W artykule przedstawiono nowoczesne metody pomiaru częstotliwości zapewniające zminimalizowanie błędu kwantowania dzięki użyciu zaawansowanych metod pomiarowych, predestynowanych do realizacji komputerowych. Układ zrealizowano przy użyciu 32-bitowego mikrokontrolera STM32F103CBT6 oraz komputera osobistego. Zaprezentowano algorytmy sterujące napisane dla mikrokontrolera w języku C oraz aplikację sterującą w środowisku LabVIEW. Przedstawione wyniki eksperymentu zobrazowały przewagę omówionych nowoczesnych metod w porównaniu do metod klasycznych.
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The paper presents modern frequency measurement methods ensuring minimization of the quantization error. The minimization is achieved by using advanced measurement methods predestined for computer realization. The synchronous (Fig. 2) and weight algorithm (Fig. 4) methods are described. The synchronous method decreases the quantization error which is the results of no synchronization between the start and stop gating time Tp and the first and last impulse formed from the measured frequency signal. For low frequency measurements there was used the weight algorithm. This method guarantees minimization of the quantization error thanks to ascribing the weight coefficients to partial results of the measured Txi periods that are located inside the multiple n periods of the measured signal. The paper presents practical realization of the measurement with the constructed measuring system. The system was made by using a 32-bit microcontroller STM32F103CBT6 with counters, DMA and interrupt modules. In the paper there are described the control algorithms in C language for the microcontroller program (Fig. 7) and virtual control panel created in LabVIEW (Fig. 8). The results obtained show the advantages of the discussed methods in comparison to the classical methods (Figs. 10, 11 ).
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Subharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in the presence of three-to-one internal resonance is investigated. Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a firs-order non-linear ordinary differential equations governing the modulation of the amplitudes and phases. Steady state solutions and their stability are computed for selected values of the system parameters. The results obtained by the two methods are in excellent agreement. Numerical solutions are carried out and graphical representations of the results are presented and discussed.
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