In this paper, an automatic voltage regulator (AVR) embedded with fractional order PID (FOPID) is employed for the alternator terminal voltage control. A novel meta-heuristic technique, a modified version of grey wolf optimizer (mGWO) is proposed to design and optimize the FOPID AVR system. The parameters of FOPID, namely, proportional gain ( Κ _Ρ), the integral gain ( Κ _I), the derivative gain ( Κ _D), λ and μ have been optimally tuned with the proposed mGWO technique using a novel fitness function. The initial values of the Κ _Ρ, Κ _I , and Κ _D of the FOPID controller are obtained using Ziegler-Nichols (ZN) method, whereas the initial values of λ and μ have been chosen as arbitrary values. The proposed algorithm offers more benefits such as easy implementation, fast convergence characteristics, and excellent computational ability for the optimization of functions with more than three variables. Additionally, the hasty tuning of FOPID controller parameters gives a high-quality result, and the proposed controller also improves the robustness of the system during uncertainties in the parameters. The quality of the simulated result of the proposed controller has been validatedby other state-of-the-art techniques in the literature.

This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various �� values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.