Bazanella} } @conference {Eckhard:Bazanella:2010, title = {Data-based controller tuning: Improving the convergence rate}, booktitle = {49th IEEE Conference on Decision and Control}, year = {2010}, note = {n/a}, pages = {4801{\textendash}4806}, publisher = {IEEE}, organization = {IEEE}, address = {Atlanta}, abstract = {

Data-based control design methods most often consist of iterative adjustment of the controller{\textquoteright}s parameters towards the parameter values which minimize an H2 performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization - no process model is used. The convergence to the global minimum of the performance criterion depends on the initial controller parameters, as well as on the size and direction of the steps taken at each iteration. This paper discusses these issues and provides a method for choosing the search direction and the step size at each optimization step so that convergence to the global minimum is obtained with high convergence rate.

}, doi = {10.1109/CDC.2010.5717584}, author = {D. Eckhard and A. S. Bazanella} } @conference {Eckhard:Campestrini:Bergel:Bazanella:2009, title = {Data-Based Control Design for a Process Class with Guaranteed Convergence to the Globally Optimum Controller}, booktitle = {European Control Conference 2009}, year = {2009}, note = {n/a}, pages = {993{\textendash}998}, publisher = {IEEE}, organization = {IEEE}, address = {Budapest}, abstract = {

This work addresses data-based (DB) control design; the properties and limitations inherent to DB design are discussed under a common theoretical framework and illustrated through experimental results. Theoretical results concerning the convergence and precision are discussed and specified for a particular class of processes. Two DB methods, representative of this design approach, are used to illustrate the general properties of DB design: the Virtual Reference Feedback Tuning (VRFT) and the Iterative Feedback Tuning (IFT).

}, url = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=7074534\&isnumber=7069761}, author = {D. Eckhard and L. Campestrini and M. E. Bergel and A. S. Bazanella} } @article {Garcia:Tarbouriech:GomesdaSilva:Eckhard:2009, title = {Finite {L2} gain and internal stabilisation of linear systems subject to actuator and sensor saturations}, journal = {IET Control Theory Applications}, volume = {3}, number = {7}, year = {2009}, note = {n/a}, pages = {799{\textendash}812}, abstract = {

This study addresses the control of linear systems subject to both sensor and actuator saturations and additive L2-bounded disturbances. Supposing that only the output of the linear plant is measurable, the synthesis of stabilising output feedback dynamic controllers, allowing to ensure the internal closed-loop stability and the finite L2-gain stabilisation, is considered. In this case, it is shown that the closed-loop system presents a nested saturation term. Therefore, based on the use of some modified sector conditions and appropriate variable changes, synthesis conditions in a quasi-linear matrix inequality (LMI) form are stated in both regional (local) as well as global stability contexts. Different LMI-based optimisation problems for computing a controller in order to maximise the disturbance tolerance, the disturbance rejection or the region of stability of the closed-loop system are proposed.

}, issn = {1751{\textendash}8644}, doi = {10.1049/iet-cta.2008.0221}, author = {G. Garcia and S. Tarbouriech and J. M. {Gomes da Silva Jr.} and D. Eckhard} } @conference {Conceicao:Carvalho:Rohr:Porath:Eckhard:Pereira:2009, title = {A Neural Network Strategy Applied in Autonomous Mobile Localization}, booktitle = {European Control Conference 2009}, year = {2009}, note = {n/a}, pages = {4439{\textendash}4444}, publisher = {IEEE}, organization = {IEEE}, address = {Budapest}, abstract = {

In this article, a new approach to the problem of indoor navigation based on ultrasonic sensors is presented, where artificial neural networks (ANN) are used to estimate the position and orientation of a mobile robot. This approach proposes the use of three Radial Basis Function (RBF) Networks, where environment maps from an ultrasonic sensor and maps synthetically generated are used to estimate the robot localization. The mobile robot is mainly characterized by its real time operation based on the Matlab/Simulink environment, where the whole necessary tasks for an autonomous navigation are done in a hierarchical and easy reprogramming way. Finally, practical results of real time navigation related to robot localization in a known indoor environment are shown.

}, url = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=7075099\&isnumber=7069761}, author = {A. G. S. Concei and C. Carvalho and E. R. Rohr and D. Porath and D. Eckhard and L. F. A. Pereira} } @conference {Eckhard:Bazanella:2009, title = {Optimizing the Convergence of Data-Based Controller Tuning}, booktitle = {European Control Conference 2009}, year = {2009}, note = {n/a}, pages = {910{\textendash}915}, publisher = {IEEE}, organization = {IEEE}, address = {Budapest}, abstract = {

Data-based control design methods most often consist of iterative adjustment of the controller{\textquoteright}s parameters towards the parameter values which minimize an H2 performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization - no process model is used. The convergence to the global minimum of the performance criterion depends on the initial controller parameters and on the step size of each iteration. This paper discusses these issues and provides a method for choosing the step size to ensure convergence to the global minimum utilizing the lowest possible number of iterations.

