Gain Scheduling PID Controller for Conical Tank Level Control

Abstract

Level control of nonlinear systems is an important problem in process industries. The conical tank system is a nonlinear process because the cross-sectional area varies with the height of the liquid. Conventional PID controllers often fail to provide satisfactory performance over the entire operating range of such nonlinear systems. This paper presents the design and implementation of a Gain Scheduling PID controller for controlling the liquid level in a conical tank. The nonlinear model of the conical tank is derived using mass balance principles. The operating region of the tank is divided into different sections and separate PID parameters are designed for each region. A gain scheduling mechanism is used to switch the controller parameters based on the current tank level. The proposed control system is implemented and simulated using MATLAB/Simulink. Simulation results show improved dynamic response, reduced overshoot, faster settling time and better set-point tracking compared to a conventional PID controller.

Introduction

The text explains the control of liquid level in a conical tank, which is an important industrial process in areas like chemical plants, refineries, and water treatment systems. Because the tank has a changing cross-sectional area, its behavior is nonlinear, making it difficult to control using traditional PID controllers across all operating conditions.

To address this, the paper proposes a Gain Scheduling PID controller, where different PID parameters are used for different operating regions of the tank. The system is mathematically modeled using mass balance principles and Torricelli’s law, resulting in a nonlinear differential equation that is also approximated using a FOPDT transfer function for control design.

A brief literature review highlights previous work on PID control, nonlinear control techniques, and model predictive control, showing that nonlinear systems require more adaptive and robust control strategies.

Finally, simulations are conducted to validate the proposed approach.

Conclusion

The design and simulation of a Gain Scheduling PID controller for controlling the level of a conical tank system. The nonlinear behavior of the tank was handled by dividing the operating range into multiple regions and assigning different PID gains for each region. Simulation results demonstrated that the Gain Scheduling PID controller significantly improves the dynamic performance compared to a conventional PID controller. The proposed method provides faster response, reduced overshoot, and better set-point tracking.

References

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Copyright

Copyright © 2026 Gite Pratiksha , Gadhave Mayuri, Pawar Jagdish, C. B. Kadu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.