Comparison of the Operation of Fixed Point Iteration-based Adaptive and Robust VS/SM-type Solutions for Controlling Two Coupled Fluid Tanks

In this paper controlling the fluid level in the lower fluid tank of two coupled ones by setting the ingress rate at the upper tank was considered for comparing the behavior of two solutions: the PD-type Robust VS/SM, and the adaptive, Fixed Point Iteration (FPI)-based controllers. The coupled tanks provide smooth and truncation-type nonlinearities in a relative order 2 control task, therefore it serves as a good benchmarking paradigm for the various control approaches. The controllers were simulated by simple sequential codes written in the Julia programming language. It is shown that the adaptive controller can accommodate itself to subtle details that are not taken into consideration in the robust control. The robust controller provides non-smooth, switching-type results while the adaptive one can provide smooth solution even in the presence of system modeling errors. In the case of the adaptive controller appropriate setting of the control parameters play central role. While mathematically the FPI-based solution is as simple as the Robust VS/SM controllers, in contrast to the Lyapunov function-based adaptive solutions, it easily can be inserted in the mathematical structure of the optimal controllers, so studying its behavior in the case of strongly nonlinear systems may open new ways for its successful applications.