Study On Equivalent Soft-constraint Approach For Model Predictive Control Based On Fuzzy Decision

In the field of industrial process control,especially the chemical process,there generally exist kinds of constraints on input,output and other variables.Constrained Model Predictive Control(CMPC)which can take various constraints into account provides a precise solution to the optimization control problem of a constrained system.Constraints which can not be violated called hard constraints,constraints can be violated called soft constraints.In general,region both input constraints and output constraints is satisfied called the feasible region.Output constraints often cannot be strictly enforced at all times.In the presence of disturbances,for example,it is not always possible for the controller to enforce the output constraints.The strategy is enforce them when they are feasible and relaxes them in a clear way when they are not.The two approach are minimal time approach and soft constraint approach.A soft-constraint approach to handle infeasibility is discussed violations of the state constraints are allowed,but an additional term is introduced in the objective,which penalizes constraint violations.An advantage of the method is that it is computationally cheap,requiring the solution of a single quadratic program.But how to choose the coefficient of the slack variable does not have a determine rule.For the more feasible in controller design,formal researcher put forward Model Predictive Control(MPC)with Fuzzy Decision Making(FDM),which introduce fuzzy theory into traditional model predictive control.In fuzzy decision MPC,the desired control performance is represented by membership functions.Membership functions has the advantage in description things with fuzzy concept.Fuzzy theory can be used to descript the soft constraint problem such as the control requirement “constraint can be violated to some extent”.For constraints on the outputs,which is not hard,we can use the fuzzy membership function to describe the notation that the constraints can be violated to some extent.However,fuzzy model predictive control problem is generally hard to solve.This article will try to find the equivalent soft-constraint approach for model predicted control based on fuzzy decision..For one kind of fuzzy model predictive control problem with specific membership functions and aggregation operator,we can transform it to a soft constraint optimization problem,which is basically a quadratic programming.Hence the computational burden is largely reduced.Simulation results verify this.And for the condition of another kind of aggregation(Max-min aggregator),we transform the fuzzy programming to a equivalent linear programming.