OPTIMIZING PID CONTROLLERS USING THE HIPPOPOTAMUS OPTIMIZATION ALGORITHM AND INTEGRAL ERROR CRITERIA

DESIGN DETALS
This design presents the application of the Hippopotamus Optimization Algorithm (HOA), a recent nature-inspired metaheuristic, for the optimal tuning of Proportional–Integral–Derivative (PID) controller parameters. The optimization process is guided by minimizing standard time-domain error criteria, including the Integral of Squared Error (ISE), Integral of Absolute Error (IAE), Integral of Time-weighted Absolute Error (ITAE), and Integral of Time-weighted Squared Error (ITSE). These performance indices are widely used to assess the quality of control system responses in terms of accuracy, stability, and transient behavior. These indices reflect the system’s dynamic performance and stability in response to disturbances and setpoint changes.

ISE=∫_0^∞▒〖e^2 (t)dt〗,
IAE=∫_0^∞▒|e(t)|dt,
ITAE=∫_0^∞▒t|e(t)|dt,
ITSE=∫_0^∞▒〖te^2 (t)dt〗

Using HOA, the PID tuning method to get optimal Proportional Gain (Kp), Integral Gain (Ki) and Derivative Gain (Kd) by applying the transfer function that is given as:
C(s)=K_p+K_i/s+K_d s

Results demonstrate that HOA effectively achieves faster convergence and improved system performance, yielding reduced overshoot, settling time, and steady-state error. The findings highlight the potential of the Hippopotamus Optimization Algorithm as a powerful and reliable tool for PID controller design in dynamic systems.

REFERENCES
Reference Paper-1: Tuning of PID Controller Using Particle Swarm Optimization (PSO)
Author’s Name: Mahmud Iwan Solihin, Lee Fook Tack and Moey Leap Kean
Source: IJASEIT
Year: 2011

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