Wind power is a sustainable green energy source. Power forecasting via deep learning is essential due to diverse wind behavior and uncertainty in geological and climatic conditions. However, the volatile, nonlinear and intermittent behavior of wind makes it difficult to design reliable forecasting models. This paper introduces a new approach using variational auto-encoding and hybrid transfer learning to forecast wind power for large-scale regional windfarms. Transfer learning is applied to windfarm data collections to boost model training. However, multiregional windfarms consist of different wind and weather conditions, which makes it difficult to apply transfer learning. Therefore, we propose a hybrid transfer learning method consisting of two feature spaces; the first was obtained from an already trained model, while the second, small feature set was obtained from a current windfarm for retraining. Finally, the hybrid transferred neural networks were fine-tuned for different windfarms to achieve precise power forecasting. A comparison with other state-of-the-art approaches revealed that the proposed method outperforms previous techniques, achieving a lower mean absolute error (MAE), i.e., between 0.010 to 0.044, and a lowest root mean square error (RMSE), i.e., between 0.085 to 0.159. The normalized MAE and RMSE was 0.020, and the accuracy losses were less than 5%. The overall performance showed that the proposed hybrid model offers maximum wind power forecasting accuracy with minimal error.

The compensation of nonlinear hysteretic behavior is one of the mandatory requirements in order to achieve precise reference tracking performance from a piezoelectric positioning stage. A common practice of employing an inverse hysteresis model as a feed-forward compensator must deal with modeling complexity; consequently, real-time tracking performance suffers due to modeling errors. In this paper, a two degree-of-freedom (DOF) robust digital feedback controller design scheme in the presence of a simple Bouc-Wen hysteresis feed-forward compensator is proposed to deal with the dual challenge of modeling complexity and modeling errors. The proposed control scheme takes into account the performance and robustness requirements simultaneously. The desired performance and robustness requirements are expressed by means of constraints on the shapes of closed-loop sensitivity functions (CLSFs). Then, pole placement with sensitivity function shaping methodology is adopted so that the CLSFs respect their respective constraints and the desired performance with robustness could be achieved. The presented experimental results verify the effectiveness of the proposed control scheme in achieving the peak-to-peak reference tracking error of 0.36% for the desired displacement of 12 μm with tracking frequency of 10 Hz, whereas the peak-to-peak tracking error of 4.33% is observed with a Bouc-Wen hysteresis feed-forward compensator (without the feedback controller). Overall, 91% improvement is achieved in reducing the reference tracking error with the proposed control scheme.

The nonlinear hysteresis phenomenon can occur in piezoelectric-driven nanopositioning systems and can lead to reduced positioning accuracy or result in a serious deterioration of motion control. The Preisach method is widely used for hysteresis modeling; however, for the modeling of rate-dependent hysteresis, where the output displacement of the piezoelectric actuator depends on the amplitude and frequency of the input reference signal, the desired accuracy cannot be achieved with the classical Preisach method. In this paper, the Preisach model is improved using least-squares support vector machines (LSSVMs) to deal with the rate-dependent properties. The control part is then designed and consists of an inverse Preisach model to compensate for the hysteresis nonlinearity and a two-degree-of-freedom (2-DOF) H-infinity feedback controller to enhance the overall tracking performance with robustness. The main idea of the proposed 2-DOF H-infinity feedback controller is to find two optimal controllers that properly shape the closed-loop sensitivity functions by imposing some templates in terms of weighting functions in order to achieve the desired tracking performance with robustness. The achieved results with the suggested control strategy show that both hysteresis modeling accuracy and tracking performance are significantly improved with average root-mean-square error (RMSE) values of 0.0107 μm and 0.0212 μm, respectively. In addition, the suggested methodology can achieve better performance than comparative methods in terms of generalization and precision.

Nanopositioning systems driven by piezoelectric actuators are widely used in different fields. However, the hysteresis phenomenon is a major factor in reducing the positioning accuracy of piezoelectric actuators. This effect makes the task of accurate modeling and position control of piezoelectric actuators challenging. In this paper, the learning and generalization capabilities of the model are efficiently enhanced to describe and compensate for the rate-independent and rate-dependent hysteresis using a kernel-based learning method. The proposed model is inspired by the classical Preisach hysteresis model, in which a set of hysteresis operators is used to address the problem of mapping, and then least-squares support-vector machines (LSSVM) combined with a particle swarm optimization (PSO) algorithm are used for identification. Two control schemes are proposed for hysteresis compensation, and their performance is evaluated through real-time experiments on a nanopositioning platform. First, an inverse model-based feedforward controller is designed based on the LSSVM model, and then a combined feedback/feedforward control scheme is designed using a classical control strategy (PID) to further enhance the tracking performance. For performance evaluation, different datasets with a variety of hysteresis loops are used during the simulation and experimental procedures. The results show that the proposed method is successful in enhancing the generalization capabilities of LSSVM training and achieving the best tracking performance based on the combination of feedforward control and PID feedback control. The proposed control scheme outperformed the inverse Preisach model-based control scheme in terms of both positioning accuracy and execution time. The control scheme that uses the LSSVM based on nonlinear autoregressive exogenous (NARX) models has significantly less computational complexity compared to our control scheme but at the expense of accuracy.

In this article, a combined feedback-feedforward control design scheme is presented to enhance the tracking performance of a piezo-actuated micropositioning stage by compensating the nonlinear hysteretic behavior of the piezoelectric actuator and model uncertainties of the system. Detailed investigation of the presented control scheme is performed not only in simulation by analyzing the robust stability and robust performance but also in real-time with motion trajectories of multiple frequencies. To design the presented control scheme, first of all, the dynamic model of the system is identified from the real-time experimental data by using the recursive least squares parameter adaptation algorithm. Then, Dahl hysteresis model is considered to represent the nonlinear hysteretic behavior of the piezoelectric actuator. To deal with this hysteresis nonlinearity, Dahl feedforward compensator is designed without involving inverse model calculations to avoid any computational complexity. This feedforward compensator is then combined with $\mu $ -synthesis robust feedback controller which is designed in the presence of model uncertainties of the system. The presented control scheme ensures the boundedness of the closed-loop signals and the desired tracking performance of the considered micropositioning stage. Finally, experimental tests are conducted with motion trajectories of multiple frequencies for the validation of the control scheme. An average improvement of 95% in compensating the hysteresis nonlinearity and 80% in reducing the tracking error is achieved which demonstrates the efficacy of the presented control scheme.

H-infinity control design with feed-forward compensator for hysteresis compensation in piezoelectric actuators