Analytical design of a proportional-integral controller for constrained optimal regulatory control of inventory loop

An analytical design method for a simple proportional-integral (PI) controller is developed for the optimal control of a constrained inventory loop. The proposed method explicitly deals with the important constraints in the inventory loop, such as the maximum allowable rate of change in the manipulated variable, the maximum allowable decay ratio and damping coefficient in the output response, as well as minimizing the optimal control specification. The simple and explicit form of the resulting tuning rule is clearly advantageous to practitioners.