Quasi-Normalized Static and Dynamic Analysis of Pulse-Width Pulse-Frequency Modulator in Presence of Input Noise

In this paper¡ the preferred regions of pulse-width pulse-frequency (PWPF) modulator parameters are obtained based on zero-input¡ static¡ and dynamic analysis in the presence of sensor noise as an input noise to PWPF modulator. The design parameters are reduced to 3 by using the quasi-normalized equations of PWPF modulator. Therefore¡ the results are applicable for grouped parameters¡ regardless of the value of each parameter¡ separately. Moreover¡ the computational burden is highly decreased¡ especially in a statistical analysis. The input noise of the modulator is constructed by a low pass filter driven by a white Gaussian noise. The fuel consumption and number of thruster firings are considered as performance indices. The modulator output frequency is also limited to 50 Hz. The preferred regions of quasi-normalized system are extracted based on eliminating the upper 30% (and 10%) of the plotted graphs for the above-mentioned performance indices. Finally¡ the preferred regions can simply be viewed in our resulting curves¡ i.e.¡ normalized hysteresis plotted versus normalized PWPF on-threshold for different values of modulator time constant. Each of these curves is plotted for a specified value of input noise power spectral density.