Prof. Dr. Diego Eckhard

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.

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.

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.

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.

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.

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).

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.

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.

Data-based control design methods most often consist of iterative adjustment of the controller'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.

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.

Data-based control design methods most often consist of iterative adjustment of the controller'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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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'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.

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.

Os métodos de projeto de controladores baseado em dados são um conjunto de técnicas utilizadas para ajustar os ganhos de controladores, que não utilizam um modelo matemático do processo na sintonia dos parâmetros. Alguns destes métodos são o Iterative Feedback Tuning (IFT), Correlation based Tuning (CbT), Virtual Reference Feedback Tuning (VRFT) e Optimal Controller Identification (OCI). Apesar de algumas destas t{ écnicas existirem por mais de uma década, são encontrados poucos trabalhos na literatura que demonstram a aplicabilidade dos métodos em sistemas industriais. Neste trabalho duas técnicas de projeto de controladores baseado em dados não-iterativas (VRFT e OCI) são aplicadas em em um sistema de controle de nível industrial, que utiliza uma rede Foundation Fieldbus H1. O trabalho demostra que as técnicas apresentadas podem ser aplicadas com facilidade em sistemas industriais gerando repostas dinâmicas satisfatórias.

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.