Marco Forgione

Data-driven model improvement for model-based control

We present a framework for the gradual improvement of model-based controllers. The total time of the learning procedure is divided into a number of learning intervals. After a learning interval, the model is refined based on the measured data. This model is used to synthesize the controller that will be applied during the next learning interval. Excitation signals can be injected into the control loop during each of the learning intervals. On the one hand, the introduction of an excitation signal worsens the control performance during the current learning interval since it acts as a disturbance. On the other hand, the informative data generated owing to the excitation signal are used to refine the model using a closed-loop system identification technique. Therefore, the control performance for the next learning interval is expected to improve. In principle, our objective is to maximize the overall control performance taking the effect of the excitation signals explicitly into account. However, this is in general an intractable optimization problem. For this reason, a convex approximation of the original problem is derived using standard relaxations techniques for Experiment Design. The approximated problem can be solved efficiently using common optimization routines. The applicability of the method is demonstrated in a simulation study.

Experiment design for parameter estimation in nonlinear systems based on multilevel excitation

An experiment design procedure for parameter estimation in nonlinear dynamical systems is presented in this paper. The input to the system is designed in such a way that the information content of the data, as measured by a scalar function of the information matrix, is maximized. By restricting the input to a finite number of possible levels, the experiment design problem is formulated as a convex optimization problem which can be solved efficiently. The method is applied to a Continuous Stirred Tank Reactor in a simulation study. The parameter estimation based on the input signal obtained in our procedure is shown to outperform the one based on random binary signals.

Least costly closed-loop performance diagnosis and plant re-identification

The inherent time-varying nature of dynamics in chemical processes often limits the lifetime performance of model-based control systems, as the plant and disturbance dynamics change over time. A critical step in the maintenance of model-based controllers is distinguishing control-relevant plant changes from variations in disturbance characteristics. In this paper, prediction error identification is used to evaluate a hypothesis test that detects if the performance drop arises from control-relevant plant changes. The decision rule is assessed by verifying whether an identified model of the true plant lies outside the set of all plant models that lead to adequate closed-loop performance. A unified experiment design framework is presented in the least costly context (i.e., least intrusion of nominal plant operation) to address the problem of input signal design for performance diagnosis and plant re-identification when the performance drop is due to plant changes. The application of the presented performance diagnosis approach to a (nonlinear) chemical reactor demonstrates the effectiveness of the approach in detecting the cause of an observed closed-loop performance drop based on the designed least costly diagnosis experiment.

Optimal experiment design in closed loop with unknown, nonlinear and implicit controllers using stealth identification

We present a novel optimal experiment design method that is applicable to linear time-invariant systems regulated by unknown, nonlinear and implicitly-defined controllers. Current methods require an explicit expression for the controller in order to construct the optimal excitation spectrum. Consequently, these are limited to linearly-controlled systems. The identification scheme suggested in this paper circumvents the aforementioned requirement by ensuring that the excitation signal remains unnoticed by the controller, i.e., the identification data is gathered in an open-loop fashion. Our theoretical analysis is complemented with a numerical study on a six-parameter, single-input single-output linear system controlled by an MPC. We find that our method generates least-costly excitation signals which deliver identified models that lie close to the true system whilst honoring quality constraints, validating the novel optimal experiment design framework.

A unified experiment design framework for detection and identification in closed-loop performance diagnosis

This paper presents a least-costly experiment design framework for closed-loop performance diagnosis using prediction error identification. The performance diagnosis methodology consists in verifying whether an identified model of the true system lies in a performance-related region of interest. The experiment design framework minimizes the overall excitation cost incurred for detecting the cause of the performance drop and re-identifying the system dynamics when the degraded performance is due to control-relevant system changes. The optimal design of excitation signals is performed for a desired detection rate and a pre-specified level of accuracy required for the re-identified model.

Iterative Learning Control of supersaturation in batch cooling crystallization

An Iterative Learning Control (ILC) algorithm for supersaturation control in batch cooling crystallization is presented in this paper. The ILC controller is combined with a PI controller in order to reject the disturbances present in the thermal dynamics as much as possible. Convergence and robustness properties of the proposed ILC+PI control scheme are investigated. The simulation studies reveal that the controller is well capable of tracking a predetermined supersaturation trajectory in the presence of model imperfections, measurement noise and actuation deficiencies.

Experiment design for batch-to-batch model-based learning control

An Experiment Design framework for dynamical systems which execute multiple batches is presented in this paper. After each batch, a model of the system dynamics is refined using the measured data. This model is used to synthesize the controller that will be applied in the next batch. Excitation signals may be injected into the system during each batch. From one hand, perturbing the system worsens the control performance during the current batch. On the other hand, the more informative data set will lead to a better identified model for the following batches. The role of Experiment Design is to choose the proper excitation signals in order to optimize a certain performance criterion defined on the set of batches that is scheduled. A total cost is defined in terms of the excitation and the application cost altogether. The excitation signals are designed by minimizing the total cost in a worst case sense. The Experiment Design is formulated as a Convex Optimization problem which can be solved efficiently using standard algorithms. The applicability of the method is demonstrated in a simulation study.

Batch-to-batch strategies for cooling crystallization

Two batch-to-batch (B2B) algorithms for supersaturation control in cooling crystallization are presented in this paper. In Iterative Learning Control (ILC) a nominal process model is adjusted with an additive correction term which depends on the error in the last batch. In Iterative Identification Control (IIC) the physical parameters of the process model are recursively estimated by adopting a Bayesian identification framework. Both B2B algorithms compute an optimized input for the next batch that is fed to a lower level PI feedback controller in order to reject the process disturbances. The tracking performance of these B2B+PI control schemes is investigated in a simulation study.

Least-costly experiment design for uni-parametric linear models: An analytical approach

Least-costly experiment design has received ample attention over the past decades, and efficient numerical algorithms that can compute optimal excitation spectra for linear models have been found. The interpretation of such spectra, however, has received far less attention. We restrict ourselves to uni-parametric models, for which an analytical solution to the experiment design problem is derived. This solution enables us to address, among other things, the following questions: What determines the frequency and amplitude of the excitation signal? Does the optimal frequency depend on the location(s) that the parameter occupies in the transfer function? With the optimal signal, is a closed-loop identification experiment cheaper than an open-loop one?