On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Gain Scheduling Control of an Islanded Microgrid Voltage

The aim of this research study has been to design a gain scheduling (GS) digital controller in order to control the voltage of an islanded microgrid in the presence of fast varying loads (FVLs), and to compare it to a robust controller. The inverter which feeds the microgrid is connected to it through an inductance-capacitor-inductance (LCL) filter. The oscillatory and nonlinear behaviour of the plant is analyzed in the whole operating zone. Afterwards, the design of the controllers which contain two loops in cascade are described. The first loop concerns the current control, while the second is linked to the voltage regulation. Two controllers, one defined as Robust and another one as GS controller, are designed for the two loops, emphasizing in their robustness and their ability to damp the oscillatory plant behaviour. To finish, some simulations are carried out to study and compare the two kinds of controllers in different operating points. The results show that both controllers damp the oscillatory behaviour of the plant in closed loop (CL), and that the GS controller ensures a better rejection of current disturbances from FVLs.

Building up a frequency stabilisation based on a wavemeter for a diode laser and characterisation for a digital mirror device for artificial potentials

It has built and characterised a laser and It has learned what each of the components does. It has been able to run the laser in single-mode and stabilised it around a desired setpoint thanks to a PID controller that It has programmed. It has established a communication between the PID controller programmed in LabVIEW and Arduino Due, the DAC that It has chosen after comparing it with another candidate. It has learned some basics of how the LightCrafter 4500 DMD works. The projected light is the composition of the lights of three LED’s, each of which has a certain on-time. The mirrors chose to be in on- or off-stages depending to the amount of intensity that we want for each colour.