Prof. Dr. Diego Eckhard

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.

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.

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.

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.