Numeric-Symbolic Solution for Satellite Trajectory Control by Pole Placement

Abstract

Control design of satellites based on pole placement method results in determined or underdetermined multivariable polynomial systems. Since only the real solutions can be considered for hardware implementation, we are looking for exclusively these solutions. In this study we suggest a numeric-symbolic approach to compute only the real solutions directly. Employing computer algebra (Dixon or reduced Gröbner basis) a condition can be formulated for the free variables as parameters of the underdetermined system, which ensures only real solutions. Numerical example illustrates the procedure and the effectivity of the control law.