Summary
This paper addresses the problem of power regulation and control of wind turbines using an output feedback scheme formulated as a well‐defined linear matrix inequality (LMI) problem. To this aim, first, a piecewise linear (PWL) model is constructed for the wind turbine system with the wind speed as a parameter. Then, using the achieved PWL model a set of output feedback controllers are formulated and solved as an LMI problem. To implement the designed controller in practice, 2 different approaches are proposed, ie, online and off‐line approaches. In the first approach (online), an exact optimal control law is obtained by online evaluation of the PWL model and then solving the associated LMI problem which leads to a relatively high computational complexity. To deal with this computational complexity, an alternative approximate approach is proposed which puts parts of online computations to off‐line precalculation with the cost of sub‐optimality. In this approach, the controller is predesigned for some predefined operating points and then the sub‐optimal controller is achieved by introducing a convex combination of precalculated controllers while guaranteeing the constraints satisfaction. Finally, the performance and characteristics of the proposed approaches are verified using simulation results.
In this paper, the model predictive control (MPC) approach is utilized to stabilize the output power of the wind turbines at the region above the rated wind speed. The controller is designed based on two different approaches and results have been compared. First, by putting the advantages of the MPC approach into practice, the optimal output power regulation of the wind turbine is obtained using a control oriented linear parameter varying (LPV) model of the wind turbine. However, this method inherently requires high computational cost and thus powerful hardware and processors. To cope with this limitation, an efficient suboptimal approach is proposed that significantly reduces the online computational complexity of the controller. In this approach, the main part of the controller design procedure is done off-line prior to the closed-loop wind turbine power generation and a set of optimal controllers were designed using the MPC scheme. Then, a convex combination of the calculated controllers is used for online power regulation of the wind turbine. It is noted that the selected wind turbine is a horizontal axis wind turbine operating at various speeds ranging from 10-25 m/s. Finally, using a set of simulation results we investigate the performance of the proposed approach.
In this paper, the theory of control is considered on nonlinear systems. A closed-loop controller with a strong idea has been introduced to track system states and guarantee asymptotically stability. The proposed method is the indirect terminal sliding mode control technique based on adaptive and fuzzy rules, which has used the continuous barrier function as a new approach in its design to improve the performance of this controller. One of the significant challenges in the sliding mode control method is the chattering phenomenon due to the discontinuous sign function in the control law. In the proposed approach, the control law is obtained continuously and smoothly due to the mentioned continuous function and subsequently solves the chattering problem. Another feature of the proposed method is the asymptotical stability of the system dynamics within finite time, which is proved based on the Lyapunov function. The proposed Lyapunov function includes the function of fractional power of a sliding surface. On the other hand, the obtained control law using the sliding mode method is estimated using the fuzzy system. The adaptive approach adjusts the fuzzy law parameters and the unknown bound of external disturbance.INDEX TERMS Finite-time stability, Continuous barrier function, Sliding mode, Fuzzy estimator.
This study proposes the adaptive continuous barrier function as the fractional‐order control system using the terminal sliding mode control technique with chattering‐free property to stabilize chaotic systems that have unknown uncertainties. The important reason for using the fractional‐order controller is its greater flexibility than the integer‐order controller. Using adaptive approach and Lyapunov's stability theory, an adaptive continuous barrier fractional‐order chattering‐free finite‐time controller for a category of chaotic systems with the unknown uncertainties and external disturbances is presented. The suggested controller can stabilize the chaotic system excellently with a continuous and smooth control law even without knowing the boundaries and in the presence of unknown disturbances due to the model uncertainties. According to MATLAB simulation results, the high efficiency of the suggested control technique to control the chaotic systems in the attendance of unknown perturbations is obviously confirmed.
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