Abstract The reachability of standard and fractional-order continuous-time systems with constant inputs is addressed. Positive and non-positive continuous-time linear systems are considered. Necessary and sufficient conditions for the existence of such constant inputs that steers the system from zero initial conditions to the given final state in desired time are derived and proved. As an example of such systems the electrical circuits with DC voltage sources are presented.
The minimum-time problem for a glider flying in the vertical plane is considered. The glider is regarded as a particle moving in the atmosphere in given thermal conditions. The problem is formulated in optimal control and solved using direct pseudospectral Chebysev's method. The data are taken for the Word Class Glider PW-5 "Smyk". Computed optimum results are compared with glider's trajectories from the Second Domestic Glider Championship 2006, Suwałki, Poland.
Small-scale vertical-axis wind turbines can be used as a source of electricity in rural and urban environments. According to the authors’ knowledge, there are no validated simplified aerodynamic models of these wind turbines, therefore the use of more advanced techniques, such as for example the computational methods for fluid dynamics is justified. The paper contains performance analysis of the small-scale vertical-axis wind turbine with a large solidity. The averaged velocity field and the averaged static pressure distribution around the rotor have been also analyzed. All numerical results presented in this paper are obtained using the SST k-ω turbulence model. Computed power coefficients are in good agreement with the experimental results. A small change in the tip speed ratio significantly affects the velocity field. Obtained velocity fields can be further used as a base for simplified aerodynamic methods.