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This study proposes a direct parameter estimation approach from observed input-output data of a stochastic singleinput-single-output fractional-order continuous-time Hammerstein-Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input-output data by considering the system to be a multi-input-single-output linear fractional-order continuoustime model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input nonlinear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein-Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein-Wiener output model.

Abstract:The paper presents the design and the implementation of different advanced control strategies that are applied to a nonlinear model of a thermal unit. A data-driven grey-box identification approach provided the physically-meaningful nonlinear continuous-time model, which represents the benchmark exploited in this work. The control problem of this thermal unit is important, since it constitutes the key element of passive air conditioning systems. The advanced control schemes analysed in this paper are used to regulate the outflow air temperature of the thermal unit by exploiting the inflow air speed, whilst the inflow air temperature is considered as an external disturbance. The reliability and robustness issues of the suggested control methodologies are verified with a Monte Carlo (MC) analysis for simulating modelling uncertainty, disturbance and measurement errors. The achieved results serve to demonstrate the effectiveness and the viable application of the suggested control solutions to air conditioning systems. The benchmark model represents one of the key issues of this study, which is exploited for benchmarking different model-based and data-driven advanced control methodologies through extensive simulations. Moreover, this work highlights the main features of the proposed control schemes, while providing practitioners and heating, ventilating and air conditioning engineers with tools to design robust control strategies for air conditioning systems.

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