(131d) PID Controller Design for Constrained Optimal Control of Inventory Loop

An analytical design method for a simple proportional-integral (PI) controller is developed for the optimal control of the liquid level loop to explicitly handle important control specifications. The constrained optimal control problem for the liquid level loop is formulated by using a proper variable transformation and converted into an unconstrained optimization problem to find an optimal PI controller tuning rule. The proposed PI controller minimizes the rate of change of the outlet flow and the deviation of the level subject to two important constraints in the level loop: the maximum allowable rate of change in the outlet flow rate and the maximum allowable deviation of the level. The simulation results show that the constrained optimal control of the liquid level loop can be successfully implemented using a simple PI controller with the proposed design method. In addition, the analytical form of the resulting tuning rule has a clear advantage to practitioners in refinery industry.