Fixed-time observer-based tracking controller for a hysteretic piezoelectric deformable mirror of an adaptive optic system.

Piezoelectric deformable mirrors (DM) are benefited from the high accuracy and swift dynamics. The hysteresis phenomenon, which inherently exists in piezoelectric materials, degrades the capability and precision of the adaptive optics (AO) systems. Also, the dynamics of piezoelectric DMs make the controller design more complicated. This research aims to design a fixed-time observer-based tracking controller (FTOTC), which estimates the dynamics, compensates the hysteresis, and ensures tracking to the actuator displacement reference, in the fixed time. Unlike the existing inverse hysteresis operator-based methods, the proposed observer-based controller overcomes the computational burdens and estimates the hysteresis in real-time. The proposed controller tracks the reference displacements, while the tracking error converges in the fixed time. The stability proof is presented by two consecutive theorems. Numerical simulations demonstrate superior tracking and hysteresis compensation by the presented method, from a comparison viewpoint.

Adaptive robust maximum power point tracking control for perturbed photovoltaic systems with output voltage estimation.

The problem of maximum power point tracking (MPPT) in photovoltaic (PV) systems, despite the model uncertainties and the variations in environmental circumstances, is addressed. Introducing a mathematical description, an adaptive sliding mode control (ASMC) algorithm is first developed. Unlike many previous investigations, the output voltage is not required to be sensed and the upper bound of system uncertainties and the variations of irradiance and temperature are not required to be known. Estimating the output voltage by an update law, an adaptive-based H∞ tracking algorithm is then developed for the case the perturbations are energy-bounded. The stability analysis is presented for the proposed tracking control schemes, based on the Lyapunov stability theorem. From a comparison viewpoint, some numerical and experimental studies are also presented and discussed.

Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua's circuit.

The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are L(2) signals, an adaptive control incorporated with H(∞) control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua's circuits.