A lightweight metaheuristic-driven adaptive PID approach for nonlinear conical tank regulation

Nonlinear process systems, such as conical tanks, pose significant control challenges owing to their varying cross-sectional geometry, which causes the dynamic behavior to change with the liquid height. Traditional fixed-parameter PID controllers often fail to deliver consistent performance across the entire operating range. To address this, a Flamingo Search-based Model Reference Adaptive PID (MRAC-PID) controller is proposed to adaptively tune the PID gains. In contrast to traditional metaheuristic optimizers, e.g., Particle Swarm or Genetic Algorithms, which require extensive computing and considerable time to converge, the Flamingo Search Algorithm (FSA) is optimized quickly and with no substantial computing cost, and thus is applicable to embedded implementation. The controller was implemented on a system based on ESP32-Jetson Nano hardware and tested experimentally in different operating conditions. The findings prove the innovativeness of the integration of the FSA in an MRAC framework of nonlinear liquid-level control, resulting in a lowest rise time of 8 s, settling times of 30–45 s, and a minimum overshoot of 2–5%, whilst steady-state errors are kept under 0.5 cm. Robustness analysis further confirmed phase margins of 85–90° and gain margins exceeding 20 dB. The proposed method had lower overshoot, faster settling, and better disturbance rejection compared to Ziegler-Nichols and Cohen-Coon tuned PID controllers. The results prove the proposed framework as a computationally efficient, robust, and scalable approach to real-time nonlinear process control.