# Estimation of the Dynamic Relative Gain Array for Control Configuration Selection

Sammanfattning: The control of multi-input multi-output systems (MIMO) is more difficult than for single-input single-output systems (SISO) due to the multitude of input-output couplings. Coupling, simply means that a change in any input leads to changes in many outputs. Nevertheless, in many cases, a simple decentralised controller is usually sufficient to achieve desired performance goals. However, there is a need for systematic techniques that can suggest the most promising configurations or pairings for the decentralized controller. The relative gain array (RGA) has proven itself to be an efficient tool to solve the pairing problem. It is easily calculated and does not depend on input-output scaling. However, it gives misleading results in some cases where system dynamics are involved and hence Dynamic Relative Gain Array (DRGA) used instead. The commonplace procedure to estimate DRGA values from the input-output data is to identify a parametric system model. Thus, the user needs to decide a model structure and a model order to calculate the system frequency response. Eventually, DRGA values are obtained based on that system frequency response over the frequency range of interest. In this work, a method which requires less user interaction is proposed. The system frequency response, and subsequently the DRGA, is directly estimated from the input-output data by employing a non-parametric identification approach. Such an approach reduces the uncertainties arising from incorrect user decisions by avoiding the parametric model identification. However, DRGA values obtained by the nonparametric identification are subject to different uncertainty sources such as system nonlinearity and noise. In this thesis various strategies are presented to reduce the effect of these uncertainties. In that direction, RGA (DRGA) of linear systems is first analysed using a random excitation signal. Due to the nonperiodic nature of the random signal, the frequency response is susceptible to leakage. To reduce the leakage effect, data is divided into sub-records and the frequency response was averaged over these sub-records. Although the data division proved to be efficient in limiting the leakage effect it has a drawback of reducing the frequency resolution. Moreover, RGA (DRGA) of weakly nonlinear systems is analysed using a multisine excitation signal. The multisine excitation is used to distinguish between the nonlinear distortion and the output noise. It is very difficult to make such distinction using the random excitation. However, long experimental time is needed in returns. To overcome the shortcomings represented by low frequency resolution and the experiment running time, local polynomial approximation approach (LPA) is investigated using both random and multisine excitation. In that direction, RGA (DRGA) of linear systems is first analysed using a random excitation signal. Due to the nonperiodic nature of the random signal, the frequency response is susceptible to leakage. To reduce the leakage effect, data is divided into sub-records and the frequency response was averaged over these sub-records. Although the data division proved to be efficient in limiting the leakage effect it has a drawback of reducing the frequency resolution. Moreover, RGA (DRGA) of weakly nonlinear systems is analysed using a multisine excitation signal. The multisine excitation is used to distinguish between the nonlinear distortion and the output noise. It is very difficult to make such distinction using the random excitation. However, long experimental time is needed in returns. To overcome the shortcomings represented by low frequency resolution and the experiment running time, local polynomial approximation approach (LPA) is investigated using both random and multisine excitation. It can be concluded that the proposed approach achieves quite accurate RGA values with the advantage of exempting the user from deriving a complete parametric model of the plant. Hence, efforts of identifying the parameters of all MIMO subsystems can be saved by finding the parameters of the most significant subsystems of a multivariable system.

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