This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.

The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.

Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.

Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.

In the finite control set model predictive control (FCS-MPC) strategy of the grid-tied inverter, the current ripple (CR) affects the selection of optimal voltage vectors, which leads to the increase of output current ripples. In order to solve this problem, this paper proposes a CR reduction method based on reference current compensation (RCC) for the FCS-MPC strategy of grid-tied inverters. Firstly, the influence of the CR on optimal voltage vector selection is analyzed. The conventional CR prediction method is improved, which uses inverter output voltage and grid voltage to calculate current ripples based on the space state equation. It makes up for the shortcomings that the conventional CR prediction method cannot predict in some switching states. The improved CR method is more suitable for the FCS-MPC strategy. In addition, the differences between the two cost functions are compared through visual analysis. It is found that the sensitivity of the square cost function to small errors is better than that of the absolute value function. Finally, the predicted CR is used to compensate the reference current. The compensated reference current is substituted into the square cost function to reduce the CR. The experimental results show that the proposed method reduces the CR by 47.3%. The total harmonic distortion (THD) of output current is reduced from 3.86% to 2.96%.