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A spherical robot consists of an externally spherical rigid body rolling on a two-dimensional surface, actuated by an auxiliary mechanism. For a class of actuation mechanisms, we derive a controller for the geometric center of the sphere to asymptotically track any sufficiently smooth reference trajectory, with robustness to bounded, constant uncertainties in the inertial properties of the sphere and actuation mechanism, and to constant disturbance forces including, for example, from constant inclination of the rolling surface. The sphere and actuator are modeled as distinct systems, coupled by reaction forces. It is assumed that the actuator can provide three independent control torques, and that the actuator center of mass remains at a constant distance from the geometric center of the sphere. We show that a necessary and sufficient condition for such a controller to exist is that for any constant disturbance torque acting on the sphere there is a constant input such that the sphere and the actuator mechanism has a stable relative equilibrium. A geometric PID controller guarantees robust, semi-global, locally exponential stability for the position tracking error of the geometric center of the sphere, while ensuring that actuator velocities are bounded.

Non-linear loads, which cause harmonic distortion, are increasingly being used in electrical power systems. This is causing a major concern and real-time harmonic

The issue of power quality is now recognised as an essential feature of a successful electric power system. This is mainly due to the rapid increase of loads, which generate noise and, at the same time, are sensitive to the noise present in the supply system. As a result, power quality monitoring has become an important issue in modern power systems.This paper presents a technique for classifying electrical power quality disturbance events. The technique is based on a novel Self-Adapting Artificial Neural Network (SAANN), which has the unique capability of adapting to new disturbance features.In the proposed technique, distinctive feature vectors from disturbance events captured are extracted using Fast Fourier Transform (FFT) and Discrete Wavelet Transform (DWT). The feature vectors are then fed to two SAANN based classifiers, which classify the captured events into different categories of power quality disturbances. The proposed technique is tested using a number of disturbance events and results are presented.

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