}, url = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=7074520\&isnumber=7069761}, author = {D. Eckhard and A. S. Bazanella} } @conference {Flores:Eckhard:GomesdaSilva:2008, title = {On the Tracking Problem for Linear Systems subject to Control Saturation}, booktitle = {17th {IFAC} World congress}, year = {2008}, note = {n/a}, pages = {14168{\textendash}14173}, publisher = {IFAC}, organization = {IFAC}, address = {Seul}, abstract = {

This paper addresses the problem of tracking constant references for linear systems subject to control saturation. Considering an unitary output feedback loop, containing an integral action, conditions in LMI form are proposed to compute a state feedback and an integrator anti-windup gain. These conditions ensure that the trajectories of the closed-loop system are bounded in an invariant ellipsoidal set, provided that the initial conditions are taken in this set and the references and the disturbances belong to a certain admissible set. Based on these conditions, optimization problems aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances are proposed.

}, doi = {10.3182/20080706-5-KR-1001.02402}, author = {J. V. Flores and D. Eckhard and J. M. {Gomes da Silva Jr.}} } @conference {Eckhard:GomesdaSilva:Tarbouriech:Prieur:2008, title = {Output dynamic feedback controller design for disturbance attenuation taking into account both sensor and actuator saturation}, booktitle = {XVII Congresso Brasileiro de Autom{\'a}tica}, year = {2008}, note = {n/a}, pages = {{\textendash}}, publisher = {SBA}, organization = {SBA}, address = {Juiz de Fora}, abstract = {

In this work, a systematic methodology to design dynamic output feedback controllers, for linear control systems presenting both actuator and sensor saturations, is proposed. A theoretical condition that ensures that the trajectories of the closed-loop system are bounded for L2 disturbances, while ensuring internal global asymptotic stability is stated. From this theoretical condition an LMI-based optimization problem to compute the controller aiming at minimizing the induced L2 gain between the disturbance and the regulated output is proposed.

}, author = {D. Eckhard and J. M. {Gomes da Silva Jr.} and S. Tarbouriech and C. Prier} } @mastersthesis {Eckhard:2008, title = {Projeto de controladores baseado em dados : converg{\^e}ncia dos m{\'e}todos iterativos}, year = {2008}, note = {n/a}, school = {Universidade Federal do Rio Grande do Sul}, type = {masters}, address = {Porto Alegre}, abstract = {

Data-based control design methods consist of adjusting the parameters of the controller directly from batches of input-output data of the process; no process model is used. The adjustment is done by solving an optimization problem, which searches the argument that minimizes a specific cost function. Iterative algorithms based on the gradient are applied to solve the optimization problem, like the steepest descent algorithm, Newton algorithm and some variations. The only information utilized for the steepest descent algorithm is the gradient of the cost function, while the others need more information like the hessian. Longer and more complex experiments are used to obtain more informations, that turns the application more complicated. For this reason, the steepest descent method was chosen to be studied in this work. The convergence of the steepest descent algorithm to the global minimum is not fully studied in the literature. This convergence depends on the initial conditions of the algorithm and on the step size. The initial conditions must be inside a specific domain of attraction, and how to enlarge this domain is treated by the methodology Cost Function Shaping. The main contribution of this work is a method to compute efficiently the step size, to ensure convergence to the global minimum. Some informations about the process are utilized, and this work presents how to estimate these informations. Simulations and experiments demonstrate how the methods work.

}, url = {http://hdl.handle.net/10183/17625}, author = {D. Eckhard} } @article {GomesdaSilva:Lescher:Eckhard:2007, title = {Design of time-varying controllers for discrete-time linear systems with input saturation}, journal = {IET Control Theory Applications}, volume = {1}, number = {1}, year = {2007}, note = {n/a}, pages = {155{\textendash}162}, abstract = {

A method for computing time-varying dynamic output feedback controllers for discrete-time linear systems subject to input saturation is proposed. The method is based on a locally valid polytopic representation of the saturation term. From this representation, it is shown that, at each sampling time, the matrices of the stabilising time-varying controller can be computed from the current system output and from constant matrices obtained as a solution of some matrix inequalities. Linear matrix inequality-based optimisation problems are therefore proposed in order to compute the controller aiming at the maximisation of the basin attraction of the closed-loop system, as well as aiming at ensuring a level of {L2} disturbance tolerance and rejection.

}, issn = {1751{\textendash}8644}, doi = {10.1049/iet-cta:20050415}, author = {J. M. {Gomes da Silva Jr.} and F. Lescher and D. Eckhard} } @conference {Eckhard:Schaf:GomesdaSilva:Pereira:2006, title = {Uma Plataforma de Experimenta}, booktitle = {XVI Congresso Brasileiro de Autom{\'a}tica}, year = {2006}, note = {n/a}, pages = {2305{\textendash}2310}, publisher = {SBA}, organization = {SBA}, address = {Salvador}, abstract = {

This paper presents a remote experimentation plataform with didactic purposes. Fisically, the plataform is basically composed by a system of coupled tanks, where the sensors and actuators are intelligent equipements which use a Foundation Fieldbus communication protocol. A supervisory system and a web server interface the experiments with internet. A distance education plataform is therefore developed to provide access to the experiments, on-line courses, and to assist the student-instructor communication.

}, author = {D. Eckhard and F. M. Schaf and J. M. {Gomes da Silva Jr.} and C. E. Pereira} }