Experiment design for batch-to-batch 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

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

\u3cp\u3eAn 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.\u3c/p\u3

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Estimating parameters with pre-specified accuracies in distributed parameter systems using optimal experiment design

\u3cp\u3eEstimation of physical parameters in dynamical systems driven by linear partial differential equations is an important problem. In this paper, we introduce the least costly experiment design framework for these systems. It enables parameter estimation with an accuracy that is specified by the experimenter prior to the identification experiment, while at the same time minimising the cost of the experiment. We show how to adapt the classical framework for these systems and take into account scaling and stability issues. We also introduce a progressive subdivision algorithm that further generalises the experiment design framework in the sense that it returns the lowest cost by finding the optimal input signal, and optimal sensor and actuator locations. Our methodology is then applied to a relevant problem in heat transfer studies: estimation of conductivity and diffusivity parameters in front-face experiments. We find good correspondence between numerical and theoretical results.\u3c/p\u3

Minimization of cross-talk in a piezo inkjet printhead based on system identification and feedforward control

\u3cp\u3eThe printing quality delivered by a drop-on-demand inkjet printhead is severely affected by the residual oscillations in an ink channel and the cross-talk between neighboring ink channels. For a single ink channel, our earlier contribution shows that the actuation pulse can be designed, using a physical model, to effectively damp the residual oscillations. It is not always possible to obtain a good physical model for a single ink channel. A physical model for a multi-input multi-output (MIMO) inkjet printhead is made even more sophisticated by the presence of the cross-talk effect. This paper proposes a system identification-based approach to build a MIMO model for an inkjet printhead. Additionally, the identified MIMO model is used to design new actuation pulses to effectively minimize the residual oscillations and the cross-talk. Using simulation and experimental results, we demonstrate the efficacy of the proposed method.\u3c/p\u3

Closed-loop performance diagnosis using prediction error identification

This paper presents a methodology to detect the origin of closed-loop performance degradation of model-based control systems. The approach exploits the statistical hypothesis testing framework. The decision rule consists of examining if an identified model of the true system lies in a set containing all models that fulfill the closed-loop performance requirements. This allows us to determine whether performance degradation arises from changes in system dynamics or from variations in disturbance characteristics. The probability of making an erroneous decision is estimated a posteriori using the known distribution of the identified model with respect to the unknown true system

Performance improvement of a drop-on-demand inkjet printhead using an optimization-based feedforward control method

The printing quality delivered by a drop-on-demand (DoD) inkjet printhead is limited due to the residual oscillations in the ink channel. The maximal jetting frequency of a DoD inkjet printhead can be increased by quickly damping the residual oscillations and by bringing in this way the ink channel to rest after jetting the ink drop. This paper proposes an optimization-based method to design the input actuation waveform for the piezo actuator in order to improve the damping of the residual oscillations. A discrete-time transfer function derived from the narrow-gap model is used to predict the response of the ink channel under the application of the piezo input. Simulation and experimental results are presented to show the applicability of the proposed method

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

Identification of dynamic models in complex networks with prediction error methods : basic methods for consistent module estimates

The problem of identifying dynamical models on the basis of measurement data is usually considered in a classical open-loop or closed-loop setting. In this paper, this problem is generalized to dynamical systems that operate in a complex interconnection structure and the objective is to consistently identify the dynamics of a particular module in the network. For a known interconnection structure it is shown that the classical prediction error methods for closed-loop identification can be generalized to provide consistent model estimates, under specified experimental circumstances. Two classes of methods considered in this paper are the direct method and the joint-IO method that rely on consistent noise models, and indirect methods that rely on external excitation signals like two-stage and IV methods. Graph theoretical tools are presented to verify the topological conditions under which the several methods lead to consistent module estimates. Keywords: System identification; Closed-loop identification; Graph theory; Dynamic networks; Identifiability; Linear system

Predictor input selection for two stage identification in dynamic networks

\u3cp\u3eRecently, the Two-Stage method has been proposed as a tool to obtain consistent estimates of modules embedded in dynamic networks [1], [2]. However, for this method the variables that are included in the predictor model are currently not considered as a user choice. In this paper it is shown that there is considerable freedom as to which variables can be included in the predictor model as inputs, and still obtain consistent estimates of the module of interest. Conditions that the choice of predictor inputs must satisfy are presented. The conditions could be used to find the smallest number of predictor inputs for instance. Algorithms are presented for checking the conditions and obtaining the estimates.\u3c/p\u3