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.

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.

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.

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.

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.

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.

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.