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## A closed-loop power controller model of series-resonant-inverter-fitted induction heating system

### Abstract

This paper presents a mathematical model of a power controller for a high-frequency induction heating system based on a modified half-bridge series resonant inverter. The output real power is precise over the heating coil, and this real power is processed as a feedback signal that contends a closed-loop topology with a proportional-integral-derivative controller. This technique enables both control of the closed-loop power and determination of the stability of the high-frequency inverter. Unlike the topologies of existing power controllers, the proposed topology enables direct control of the real power of the high-frequency inverter.
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## Energy-optimal current distribution in an electrical network – controlling by the differential or the integral systems

### Abstract

In the complex RLC network, apart from the currents flows arising from the normal laws of Kirchhoff, other distributions of current, resulting from certain optimization criteria, may also be received. This paper is the development of research on distribution that meets the condition of the minimum energy losses within the network called energy-optimal distribution. Optimal distribution is not reachable itself, but in order to trigger it off, it is necessary to introduce the control system in current-dependent voltage sources vector, entered into a mesh set of a complex RLC network. For energy-optimal controlling, to obtain the control operator, the inversion of R(s) operator is required. It is the matrix operator and the dispersive operator (it depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this the operator R(s) is replaced by the R’ operator which is a matrix, but non-dispersive one (it does not depend on s). This type of control is called the suboptimal control. Therefore, it is important to make appropriate selection of the R’ operator and hence the suboptimal control. This article shows how to implement such control through the use of matrix operators of multiple differentiation or integration. The key aspect is the distribution of a single rational function H(s) in a series of ‘s’ or ‘s⁻¹’. The paper presents a new way of developing a given, stable rational transmittance with real coefficients in power series of ‘s/s⁻¹՚. The formulas to determine values of series coefficients (with ‘s/s⁻¹’) have been shown and the conditions for convergence of differential/integral operators given as series of ‘s/s⁻¹’ have been defined.
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