Mixed-integer Model Predictive Control Research Articles

Mixed-integer MPC for the temperature control of the batch reactor

Discrete Model Predictive Control (MPC) became one of the most widespread modern control principles. Process controls with a finite number of admissible values are common in a large number of relevant applications. For this type of optimization problems, the computational complexity is exponential in the number of binary optimization variables. The solver is based on a standard branch-and-bound method and interior point method is used for solution of the relaxed problem. The simulation experiment involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve.

Management of hybrid energy supply systems in buildings using mixed-integer model predictive control

In this paper a mixed-integer model predictive controller for hybrid energy supply systems in buildings is presented. This approach is based on a hierarchical building control concept where the energy supply level is coupled to the energy consumption level only by the heat load. The supply level is characterized by non-linear dynamics due to a stratified water storage tank and a switched heat pump with minimum on/off times. The mixed-integer model predictive controller optimizes the unit commitment problem at minimum costs while satisfying the consumption level’s predicted heat load. The hybrid system is formulated as a piecewise affine model comprising continuous and discrete system inputs. Moreover, the proposed controller is able to manage the stratified storage tank including switching sequences of the heat pump with respect to energy price forecasts. The effectiveness of this approach is shown by a comparison to a model predictive controller with an a priori fixed operation mode profile, where the heat pump is only operating at night, and discussing the effect of the variation of the stratified storage tank size. The proposed concept is able to flexibly manage all sizes of stratified storage tanks with better performance than the reference control strategy, which is only effective for larger tanks. Additionally, a robustness analyses demonstrates that the mixed-integer model predictive controller can handle errors in the heat load prediction from the consumption level. Both analyses show promising results for the practical use of the proposed controller within the hierarchical control concept or as a control module in a similar but more general application.

Hierachical Fuzzy MPC Concept for Building Heating Control

This paper presents a hierachical model predictive control (MPC) structure with decoupled MPCs for building heating control using weather forcasts and occupancy information. The two level control structure embeds a fuzzy MPC (FMPC) for user comfort optimization and a mixed-integer MPC (MI-MPC) for energy optimization at minimal costs. As FMPC uses a set of local linear models classical linear MPC theory is applicable, though the underlying system dynamics is non-linear. The supply level in a large modern office building always features switching states of aggregates, hence an MI-MPC is used for energy supply optimization. Additionally, both FMPC and MI-MPC consider all relevant constraints. The innovation in this study, beside the usage of FMPC for building control, is the decoupling of the energy supply level and the user comfort with a single coupling node. Although a global optimum is not guaranteed, a decoupled control system often is more attractive for industrial applications and building operators. The perfomance of the proposed control structure is demonstrated in a simulation with a validated building model, and two different disturbance scenarios are presented.

A mixed-integer model predictive control formulation for linear systems

Since their inception in the early 1980s industrial model predictive controllers (MPC) rely on continuous quadratic programming (QP) formulations to derive their optimal solutions. More recent advances in mixed-integer programming (MIP) algorithms show that MIP formulations have the potential of being advantageously applied to the MPC problem. In this paper, we present an MIP formulation that can overcome difficulties faced in the practical implementation of MPCs. In particular, it is possible to set explicit priorities for inputs and outputs, define minimum moves to overcome hysteresis, and deal with digital or integer inputs. The proposed formulation is applied to simulated process systems and the results compared with those achieved by a traditional continuous MPC. The solutions of the resulting mixed-integer quadratic programming (MIQP) problems are derived by a computer implementation of the Outer Approximation method (OA) also developed as part of this work.