Workshop on Optimal Control of Thermal Systems in Buildings using Modelica location:University of Freiburg date:23 - 24 March 2015
In practice Model Predictive Control (MPC) is prone to model mismatch, state estimation error and disturbance prediction uncertainties which might cause instability of the controlled system. Therefore, the robustness of the controlled system should be guaranteed according to a certain level of uncertainties in the MPC.
In the context of MPC, two main types of approaches for robustness analysis exist. One type is to analyze the robustness properties of an existing control system and to conclude up to what extent of uncertainty the system with conventional MPC is robust. The other type is to design robust MPC so that the optimization problem explicitly takes into account specific measures to guarantee robustness.
The presented work is focused on robustness analysis of an existing MPC formulation. The approach is based on the method of Primbs [Primbs, 2000] which checks for satisfaction of a sufficient condition for the particular system with MPC to be robust to a given level of uncertainties. The method executes an offline routine, which is based on the optimization problem formulation and on the controller model only.
The main principle of the method is to check whether the objective function value decreases over time, which is an indication for stability. Therefore, the optimization problem is represented by means of matrix quadratic functions. This allows applying the so called S-procedure [Yakubovich, 1971], which provides a sufficient condition for the non-negativity of one or more matrix quadratic functions to imply the non-negativity of another quadratic function. An extension of the S-procedure is suggested for the needs of the particular case investigated here.
The MPC robustness analysis method is adapted and implemented for the case of a hybrid ground coupled heat pump system. The resulting linear matrix inequality problem is solved in Matlab using the YALMIP interface to call the SeDuMi solver.