In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.

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.

This paper presents a state feedback controller (SFC) for position control of PMSM servo-drive. Firstly, a short review of the commonly used swarm-based optimization algorithms for tuning of SFC is presented. Then designing process of current control loop as well as of SFC with feedforward path is depicted. Next, coefficients of controller are tuned by using an artificial bee colony (ABC) optimization algorithm. Three of the most commonly applied tuning methods (i.e. linear-quadratic optimization, pole placement technique and direct selection of coefficients) are used and investigated in terms of positioning performance, disturbance compensation and robustness against plant parameter changes. Simulation analysis is supported by experimental tests conducted on laboratory stand with modern PMSM servo-drive.