Parameter estimation for two-tank system using multiparametric programming

Multiparametric programming simplifies optimization problems by allowing solutions to be expressed as functions of varying parameters.  This method enhances the accuracy and efficiency of parameter estimation, which is crucial for dynamic systems.  This study presents a novel parameter estimation approach for two-tank system using multiparametric programming (MPP).  Two-tank system is widely employed in various applications, necessitating efficient management of liquid levels for safe and effective operation.  Accurate parameter estimation in tank systems is critical for optimal control; however, conventional estimation methods often encounter complexities and computational demands that can result in delays and inaccuracies in diagnosing system parameters.  The proposed method employs MPP to accurately identify parameters of the tank system.  In this approach, the two-tank system is modeled using ordinary differential equations that represent the dynamics of liquid levels in each tank. The Karush–Kuhn–Tucker method is utilized to solve the parameter estimation problem, deriving an explicit solution with particular focus on the cross-sectional area of the outlet pipe.  The estimated parameter values are calculated using the state variables of the two-tank system, facilitating a comprehensive evaluation of the proposed method.  The results demonstrate that the proposed method accurately estimates parameters using an explicit solution, offering faster computations and reduced complexity compared to conventional optimization methods.