This paper proposed an improved structure of Proportional Integral Derivative (PID) controller called as Integral Proportional Derivative (I-PD), applied for Automatic Generation Control (AGC) of Multi-Source Interconnected Power System (IPS). The parameters of the proposed controller are optimized with a newly developed, powerful, nature-inspired meta-heuristic technique known as Fitness Dependent Optimizer (FDO). To show the efficacy of the proposed controller and the technique used, they have been tested on three different system models. Initially, a two-equal area of diverse source generation including reheat-thermal, gas, and hydro power system is considered. In the second scenario, the same power system model is used with addition of two non-linearities; Generation Rate Constraint (GRC) and Governor Dead Band (GDB). Lastly, multiple non-linearities including Governor Dead Band (GDB), Time Delay (TD), Generation Rate Constraint (GRC), and Boiler Dynamics (BD) have been considered to make the initial system more realistic and practical. The outcome from the proposed techniques is also compared with some recently meta-heuristic algorithms such as Teaching Learning Based Optimization (TLBO), Particle Swarm Optimization (PSO) and Firefly Algorithm (FA). From the results, it has been perceived that the proposed technique shows superior performance in respect of Overshoot (Osh), Undershoot (Ush) and Settling Time (Ts) of the system frequency.
In this paper, a modified form of the Proportional Integral Derivative (PID) controller known as the Integral- Proportional Derivative (I-PD) controller is developed for Automatic Generation Control (AGC) of the two-area multi-source Interconnected Power System (IPS). Fitness Dependent Optimizer (FDO) algorithm is employed for the optimization of proposed controller with various performance criteria including Integral of Absolute Error (IAE), Integral of Time multiplied Absolute Error (ITAE), Integral of Time multiplied Square Error (ITSE), and Integral Square Error (ISE). The effectiveness of the proposed approach has been assessed on a two-area network with individual source including gas, hydro and reheat thermal unit and then collectively with all three sources. Further, to validate the efficacy of the proposed FDO based PID and I-PD controllers, comprehensive comparative performance is carried and compared with other controllers including Differential Evolution based PID (DE-PID) controller and Teaching Learning Based Optimization (TLBO) hybridized with Local Unimodal Sampling (LUS-PID) controller. The comparison of outcomes reveal that the proposed FDO based I-PD (FDO-I-PD) controller provides a significant improvement in respect of Overshoot (Osh), Settling time (Ts), and Undershoot (Ush). The robustness of an I-PD controller is also verified by varying parameter of the system and load variation.
In this paper, a heuristic scheme based on the hybridization of Bernstein Polynomials (BPs) and nature-inspired optimization techniques is presented to achieve the numerical solution of Nonlinear Optimal Control Problems (NOCPs) efficiently. The solution of NOCP is approximated by the linear combination of BPs with unknown coefficients. The unknown coefficients are estimated by transforming the NOCP into an error minimization problem and formulating the objective function. The Genetic Algorithm (GA) and Fitness Dependent Optimizer (FDO) are used for solving the objective function and obtaining the optimum values of the unknown coefficients. The findings and statistical results indicate the represented hybrid scheme offers encouraging results and outperforms the most recent and popular methods proposed in the literature, which ultimately validates the efficacy and productivity of the recommended approach. Furthermore, statistical analysis is incorporated to examine the reliability and stability of the suggested technique. Consequently, the remarkable difference is evident in simplicity, flexibility, and effectiveness compared to the other methods considered.INDEX TERMS Optimal control problems, optimization problem, Bernstein polynomials, fitness dependent optimizer, genetic algorithm.
This paper presents a pragmatic approach established on the hybridization of nature-inspired optimization algorithms and Bernstein Polynomials (BPs), achieving the optimum numeric solution for Nonlinear Optimal Control Problems (NOCPs) of dynamical systems. The approximated solution for NOCPs is obtained by the linear combination of BPs with unknown parameters. The unknown parameters are evaluated by the conversion of NOCP to an error minimization problem and the formulation of an objective function. The Fitness Dependent Optimizer (FDO) and Genetic Algorithm (GA) are used to solve the objective function, and subsequently the optimal values of unknown parameters and the optimum solution of NOCP are attained. The efficacy of the proposed technique is assessed on three real-world NOCPs, including Van der Pol (VDP) oscillator problem, Chemical Reactor Problem (CRP), and Continuous Stirred-Tank Chemical Reactor Problem (CSTCRP). The final results and statistical outcomes suggest that the proposed technique generates a better solution and surpasses the recently represented methods in the literature, which eventually verifies the efficiency and credibility of the recommended approach.INDEX TERMS bernstein polynomials, dynamical systems, fitness dependent optimizer, genetic algorithm, nonlinear optimal control problems, optimization problem, optimization techniques.
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