Key Takeaways & Executive Findings
- •• Enhanced Hippopotamus Optimization (EHO) integrates Latin hypercube sampling, adaptive lens reverse learning, and an adaptive perturbation mechanism to improve population diversity and global search for PID parameter tuning. • EHO demonstrates superior accuracy, convergence speed, and stability compared to five other algorithms and the classical Ziegler–Nichols method across diverse system types. • In CEC2022 benchmark tests, EHO outperforms the original hippopotamus optimization and multiple classical/state-of-the-art intelligent algorithms. • For quadrotor UAV cascade PID trajectory tracking, EHO achieves significantly lower integral time absolute error (ITAE) values—59.979, 22.162, and 0.017 for x, y, z channels—than baseline methods.
Abstract
Effectively tuning the parameters of proportional–integral–derivative (PID) controllers has persistently posed a challenge in control engineering. This study proposes enhanced hippopotamus optimization (EHO) to address this challenge. Latin hypercube sampling and adaptive lens reverse learning are used to initialize the population to improve population diversity and enhance global search. Additionally, an adaptive perturbation mechanism is introduced into the position update in the exploration phase. To validate the performance of EHO, it is benchmarked against hippopotamus optimization and four classical or state-of-the-art intelligent algorithms using the CEC2022 test suite. The effectiveness of EHO is further evaluated by applying it in tuning PID controllers for different types of systems. The performance of EHO is compared with five other algorithms and the classical Ziegler–Nichols method. Analysis of convergence curves, step responses, box plots, and radar charts indicates that EHO outperforms the compared methods in accuracy, convergence speed, and stability. Finally, EHO is used to tune the cascade PID controller for trajectory tracking in a quadrotor unmanned aerial vehicle to assess its applicability. The simulation results indicate that the integrals of the time absolute error for the position channels (x, y, z), when the system is optimized using EHO over an 80 s runtime, are 59.979, 22.162, and 0.017, respectively. These values are notably lower than those obtained by the original hippopotamus optimization and manual parameter adjustment.
1. Introduction
Proportional–integral–derivative (PID) controllers are widely used in industrial systems due to their simple structure, straightforward implementation, and model independence, which contribute to their versatility and robustness. Achieving optimal performance with a PID controller necessitates precise tuning of its three parameters: proportional gain, integral gain, and derivative gain. Proper tuning can ensure desired performance characteristics, such as minimal overshoot, fast settling time, and robustness to disturbances. However, effective tuning of a PID controller presents significant challenges due to the intricate dynamics of the controlled systems and the inherent trade-offs in parameter adjustments. This study explores advanced optimization techniques to automate the PID controller tuning process, aiming to enhance control performance and robustness across various applications.
Tuning PID controller parameters has been recognized as a challenging and significant issue, making it a popular research topic in both academic and industrial settings. Trial and error is one of the most intuitive and straightforward methods for tuning PID controllers. It involves manually adjusting the PID parameters, observing the system response, and iterating the process until the desired performance is achieved. Despite its simplicity, trial and error can be time-consuming, and requires a significant level of expertise to achieve optimal results. Traditional methods for tuning PID controller parameters are also widely used due to their simplicity and ease of implementation. These methods provide practical rules and guidelines to set the PID controller parameters based on the system response characteristics. The most well-known traditional methods include the Ziegler–Nichols (ZN) method (Ziegler and Nichols, 1942), Chien–Hrones–Reswick (CHR) method (Chien et al., 1952), and Cohen–Coon (CC) method (Cohen and Coon, 1953), providing general guidelines, but often requiring extensive manual adjustments and iteration.
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Kailong MOU, Mengjian ZHANG, Deguang WANG, Ming YANG, Chengbin LIANG (2025). Enhanced hippopotamus optimization algorithm for tuning proportional–integral–derivative controllers. Frontiers of Information Technology & Electronic Engineering. https://doi.org/10.1631/FITEE_2400492
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Frequently Asked Questions
What is the Enhanced Hippopotamus Optimization (EHO) algorithm?
EHO is a metaheuristic optimization algorithm proposed for tuning PID controllers. It enhances the original hippopotamus optimization by using Latin hypercube sampling and adaptive lens reverse learning for population initialization, and introduces an adaptive perturbation mechanism in the exploration phase to improve global search and convergence performance.
How does EHO improve PID controller tuning compared to traditional methods?
Traditional methods like Ziegler–Nichols rely on heuristic rules and manual adjustments, which are time-consuming and often suboptimal. EHO automates the search for optimal PID gains, achieving lower overshoot, faster settling time, and better disturbance rejection across various system types, as demonstrated by superior performance on CEC2022 benchmarks and simulation tests.
What performance metrics were used to evaluate EHO?
The study evaluated EHO using convergence curves, step responses, box plots, and radar charts. For quadrotor trajectory tracking, the integral of the time absolute error (ITAE) was used, achieving values of 59.979, 22.162, and 0.017 for the x, y, and z position channels, respectively.
In which application was EHO tested for practical feasibility?
EHO was applied to tune a cascade PID controller for trajectory tracking in a quadrotor unmanned aerial vehicle (UAV). The simulation results showed notably lower ITAE values than those obtained by the original hippopotamus optimization and manual parameter adjustment.
What are the key components of the EHO algorithm's novelty?
The novelty lies in three enhancements: (1) Latin hypercube sampling for diverse initial population; (2) adaptive lens reverse learning to strengthen global search capability; and (3) an adaptive perturbation mechanism in the exploration phase to maintain population diversity and avoid premature convergence.
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