# Robust Control Examples Applied to a Wind Turbine Simulated Model
## 1 Introduction
Therefore, this paper suggests to model the wind turbine plant via Takagi-Sugeno (TS) fuzzy prototypes [6], whose parameters are obtained by identification procedures. This approach is also motivated by previous works by the same authors [7]. On the other hand, concerning the control design, the paper proposes also a fuzzy control method for the regulation of the blade pitch angle, and the generator torque of the wind turbine system. With respect to similar works (see, e.g., [8]), this paper suggests an off-line identification approach, without any on-line optimization schemes, thus enhancing real-time implementations. Note also that the works by the same authors (see, e.g., [9]), addressed a different design procedure of the fuzzy regulator, that consists of fuzzy PI controllers. On the other hand, this paper proposes the direct estimation of the fuzzy regulator by means of an identification scheme. Regarding the second model-based strategy presented in this paper, it relies on an adaptive control scheme [10]. Again, with respect to pure nonlinear control methods [11], it does not require a detailed knowledge about the model structure. Therefore, this work suggests the implementation of controllers based on adaptive schemes, used for the recursive derivation of the controller model. In particular, a recursive Frisch scheme extended to the adaptive case for control design is considered in this study, as proposed, e.g., in [9] by the same authors, which makes use of exponential forgetting laws. This allows the on-line application of the Frisch scheme to derive the parameters of a time-varying controller. Since it is necessary to evaluate the robustness and the reliability of the designed control methods with respect to modeling uncertainties, disturbance, and measurement errors, the verification and validation tools use extensive Monte Carlo simulations. In fact, the wind turbine system contains elements that cannot be described by analytical models. Thus, the Monte Carlo analysis represents a solution for testing the robustness and reliability features of the control schemes when applied to the wind turbine model. This paper compares the proposed methodologies also with respect to different control methods based on sliding mode techniques, neural controllers, or gain scheduling methods. However, with respect again to [9] by the same authors, different comparisons are proposed in this work that exploit proper performance metrics. It is worth highlighting the main features of the proposed data-drive and model-based approaches. Indeed, the term \"model-based\" could be misleading in this case. In fact, the adaptive control approach suggested in this work should be considered as \"active\" control method, instead. In fact, the control design relies on an identified model of the process under investigation. In this way, the parameters of the process model are identified on-line via a recursive estimation procedure, in order to adapt this identified model with respect to both the different operating conditions and possible process uncertainty. Due to this adaptation scheme, the control design technique is able to achieve robustness characteristics with respect to possible uncertainty and disturbance effects. On the other hand, the proposed on-line control scheme can be applied to nonlinear dynamic processes, due to its capabilities to recursively track the changes of the controlled process. Moreover, the adaptive control law can be designed by means of different rules that are functions of the process model parameters, thus making the control design solutions robust with respect to disturbances. Another key aspect concerns the identification method exploited for estimating the model parameters. The proposed approach relies on an Error-In-Variable (EIV) scheme [12], which is more general and less conservative than standard identification techniques. For example, the classical Least Square Method (LSM) assumes that only the output is possibly affected by uncertainty (noise) [13].