Prof. Dr. Diego Eckhard

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.