Robust model predictive control of HVAC systems with uncertainty in building parameters using linear matrix inequalities

ABSTRACT In this work, a new robust controller is proposed for building climate control in presence of parametric uncertainties. The design of the controller is based on the Model Predictive Control (MPC) framework and it includes time-varying constraints. The robust design is implemented by explicitly considering parametric uncertainty in the synthesis of the control law. Variations of the parameters of the buildings are represented in the form of polytopic uncertainty. The robust control action is obtained by minimizing an appropriate ‘worst-case’ cost function, which leads to the definition of a min–max optimization problem. This optimization problem is formulated using Linear Matrix Inequalities (LMIs) that allow for efficient numerical computation of the control command. Simulation results show that the proposed approach is successful in keeping the indoor temperature of the building in the desired range even in presence of large model uncertainties. The proposed controller is also compared with a nominal controller synthesized without accounting for parametric uncertainty. Numerical results confirm 24% better performance of the robust design in comparison with the nominal controller with same conditions. Further, simulation results also demonstrate that the robust control system achieves 17% better performance in the case of severe conditions of uncertainty.