Abstract
It is known that the standard Nelder-Mead algorithm (NMA) is subject to the problem of local minimum. This paper proposes an improved Nelder-Mead algorithm (INMA) based on dynamically varying the reflection, expansion, contraction and the shrinkage coefficients, following a cosine function. Dynamical coefficients intensify the search space exploration and also increase the ability of quickly finding the optimal solution. Firstly, the effectiveness and validity of this approach are confirmed by using some benchmark functions. Secondly, the approach is also verified by applying it for tuning a Proportional–Integral–Derivative (PID) controller used to regulate the voltage of a synchronous generator (SG) under different loading conditions. The PID controller parameters are obtained by a minimisation of the quadratic output error between the reference and the SG output voltage calculated from the adopted model. A comparison is established between INMA, standard NMA, genetic algorithm (GA) and particle swarm optimisation (PSO). The Obtained results show that the INMA has a better performance compared to other algorithms.
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