  This paper derives a symbolic multi-body rigid nonlinear model for a space
telescope using Stoneking's implementation of Kane's method. This symbolic
nonlinear model is linearized using Matlab symbolic functions {\tt diff} and
{\tt inv} because the analytic linearization is intractable for manual
derivation. The linearized system model is then used to design the controllers
using both linear quadratic regulator (LQR) and robust pole assignment methods.
The closed-loop systems for the two designs are simulated using both the rigid
model as well as a second model containing flexible modes. The performances of
the two designs are compared based on the simulation testing results. Our
conclusion is that the robust pole assignment design offers better performance
than that of the LQR system in terms of actuator usage and pointing accuracy.
However, the LQR approach remains an effective first design step that can
inform the selection of real eigenvalues for robust pole assignment. The
proposed method may be used for the modeling and controller designs for various
multi-body systems.
