A New Application of the Hill Repressor Function: Automatic Control of a Conic Tank Level and Local Stability Analysis

Abstract

The Hill function is commonly used as a building block to model different dynamic patterns found in the response of genetic regulatory circuits within microorganisms and cells. These circuits are characterized by fast response and robustness against unmeasured disturbances. Therefore, microorganisms and cells can survive even if they are subjected to strong changes in their environment. However, as far as we know, the Hill function has not been used before to design process control systems. In this work, the repressor Hill function is applied to control the level of a conic tank. To eliminate the offset, we added integrative action. A local analysis was applied to define stability limits for the control parameters. A cost function that includes the error and the control effort was used to compare the performance of the Hill control against a standard PI and a PID-Dahlin controller.