The four-tank benchmark: a simple solution by embedded model control

The four-tank benchmark is a multivariate and nonlinear control problem which has been widely studied in the literature. Two pairs of tanks in series are supplied by two pumps. Under certain configurations, the Embedded Model Control approach provides a simple decoupled solution by separately controlling the two output tank levels and treating the input flow as a partly unknown disturbance. Neglected dynamics in a form of unknown delays both in sensors and actuator dynamics is considered. The core of the control unit is a discrete-time embedded model consisting of unknown disturbance dynamics and partly known nonlinear interactions. The embedded model is driven by the plant command and by a feedback vector which is retrieved from the model error. The feedback is capable of keeping updated the unknown disturbance prediction, ready to be cancelled by the control law. The control gains are tuned using two sets of closed-loop eigenvalues in order to trade-off between disturbance rejection and robust stability. Simulated runs under different tank interactions prove design effectiveness.