Pulse-Width Pulse-Frequency Modulators are used in spacecraft thruster control. The nonlinear properties of the PWPF modulator can be described with fractional-order behaviors, although the actual behavior is almost linear. PWPF modulators are created from a first-order lag filter and a Schmitt trigger inside a feedback loop. The lag filter integrates the error. This controller modulates the pulse width and pulse frequency simultaneously to operate in a quasi-linear mode. Using this in spacecraft attitude control improves fuel consumption as well as improving pointing accuracy in the presence of vibrations. The pointing accuracy of the final system cannot be less than the dead zone of the PWPF modulator.
Some of the static characteristics variables are, the On time, Off time, frequency, duty cycle, internal deadband, and internal saturation level. They are defined in the following table.
| Characteristic Variable | Expression |
| On Time | \(T_{ON}=-T_mln(1-\frac{h}{U_{ON}-K_m(C-U)})\) |
| Off Time | \(T_{OFF}=-T_mln(1-\frac{h}{K_mC-U_{OFF}})\) |
| Modulator Frequency | \(f=\frac{1}{T_{On}+T_{OFF}}\) |
| Duty Cycle | \(DC=\frac{T_{ON}}{T_{ON}+T_{OFF}}\) |
| Equivalent Internal Deadband | \(C_d=\frac{U_{ON}}{U_{OFF}}\) |
| Equivalent Internal Saturation Level | \(C_s=1+\frac{U_{OFF}}{K_m}\) |
[[Pulse Modulators]] – classification of modulators
Disadvantages of PWPF Modulators
[[Schmitt Trigger
[[Satellite Motion Tasks]] – can use control schemes like the PWPF Modulator
[[Single-Axis Satellite Dynamics – uses control inputs to PWPF modulator for thruster
- wangFractionalDescribingFunction2013
- khaliliOptimalTuningSingleAxis2020
Backlinks:
[[Chattering]]
[[Deadband Control]]
[[First-Order Systems]]
Phase Lag
[[Pulse Modulators]]
[[Reaction Control System]]