Nonlinear Model Predictive Control (NMPC) for Twin Rotor MIMO System (TRMS)

Twin Rotor MIMO System (TRMS) is a dynamic model with high non-linearity that resembles a helicopter with reduced degree-of-freedom (DOF). Besides, cross-coupling between main rotor and tail rotor contributes to the difficulty in controlling the system. Majority of the previous researches have not focused on continuous actual dynamic disturbance test. The objectives of this project are to model TRMS and control the system against major disturbance (wind effect) and set-point changes. The first phase of the project started with mathematical modelling of direct current (DC) motors, where the relationship between input voltage and angular velocity was captured. The next phase would be the modelling of the whole system and design of controller. During the second phase, the modelling would involve aerodynamics and other Physics laws. Once the complete model was formed, Proportional, Integral and Derivative (PID) and Linear Quadratic Regulator (LQR) controllers were designed to optimize the dynamic system. The system has been tested using wind variation as actual dynamic disturbance to validate the disturbance rejection performance. It was found that the best performance from combination of PID and LQR controllers gave 89% improvement in term of pitch overshoot and 33% improvement in term of yaw overshoot during disturbance rejection compared to PID-only controller

Cancellation of divergences in unitary gauge calculation of H→γγH \to \gamma \gamma process via one W loop, and application

Following the thread of R. Gastmans, S. L. Wu and T. T. Wu, the calculation in the unitary gauge for the $H \to \gamma \gamma$ process via one W loop is repeated, without the specific choice of the independent integrated loop momentum at the beginning. We start from the 'original' definition of each Feynman diagram, and show that the 4-momentum conservation and the Ward identity of the W-W-photon vertex can guarantee the cancellation of all terms among the Feynman diagrams which are to be integrated to give divergences higher than logarithmic. The remaining terms are to the most logarithmically divergent, hence is independent from the set of integrated loop momentum. This way of doing calculation is applied to $H \to \gamma Z$ process via one W loop in the unitary gauge, the divergences proportional to $M_Z^2/M^3$ including quadratic ones are all cancelled, and terms proportional to $M_Z^2/M^3$ are shown to be zero. The way of dealing with the quadratic divergences proportional to $M_Z^2/M^3$ in $H \to \gamma Z$ has subtle implication on the employment on the Feynman rules especially when those rules can lead to high level divergences. So calculation without integration on all the $\delta$ functions until have to is a more proper or maybe necessary way of the employment of the Feynman rules.Comment: 1 figure, 34 pages (updated

Observational constraints on the energy scale of inflation

Determining the energy scale of inflation is crucial to understand the nature of inflation in the early Universe. We place observational constraints on the energy scale of the observable part of the inflaton potential by combining the 7-year Wilkinson Microwave Anisotropy Probe data with distance measurements from the baryon acoustic oscillations in the distribution of galaxies and the Hubble constant measurement. Our analysis provides an upper limit on this energy scale, 2.3 \times 10^{16} GeV at 95% confidence level. Moreover, we forecast the sensitivity and constraints achievable by the Planck experiment by performing Monte Carlo studies on simulated data. Planck could significantly improve the constraints on the energy scale of inflation and on the shape of the inflaton potential.Comment: 7 pages, 3 figures, RevTeX, published versio