Modeling proportional–integral controllers in tracking and economic model predictive control

Abstract

In industrial applications, model predictive control (MPC) is typically installed in a hierarchical operational framework above regulatory layer proportional–integral (PI) controllers. Traditional MPC implementations do not include a dynamic model of the regulatory layer PI controller in the MPC optimization problem. This paper presents case studies to illustrate the advantages of modeling the PI controller in the MPC optimization problem. A PI controller implemented with an antiwindup scheme introduces significant nonlinearity into the MPC model that can be challenging to optimize with standard nonlinear solvers. Therefore, an approximate linear PI control law model is proposed for use in the MPC optimization problem. Hard constraints of the plant actuator manipulated by the PI controller are also included in the MPC problem. We illustrate using simulation studies that this PI controller modeling approach in the MPC optimization problem provides the following advantages: (i) systematic constraint handling in the presence of an unmeasured disturbance in the PI feedback loop, (ii) disturbance rejection forecast of the PI controller in the MPC optimization problem for a slow PI feedback loop, and (iii) optimizing plant economics of a cascade control architecture in which the PI controller manipulates a variable that directly influences the economic objective. Case studies on a continuous stirred tank reactor (CSTR) and heating, ventilation, and air-conditioning (HVAC) system are presented to highlight these advantages of modeling the PI controller in the MPC optimization problem.