Rotational Motion: Satellite Attitude Control Model Satellites, as shown in Fig. 2.7, usually require attitude control so that antennas, sensors, and solar panels are properly oriented. Antennas are usually pointed toward a particular location on earth, while solar panels need to be oriented

Question

Rotational Motion: Satellite Attitude Control Model

Satellites, as shown in Fig. 2.7, usually require attitude control so that antennas, sensors, and solar panels are properly oriented. Antennas are usually pointed toward a particular location on earth, while solar panels need to be oriented toward the sun for maximum power generation. To gain insight into the full three-axis attitude control system, it is helpful to consider one axis at a time. Write the equations of motion for one axis of this system and show how they would be depicted in a block diagram. In addition, determine the transfer function of this system and construct the system as if it were to be evaluated via MATLAB’s SIMULINK.

Accepted Answer

Figure 2.8 depicts this case, where motion is allowed only about the axis perpendicular to the page. The angle [latex] θ [/latex] that describes the satellite orientation must be measured with respect to an inertial reference—that is, a reference that has no angular acceleration. The control force comes from reaction jets that produce a moment of [latex] F_c d [/latex] about the mass center. There may also be small disturbance moments [latex] M_D [/latex] on the satellite, which arise primarily from solar pressure acting on any asymmetry in the solar panels. Applying Eq. (2.14) yields the equation of motion

[latex] M = I \alpha [/latex] (2.14)

[latex] F_c d + M_D = I \ddot{θ} .[/latex] (2.15)

The output of this system, [latex] θ, [/latex] results from integrating the sum of the input torques twice; hence this type of system is often referred to as the double-integrator plant. The transfer function can be obtained as described for Eq. (2.7) and is

[latex] \frac{\Theta (s)}{U(s)} =\frac{1}{I} \frac{1}{s^2} , [/latex] (2.16)

[latex] \frac{V (s)}{U(s)} = \frac{\frac{1}{m}}{s+ \frac{b}{m}}. [/latex] (2.7)

where [latex] U = F_c d + M_D. [/latex] In this form, the system is often referred to as the [latex] ^1/_{s^2} [/latex] plant.

Figure 2.9 shows a block diagram representing Eq. (2.15) in the upper half and a block diagram representing Eq. (2.16) in the lower half. This simple system can be analyzed using the linear analysis techniques that are described in later chapters, or via MATLAB as we saw in Example 2.1. It can also be numerically evaluated for an arbitrary input time history using SIMULINK. SIMULINK is a sister software package to MATLAB for interactive, nonlinear simulation and has a graphical user interface with drag and drop properties. Figure 2.10 shows a block diagram of the system as depicted by SIMULINK.

Question 2.EX.3: Rotational Motion: Satellite Attitude Control Model Satelli...

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