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Optimal Control of Switched-input and Uncertain Systems


K. Nolde

no. 17886

The thesis is concerned with three application projects that deal with optimal control of switched-input and uncertain systems. In switched-input systems some or all of the system inputs take binary values. In uncertain systems the dynamics or the output are affected by random parameters. In the thesis it is shown how to effectively compute optimal control inputs for switched-input and uncertain systems.

In order to show this, an application-driven approach is taken. In this approach optimal controllers for switched-input and/or uncertain systems from different applications are designed. The projects are presented in three parts of the thesis:

In the first part the development of an optimal controller for thermal printheads is presented. A first-order linear system with a non-linear output mapping containing stochastic noise is proposed as a model for the printing dynamics. The model parameters are identified and an optimal control problem is formulated to determine the printhead input. The control algorithm is successfully tested on a standard thermal printer. A sensitivity analysis is performed using simulations and experiments in order to analyze the printing quality on varying setups with different printheads, printing media and ribbons. A tuning strategy is derived to adapt to changing setups without having to recompute the optimization problem. Robustness of the resulting controller is shown in experiments. Comparing the proposed controller to a current control implementation shows a significant quality gain in barcode readability (ISO/IEC 15416).

The second part presents two load tracking scheduling problem. The first problem deals with the scheduling of employees so that the employee presence tracks a pre-specified demand curve. Requirements such as minimum employee presence or constraints on the shift length have to be respected. The second problem is concerned with the energy-cost optimal scheduling of a steel plant. In the steel plant the total electrical load generated by all machines must track a pre-specified energy curve as close as possible, while respecting constraints that arise from production. For both problems a comparison of discrete-time and continuous-time models of the scheduling problems is made. The results show that in the workforce planning a solution is computed faster for the discrete-time model. In the steel plant scheduling the continuous-time model is superior. It is argued that discrete-time models are superior for problems where only few possible switching time points exist, i. e. time points when tasks can start or end. Continuous-time formulations do not seem restricted by the number of possible time points, but their limitation appears to be in the number of possible arrangements of the tasks that are to be scheduled. Also, we show an example for the continuous-time problem where small parameter changes lead to large changes in the computation time.

The third part is concerned with the medium term control of a hydro-thermal system. In this project a multistage stochastic programming formulation is presented for monthly production planning of the system. Stochasticity from variations in water reservoir inflows and fluctuations in demand of electric energy are considered explicitly. The problem can be solved efficiently via Nested Benders Decomposition. The solution is implemented in a model predictive control setup, and performance of this control technique is demonstrated in simulations. Tuning parameters such as prediction horizon and shape of the stochastic programming tree are identified and their effects are analyzed.

In the conclusion of the thesis the results of the different projects are related to each other. Three different approaches that were successful in computing input signals for switched-input systems are summarized. The conclusion also combines the different concepts that were used for treating uncertainty in the systems. Observations on the computational complexity of the application projects are given.


Type of Publication:

(03)Ph.D. Thesis

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2008:IFA_3117,
    author={K. Nolde},
    title={{Optimal Control of Switched-input and Uncertain Systems}},
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