Robust Control of a Plasma Wind Tunnel: An LPV Discrete-Time System Depending on Fast/Slowly-Varying Parameters

In this paper, the problem of controlling a plasma wind tunnel, to simulate the re-entry conditions of space vehicles by reproducing desired profiles of pressure and temperature on a test model, is considered. The proposed control strategy consists of two terms: (1) a feedforward control action, obtained off-line via a receding horizon technique, to guarantee the trajectory following in absence of external disturbances; (2) an output feedback control action to compensate for possible misalignment between the desired trajectory and the actual one. To take into account the numerical implementation, the feedback controller is designed in the discrete-time setting. It is shown that the linearized model of the plant can be described by a linear parameter varying (LPV) discrete-time system depending on nine uncertain parameters; eight of such parameters exhibit small excursions and no bound on their rate of variation is available, while the last parameter turns out to be slowly-varying and a bound on the rate of its variation is known. The feedback control action is designed so to robustly stabilize the overall closed loop system versus the above-mentioned uncertain parameters; a novel technique recently developed by the authors, which takes into account the information on the rate of variation of the parameters, is used in the synthesis of the controller. Numerical simulations are carried out on the nonlinear system to show the effectiveness of the proposed control scheme.