Rotations are an integral part of various computational techniques and mechanics. The objective in this paper is twofold: first to have a classical insight into the history of quaternions, a problem that Hamilton faced for over a decade and secondly to look at into its applications from computer graphics perspective. Thorough revision of quaternion algebra and its use case as a rotation operator has been presented. A quaternion simulation algorithm has been written and practiced to generate simulation results. Results show that though quaternions supersede Euler angles technically but are tricky to use and control for e.g. when same quaternion is applied on a different vector axis, the particle is not able to reach its initial position and an incomplete rotation effect has been recorded and observed.
An affine nonlinear autoregressive moving average (NARMA) model is derived from the neural network (NN) based general NARMA model in this paper, by using Taylor series expansion. The predictive error of this affine NARMA model will be quite acceptable, at least for the control purpose, if the amplitude of control input is properly limited. Therefore, an adaptive control scheme based on this model is proposed and applied to the design of adaptive power system stabilizer (APSS) since the amplitude of PSS output is usually well limited. The feature of this control scheme is that the control input can be online analytically obtained. Thus, comparing to the traditional NN based APSS (TAPSS), the affine NARMA model based APSS (AAPSS) does not need the training of a NN as neuro-controller, which may be a troublesome and time consuming step during the design. Moreover, the AAPSS can generally perform better than the TAPSS. Simulation studies on a single machine infinite bus system and a multi-machine system show that the AAPSSs can consistently well perform to damp electromechanical oscillations in the systems over a wide range of operating conditions.