Thruster Schmitt Mapping Software

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Description

The Thruster Schmitt Mapping Software converts desired thrust force commands into thruster on-time requests using Schmitt trigger logic. This module addresses the fundamental challenge of pulse-width modulation for thrusters that have minimum impulse bit constraints, preventing excessive thruster cycling while maintaining accurate impulse delivery. The software supports both on-pulsing and off-pulsing modes, enabling its use with various thruster configurations and control architectures.

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Example Use Cases

• Attitude Control: Map torque-derived thrust commands to thruster firing times for reaction control systems.
• Station Keeping: Convert low-thrust force requests to pulse-modulated thruster commands with minimum impulse bit protection.
• Thruster Limit Cycling Prevention: Reduce thruster wear by preventing rapid on-off cycling near the control dead band.

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Module Implementation

The Thruster Schmitt Mapping Software is a Software component that processes thrust force commands and produces thruster on-time requests with hysteresis-based switching logic.

On-Time Calculation

The basic thruster on-time is computed from the force request and maximum thrust capability:

$$t_{\text{on},i}=\frac{F_i}{F_{\text{max},i}}\cdot \Delta t$$

where:

• $t_{\text{on},i}$ is the requested on-time for thruster $i$
• $F_i$ is the commanded force for thruster $i$
• $F_{\text{max},i}$ is the maximum thrust of thruster $i$
• $\Delta t$ is the control period (time step)

Off-Pulsing Mode

In off-pulsing mode, thrusters are nominally on and pulse off to reduce thrust. The force command is adjusted:

$$F_i^{\prime }=F_i+F_{\text{max},i}$$

This allows negative force commands to be mapped to reduced thrust output.

Schmitt Trigger Logic

When the computed on-time is less than the minimum fire time, Schmitt trigger logic with hysteresis is applied to prevent rapid switching. The duty cycle fraction is computed as:

$$d=\frac{t_{\text{on}}}{t_{\text{min}}}$$

where $t_{\text{min}}$ is the minimum thruster fire time.

The switching logic uses two thresholds:

Condition	Action
$d\ge d_{\text{on}}$	Turn thruster on, output $t_{\text{min}}$
$d\le d_{\text{off}}$	Turn thruster off, output $0$
$d_{\text{off}}<d<d_{\text{on}}$	Maintain previous state

This hysteresis band between $d_{\text{off}}$ and $d_{\text{on}}$ prevents chattering when the commanded thrust hovers near the switching threshold.

Saturation Handling

When the computed on-time exceeds the control period, the output is slightly oversaturated:

$$t_{\text{on}}=1.1\cdot \Delta t\text{if}{t}_{\text{on}}\ge \Delta t$$

This ensures continuous thrust delivery when full thrust is commanded, avoiding numerical edge cases.

State Persistence

The module maintains the previous on/off state for each thruster to implement the hysteresis behavior. This state is used when the duty fraction falls within the hysteresis band.

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Assumptions/Limitations

• All thrusters are assumed to have the same minimum fire time constraint.
• Force commands less than zero are clamped to zero after off-pulsing correction.
• The first update cycle outputs a default state based on the pulsing mode without Schmitt logic.
• The module does not model thruster valve dynamics or response delays.
• The hysteresis band must satisfy $d_{\text{off}}<d_{\text{on}}$ for proper operation.
• Thruster configuration must be provided before simulation