Locally Optimal PI Controller for a Two-Tank System

The paper provides an extensive experimental analysis of an optimal PI controller for the two-tank system. The two-tank system is a benchmark hydrodynamic system. The PI controller has proportional action placed in a feedback path of the system, thus supporting aperiodic response of the system. The optimal PI controller tuning is based on transfer function of the system, and it minimizes surface between the error signal and the time axis. The choice of the minimization criterion is adequate as the system has aperiodic step response. The extensive experimental analysis is performed on the laboratory testbed to assess the performance of the optimally tuned PI controller when applied to the two-tank systems in step response tasks, reference tracking tasks, and disturbance rejection tasks. The results of the experiments verify the design procedure of the PI controller. The designed PI controller provides noticeable slow start of the system, thus forcing an actuator to operate on a border line of the dead zone for a significant period. To remedy the situation, a feedforward modification of the controller is proposed. Gain of the feedforward part is time varying. At the beginning of the system operation, it provides significant value of the control signal and safe start of the system. On the other hand, as time advances, the gain of the feedforward part vanishes to zero. Although the feedforward modification detunes optimal behavior of the system, it adds value to the operation of the system. Experimental analysis performed on the laboratory testbed verifies utilities introduced by the feedforward controller modification.