Limitations of a PI controller for a first-order nonlinear process with dead time

A nonlinear process, the conical tank level process whose parameters vary with respect to the process variable, is considered. The time constant and gain of the chosen process vary as a function of level. A deliberate dead time is introduced in the system by delaying the valve opening. The limitations of the conventional PI controller tuned using Ziegler-Nichols settings for the chosen process are brought out. The servo and regulatory responses through simulation and experimentation for various magnitudes of set-point changes and load changes at various operating points with the controller tuned only at a chosen nominal operating point are obtained and analyzed. Regulatory responses for output load changes are studied. A benchmark system is presented to understand clearly how variations of system parameters affect the performance of the controller. A gain scheduled controller is proposed to handle the control problem. Present work illustrates the simplicity and effectiveness of the gain scheduling.