Reaction Wheel Array Power Model

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Description

This is a custom Power Node Model that is added to a Reaction Wheel Array object. The motor power model is able to connect the functionality of a reaction wheel with the power network. It can map voltage commands controlling the motor with the power bus and ensure that when the battery has zero power charge, the reaction wheels are unable to provide a new torque. By default, a reaction wheel will have no power implementation and will assume no power requirements.

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Example Use Cases

• Simulating Current Draw: Determining when reaction wheels will cause current spikes on the power bus
• Power Disabling: Having reaction wheel torques dependent on power within a battery, emulating a realistic power system.

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Module Implementation

The power motor creates an empty Power Model that attempts to provide a voltage sink based on the reaction wheel modal. This power component is what actually connects the reaction wheel to the power system. This model is controlled by the reaction wheel power component and the power values are updated based on the input voltage array message.

On the update call, if the voltage input $V_{\mathrm{in}}$ is zero, then the reaction wheels should have no power and be unable to adjust their torques. As such, the spoof voltage $V_s$ and the spoof resistance $R_s$ are set to $0$. All voltages on the output array motor voltage message are also set to $0$. If $V_{\mathrm{in}}>0$, then a lookup table function $L(V)$ is called which calculates the resistance and current based on each of the voltage nodes on the In_ArrayMotorVoltageMsg, containing the desired input voltages from the reaction wheels. Here,

$$R=\sum _n{L}_R(V_n),I=\sum _n{L}_I(V_n)$$

for the respective resistance and current lookup table functions, taking in the voltage for wheel $n$. A lookup table is provided that maps voltages $V$ to power output $P$. Given some voltage $V_n$, the lookup table finds the power drawn at the first voltage in which $V<V_i$, for some voltage $V_i$ in the lookup table (assuming the table is ordered in increasing voltages). Then, assuming that $P_1$ and $P_2$ are the power values at voltage $V_{i-1}$ and $V_i$ respectively, then:

$$\begin{gathered} L_R(V_n):=\frac{V_{i-1}^2}{P_{i-1}}+\alpha (\frac{V_i^2}{P_i}-\frac{V_{i-1}^2}{P_{i-1}}) \\ {L}_I(V_n):=\frac{V_{i-1}}{P_{i-1}}+\alpha (\frac{V_i}{P_i}-\frac{V_{i-1}}{P_{i-1}}) \end{gathered}$$

where $\alpha$ is the ratio between the two values and is used for linear interpolation between the lookup table values such that:

$$\alpha =\frac{(V_n-V_1)}{(V_2-V_1)}$$

Additionally, the voltage node is calculated to be the sum of the input voltages where:

$$V=\sum _n{V}_n$$

The next step adjusts the spoof component power properties based on the reaction wheel power values. If $V>V_{\mathrm{in}}$, then:

$$V=V_{\mathrm{in}},V_s=0,R=0$$

and the scale factor $s$ is defined as the ratio between the two voltages $s=V_{\mathrm{in}}/V$. If the total voltage $V<V_{\mathrm{in}}$, then:

$$V_s=V_{\mathrm{in}}-V,R_s=R\frac{V_s}{V}$$

Finally, the output array motor voltages are calculated such that for each wheel $n$, the output voltage is:

$$V_{\mathrm{ou}{\mathrm{t}}_{\mathrm{n}}}=s{V}_{\mathrm{i}{\mathrm{n}}_{\mathrm{n}}}$$

where $s$ is the defined scale factor and $1$ when not defined.

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Assumptions/Limitations

• Currently, the motor power model only functions with the reaction wheel on its own linear line and has certain issues with calculating the correct power when in series to other components.