Parametric output regulation using observer-based PI controllers with applications in flexible spacecraft attitude control

A parametric multiobjective design approach based on a proportional-integral (PI) controller and a full-state observer is proposed for output regulation in a multivariable linear system. First, a complete parametric form of the observer-based PI control law is established, which yields a closed-loop system with the desired eigenstructure and ensures that the regulated output asymptotically tracks a given constant signal in the presence of constant but unknown disturbances. All design degrees of freedom are preserved and characterized using a set of parameter vectors. Second, a separation principle of eigenvalue sensitivities is proven, and based on this result, the parameters of the closed-loop system are comprehensively optimized to reduce the eigenvalue sensitivity and the control gain, and also to enhance the tolerance to time-varying disturbances. Finally, the proposed method is applied to attitude control of a flexible spacecraft. Moreover, numerical simulations based on practical engineering parameters are performed to verify the superiority of the proposed method over traditional proportional-integral-derivative (PID) control methods.