LMI Control Design for Nonlinear Vapor Compression Cycle Systems

To effectively control vapor compression cycle (VCC) systems whose dynamics are highly nonlinear, it is necessary to develop plant models and control laws for different operating regions. This paper presents a first-principles modeling framework that captures four operation modes over the operating envelope to construct an invariant-order switched system. To synthesize a multi-input multi-output (MIMO) control system, the Linear Quadratic Regulator (LQR) technique is framed as a control optimization problem with Linear Matrix Inequality (LMI) constraints which can be simultaneously solved for the set of considered linear systems. Stability and performance characteristics of the controlled system are guaranteed using a common quadratic Lyapunov function. Simulation results in a case study show that the LMI-based controller can maintain system operation at optimal set-points with mode switching over a wide operating envelope.