Constraint boundary effect in model predictive control and corresponding solution

In constrained predictive control, the optimal control sequence may reach the boundary of the feasible domain during optimization due to the existence of constraints, in other words, one or more variables will be saturated, which is the constraint boundary effect. However, it is undesirable that the manipulated variables get saturated in process control. Therefore, firstly based on a steady-state model, it is proved that the optimal solution will reach the desired value when it is in the feasible domain; it is shown that the optimal solution can be viewed as the projection of the desired value onto the feasible region when the desired value is outside of the feasible region. Secondly, to avoid the saturation of variables when the system is in a transient or steady state, the parameters of the objective function are altered and the control performance is improved. The terminal constraint is imposed to guarantee the stability. Finally, the simulation of a constrained continuous stirred tank reactor (CSTR) model verifies the correctness of the proposed method and the effectiveness of adjustment of objective function.