Sigmoidal Activation of Proportional Integral Control Applied to Water Management

A conventional proportional integral (PI) controller is modified with a nonlinear activation function (sigmoid function) applied directly to the controller output in order to improve the stability and target fidelity of the system response to large variational inputs in both state and internal controller gain variables. The controller is implemented in a simulated water management role applied to a major subregional pumping station between Lake Okeechobee, the Loxahatchee National Wildlife Refuge (WCA1), and the West Palm Beach supply canal (C51) in the South Florida geographic region. The simulation consists of an integrated hydrological numerical model implemented in the Regional Simulation Model (RSM), which is currently under development at the South Florida Water Management District. Analysis of the modified controller in the Laplace domain establishes the expected control behavior, and subsequent results of the simulation for the conventional PI and the sigmoid modified controller are presented and compared. The modified controller achieves significant improvement in stability while simultaneously reducing the control signal energy.