Analysis On The Controllability Of Model Predictive Control Under The Situation Of Soft Constraints Being Activated

As for a process control problem,control system is designed to fulfill requirements of stability,accuracy and rapidity.At the premise of stability,the system variables are controlled to reach the control target exactly and rapidly.Compared to other conventional control strategies,model predictive control(MPC)algorithm has made great advances for improving control performance and stability.Particularly in dealing with constrained multi-input,multi-output control problems,constrained model predictive control(CMPC)algorithm solves the problem will on the special rolling optimization algorithm,and drives the system variables reach the optimal solution under the constraint effect.In the practical industry process,the feasible region is usually composed by the intersection of the constraints of input and output variables.And the desired value is generally obtained from the operator or figured out after synthesizing factors such as process technology,profit,consumption and so on.It has been proven that the desired value is always located at bound of definite constraints of feasible region(system constraints),where the partial input and output variables become constants for constraints and cannot participate in controlling.Meanwhile,the system framework,free degree and feasible region change slightly.The change of feasible region directly affects the feasibility and stability of control.For steady state model,locating the desire value at the bound of feasible region may weaken the stabilities of control.While,for dynamic process of control,the motion of system variables may activate the constraints.Constraints limit the optimal trajectory of variables at some time leading to infeasibility of control strategy and unreachability of control target.Despite CMPC deals with constraints well,the problem about infeasibility and unreachability is still occurring.For solving the above problems,this paper proposed a new control target adjustment mechanism and a new soft constraint adjustment mechanism to ensure the reachability and the feasibility.After processing,the new CMPC ensures that system variables don't activate constraints in the control process.Thus,the system variables move to the optimal value according to the optimal control trajectories,which is under approximately unconstrained state.To some extent MPC with constraints has been transformed into MPC without constraints.This is of great significance to the current large-scale industrial control process with universal constraints.To get the essence on influence about the dynamic process of MPC to control effect,the effect on feasible region is analyzed,which is about the P step prediction of output variables of state space models controlled by CMPC.And the effect of dynamic constraints of outputs to feasibility is analyzed as well.Based on all above,the control target adjustment mechanism is proposed,which is applied after implementing the soft constraints adjustment,when the new system constraints are all hard constraints and cannot be adjusted any more.The mechanism makes the system variables reach the optimal value under constraint permission at stable state.For partial control system,it can be accepted by technical requirements that the constraints are violated in some moment or in a limited time.Based on the analysis of system structure change with two situations about the desired value set at boundary of hard constraints and soft constraints,the control feasibility of adjusting constraints is discussed,and the objective function is altered.Then the upper bound and infimum of dynamic reachable set of outputs in the control process are obtained.After studying all above,a soft constraint adjustment mechanism is proposed to apply for a situation when the soft constraints are activated.Through relaxing the soft constraints,the unreachability of control target caused by constraints being activated is avoided.