Parametric investigation of Linear Quadratic Gaussian and Model Predictive Control approaches for thermal regulation of a high precision geometric measurement machine

Abstract

A numerical comparison between Linear Quadratic Gaussian (LQG) Compensator and Model Predictive Control (MPC) is investigated in this paper for thermal regulation of a high precision dimensional measurement machine subject to four thermal disturbances (laser interferometers). The aim is to control temperature at four locations thanks to four surface actuators, whatever the shape of perturbation signals in the range of magnitude of a few Watt considered for the actual device. Since the complex 3D thermal model of the machine cannot be used for real-time control, a modal reduced model is built and then used for state feedback control.Two configurations (points to be controlled close to or far from actuators and perturbations) are studied. A parametric analysis is carried out and shows the main differences between both control techniques. For MPC, the lower the penalization coefficient is, the better the results are, provided that the number of time steps for prediction horizon is sufficiently large. On the contrary, for LQG, it has been observed that decreasing the cost parameter down to its critical value for which the LQR Riccati equation cannot be solved anymore, leads to the control failure.