Two-State Bilinear Predictive Control for Hot-Water Storage Tank

The paper presents original predictive algorithm for use in two-state (or binary) input control of nonlinear systems which are described with state-constrained bilinear models. It is shown in the paper, that instead of non-linear continuous-time model, non-stationary linear discrete-time model can be used to predict the system response. On the other hand, state constrains can be attached to the criterion index to be minimized in the predictive control law. This inclusion assures the closed-loop stability of the control system and simplifies minimization problem. The proposed algorithm is particularly valuable for applications in heating systems where bilinearity follows from the heat exchange due to flow of liquid medium and constrains concern temperature regime. Application of the algorithm to control a hot water tank is presented in the paper. The tank is modeled by stratified model. Necessity of state observation is pointed out and the observer is derived. Speed of observer convergence is discussed. Performance of the proposed algorithm has been compared with standard relay controller. Experiments have been carried out in real-life environment. Simulations have been used to tune the resulting predictive controller.