Power maximization has always been a practical consideration in wind turbines. The question of how to address optimal power capture, especially when the system dynamics are nonlinear and the actuators are subject to unknown faults, is significant. This paper studies the control methodology for variable-speed variable-pitch wind turbines including the effects of uncertain nonlinear dynamics, system fault uncertainties, and unknown external disturbances. The nonlinear model of the wind turbine is presented, and the problem of maximizing extracted energy is formulated by designing the optimal desired states. With the known system, a model-based nonlinear controller is designed; then, to handle uncertainties, the unknown nonlinearities of the wind turbine are estimated by utilizing radial basis function neural networks. The adaptive neural fault tolerant control is designed passively to be robust on model uncertainties, disturbances including wind speed and model noises, and completely unknown actuator faults including generator torque and pitch actuator torque. The Lyapunov direct method is employed to prove that the closed-loop system is uniformly bounded. Simulation studies are performed to verify the effectiveness of the proposed method.
Finding optimal trajectory is critical in several applications of robot manipulators. This paper is applied the open-loop optimal control approach for generating the optimal trajectory of the flexible mobile manipulators in point-to-point motion. This method is based on the Pontryaginʹs minimum principle that by providing a twopoint boundary value problem is solved the problem. This problem is known to be complex in particular when combined motion of the base and manipulator, nonholonomic constraint of the base and highly non-linear and complicated dynamic equations as a result of flexible nature of links are taken into account. The study emphasizes on modeling of the complete optimal control problem by remaining all nonlinear state and costate variables as well as control constraints. In this method, designer can compromise between different objectives by considering the proper penalty matrices and it yields to choose the proper trajectory among the various paths. The effectiveness and capability of the proposed approach are demonstrated through simulation studies. Finally, to verify the proposed method, the simulation results obtained from the model are compared with the results of those available in the literature.
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