Run-Time Efficiency of Bilinear Model Predictive Control Using Variational Methods, With Applications to Hydronic Cooling

Abstract

Effective real-time execution of nonlinear model predictive control (NMPC) on embedded systems is significantly dependent on the controller formulation. This paper studies the effect of model structure and cost functions on the computation time of scalar bilinear NMPC using variational methods, with hydronic cooling applications. Two algebraically equivalent nonlinear model structures common in literature are primarily considered: a linear state equation with state-dependent control constraints and a bilinear state equation with time-invariant rectangular control constraints. Additionally, the effects of three cost function formulations are also considered: minimum-time, quadratic regulation, and efficient state constraints. High-fidelity computer simulations, hardware-in-the-loop testing, and experiments on a bench-scale hydronic cooling system are used to study sources of computational complexity, rates of convergence, initialization techniques, and overall effectiveness of the different models and costs. These results suggest that NMPC with bilinear state equations, minimizing pump power and a one-sided quadratic state cost, converges sufficiently fast and reliably. This presents an attractive alternative to the traditionally constrained linear quadratic regulator-based NMPC on embedded systems.