Formulações explícitas para controladores preditivos generalizados: uma abordagem multiparamétrica

Abstract

Generalized Predictive Control (GPC) is one of the most traditional and popular Modelbased Predictive Control (MPC) techniques in industry and academia and has been applied over decades in several systems to improve the control performance. This type of controller uses process model information to predict future system behavior. In addition, GPC can deal directly with both MIMO systems and process constraints. However, when considering the constraint set, the controller needs to solve a Quadratic Programming (QP) (or a Linear Programming – LP) in real time, which can be prohibitive in certain cases, such as for embedded systems. This work uses multiparametric programming (mp) to generate an Explicit Piece-wise Affine (PWA) control law for GPC (mp-GPC) which holds the same control performance without the need to keep solving the optimization problem at each sample time. Hence, initially, the proposed formulation is compared with GPC based on online QP. The results show that the performance is maintained, reducing the computational time to calculate the control action. Then, a new format is proposed, which differs from the last one by the number of parameters needed in the mp formulation. Both propositions are applied in three different situations: a MIMO system, a process with input-output delays and a underactuated system. A comparison is made by checking the computational time spent to calculate the control signal, as well as the time required for mp resolution. Finally, studies involving a Hybrid Multiparametric GPC formulation were done , which makes use of the resolution of a multiparametric Mixed-Integer Linear Programming (mp-MILP). A nonlinear valve is used as a case study, in which its nonlinear characteristics are treated as a set of inequalities for the optimization problem, in order to minimize its effects.