Locally Optimal PI Controller for a
Two-Tank System
Igor Krčmar, Velibor Đalić, Aleksandar Rakić, and Petar Marić
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.