Development and application of a gradient method for solving differential games
A technique for solving n-dimensional games is developed and applied to two pursuit-evasion games. The first is a two-dimensional game similar to the homicidal chauffeur but modified to resemble an airplane-helicopter engagement. The second is a five-dimensional game of two airplanes at constant altitude and with thrust and turning controls. The performance function to be optimized by the pursuer and evader was the distance between the evader and a given target point in front of the pursuer. The analytic solution to the first game reveals that both unique and nonunique solutions exist. A comparison between the gradient results and the analytic solution shows a dependence on the nominal controls in regions where nonunique solutions exist. In the unique solution region, the results from the two methods agree closely. The results for the five-dimensional two-airplane game are also shown to be dependent on the nominal controls selected and indicate that initial conditions are in a region of nonunique solutions.
State space analysis of control systems
In order to introduce some key ideas in state-variable system modeling, we need to use signal-flow graphs. These graphs allow for only three types of operations: • Addition of incoming signals at a node: Here the node is a small circle. Any signal flowing out of a node is the sum of all the signals flowing in. • Amplification by a fixed factor, positive or negative: the gain is just written above the signal path. • Integration: This is denoted by a box containing the integral sign, or 1/s.
Simulation and control of hybrid renewable energy system connected to the grid
This paper presents a control and simulation of hybrid renewable energy system connected to the grid. The studied system includes a photovoltaic panel, synchronous permanent magnet generator based wind turbine, and a battery for storage energy. The PV array and wind systems are connected to the common DC bus by a boost converter. The battery is connected by a bi-directional DC/DC converter, and then integrated into the AC utility grid via a common DC/AC inverter. In order to extract the maximum energy, a simulation study has been carried out according to the meteorological conditions (wind speed and variable solar irradiance) while maintaining power quality at a satisfactory level. In order to capture the maximum power, a MPPT algorithm is applied for both wind turbine and photovoltaic panel. The modeling and simulation of the whole system has been performed under Matlab/Simulink environment. The obtained results show that the current and the voltage of grid side are sinusoidal and alternative forms, and the power injected to the grid is around the power produced by the hybrid system.