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This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed. [ABSTRACT FROM AUTHOR]

The first part of this article reviews the concepts of apparent power and power factor in single-phase circuits with non-negligible line impedances. The study is based on the well-known definition that the apparent power is the maximum load power subject to constant line losses and constant load voltage. In reality, however, all transmission/distribution lines have some finite impedance, and thus, the constant voltage condition cannot be maintained at the load terminals. In this article, the constant load voltage condition is relaxed and allowed to change, as long as it remains within acceptable range of application. This is a scenario that better reflects the realistic situations. Modified expressions for the apparent power and power factor are derived and discussed. The second part of the article presents a new concept called the current factor as the ratio of the minimal current to the actual current while keeping the load power constant. The current factor coincides with the power factor when the line impedances are neglected. The article explains how the current factor can be superior to the power factor when the line impedances are not negligible. The current factor is then extended to non-sinusoidal current factor for a non-linear load and is examined. [ABSTRACT FROM AUTHOR]