Stabilisation robuste et ultrarapide au moyen d'une double boucle de rétroaction et application à un système de lévitation magnétique

Abstract

Control designers have usually been interested in ensuring stability and robust margins of security of feedback systems. The improvement of time domain performances was put in background. It is proposed in this work to improve a novel control design recently developed at the École de Technologie Supérieure that is robust and ultra-fast. This design is based on a quasi-linear control, i.e. a controller in which the high-frequency cut-off depends on the open loop gain, which ensures smooth control while maintaining the robust stability margins. The design method consists in a double loop control. The inner loop uses a state feedback, or LQG, to stabilize the system. The outer loop improves the performances of the stabilized system. The main improvement is the limitation of the input signal to the process so as to avoid saturation in the process or damaging actuators. The design also achieves a fast time response with robust stability. The double loop design allows the separation of stabilization and minimization of sensitivity: The stabilization of the process is done arbitrarily from the improvement of performances. Furthermore, the minimization of the sensitivity of the closed loop system on a bandwidth of interest is achieved while keeping the overall sensitivity under a bounded value. The resulting time response offers very short settling times and with little to no overshoot. This time response can be further improved using lead-lag circuits within the intermediate frequency range without affecting the robustness previously achieved. Results of this novel method are shown to be superior when compared to other control methods. In addition to a better time response, the method allows the limitation of the input signal which is a critical point in control designs. A graphical tool that is both intuitive and powerful, allows the designer to fine-tune the control to achieve trade-offs on the different design criteria.

Date	11 Jan 2017
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	David Bensoussan (Supervisor)