Lyapunov-based adaptive state-space controller for liquid level control of a coupled tank system with unknown model

In this paper, a Lyapunov-based adaptive state space controller is designed to realize liquid level control in a coupled tank system. The proposed controller is a kind of adaptive control system that combines the principles of state space representation with Lyapunov stability theory to estimate unknown parameters and control a dynamic system. This approach ensures that the system remains stable even when the exact model parameters are unknown or change over time. Moreover, in order to test the performance of the proposed controller, proportional integral (PI) + feedforward (FF) controller is also applied to the same system under the same conditions and the results are compared. The results show that the proposed controller outperforms the PI + FF controller in terms of system response parameters such as rise time, percent overshoot, and settling time. On the other hand, when the error performance metrics integral squared error (ISE), integral time-weighted squared error (ITSE), integral time-weighted absolute error (ITAE), and integral absolute error (IAE) are evaluated, it is seen that the same situation is also realized here, and the proposed controller follows the reference signals with lower error values in real-time studies for different reference signals.