Assessment and Future Directions of Nonlinear Model Predictive ...

226 C.E. Long and E.P. GatzkeP 1(psia)605856545230MeasurementUBLBSetpoint0 100 200 300 400 500 600P 2(psia)25200 100 200 300 400 500 60060P 3(psia)5040P 4(psia)Control Valves(% Open)ObjectiveFunctionValue300 100 200 300 400 500 60035302520150 100 200 300 400 500 60010050CV1CV200 100 200 300 400 500 6004 x 104937251300 100 200 300 400 500 600 1Time (min)UnachievableControl Objectivesby PriorityFig. 2. Closed-loop Results of the Simulated Network of Pressure Tanks being Controlledby the Hard Constraint formulation for Prioritized Objective NMPC, ObjectiveFunction Values, and Unachievable Control Objectivesbegins moving the system to accommodate it (Figure 2). Note that the boundsassociated with P 2 are of high priority (priority 3 and 4). The move to satisfythese constraints requires the controller to violate the lower bounds on the pressurein tank 4 (priority 7 and 8). This means that imposing hard constraintscorresponding to these control objectives renders the associated NLP infeasible.The control objectives that lead to NLP infeasibility and the objective functionof the solution at each time step is seen in Figure 2. During this transition, thecontroller is also unable to move the system fast enough to avoid briefly violatingthe upper bound on the pressure in tank 2 (priority 4). The controller doeshowever, track the new setpoint.At t = 300 minutes, a disturbance is imposed on the system by simulatinga leak in the first tank. The controller cannot respond to the disturbance fastenough to avoid the lower bound on the pressure in this tank (priority 5). Howeverthe controller is able to quickly return the pressure within the limitingvalues. This action saturates one of the inputs. Again, P 2 is maintained withinits limits but is unable to track the setpoint in an offset free position. At t = 450minutes, while still operating under a disturbance, P 2 is returned to its original