A PARAMETRIC APPROACH TO DESIGN OPTIMIZED VELOCITY-PLUS-ACCELERATION CONTROLLER FOR SECOND-ORDER QUASI-LINEAR SYSTEMS

摘要

This paper investigates the design problem of velocity-plus-acceleration feedback law to a class of second-order quasi-linear systems whose coefficient matrices contain time-variant parameters and system state variables. Based on the solution to a type of generalized second-order Sylvester equations, we obtain the generally parameterized expressions of the velocity-plus-acceleration feedback gain matrices and right closed-loop eigenvector, and also a group of arbitrary parameters. With the proposed controller, the closed-loop system is converted into a linear constant one with expected eigenstructure. Furthermore, an effective and simple approach to realize robust optimization is provided. By using the degrees of freedom in arbitrary parameters, the overall eigenvalue sensitivity is formulated to measure the robustness of the closed-loop system. Finally, an example of attitude control of combined spacecraft is presented to prove the effectiveness of the proposed approach.