OPTIMAL PID CONTROLLER DESIGN-BARREL THEORY-BASED OPTIMIZER CONSIDERING MULTIPLE PERFORMANCE INDICES

DESIGN DETALS
The design of an optimal proportional–integral–derivative (PID) controller is essential for achieving superior dynamic performance and stability in modern control systems, particularly under nonlinearities and parameter uncertainties. This design presents an efficient metaheuristic-based framework for optimal PID controller tuning using the Barrel Theory-Based Optimizer (BTO), considering multiple performance indices, namely 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). The tuning process is formulated as an optimization problem, where the objective is to determine the optimal proportional, integral, and derivative gains that minimize these error criteria while ensuring desirable transient and steady-state characteristics.

BTO enhances the search process through an adaptive mechanism that improves weaker candidate solutions while utilizing elite solutions to guide convergence, thereby achieving a balanced trade-off between exploration and exploitation. This capability enables robust and efficient navigation of complex search spaces associated with PID tuning problems. The algorithm is implemented within a simulation environment and evaluated across different performance indices to analyze its effectiveness under varying control objectives.

Simulation results demonstrate that the BTO-based PID tuning approach significantly improves system performance by reducing overshoot, minimizing settling time, and achieving better error minimization compared to conventional tuning methods. Additionally, the comparative analysis of different performance indices reveals inherent trade-offs between response speed, accuracy, and stability. The findings confirm the robustness, reliability, and adaptability of BTO as a promising optimization technique for advanced PID controller design in complex dynamic systems.

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

Using BTO, 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

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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