Title :
Parametric H∞ loopshaping and weighted mixed sensitivity minimization
Author :
Gu, Guoxiang ; Chen, Jie ; Lee, E. Bruce
Author_Institution :
Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA
fDate :
4/1/1999 12:00:00 AM
Abstract :
Generalized H∞ loopshaping is developed for a particular weighted mixed sensitivity minimization task. A free parameter is introduced to tradeoff minimizations of sensitivity and complementary sensitivity in the H∞ performance index. A quadratically convergent algorithm is derived for computing the optimal performance index, and a state-space solution is obtained for suboptimal controllers. These results are applicable to stabilization of uncertain systems where normalized coprime factors involve parametrically weighted H∞ norm-bounded perturbations. Controller reduction is also investigated for the parametric H∞ loopshaping. Robust stability condition for using the reduced-order controller is established, and an estimate for the associated H∞ performance is obtained. Similar results are derived for normalized linear quadratic Gaussian (LQG) control
Keywords :
H∞ control; control system synthesis; convergence; minimisation; performance index; robust control; sensitivity; stability criteria; state-space methods; suboptimal control; H∞ performance index; LQG control; complementary sensitivity; controller reduction; normalized coprime factors; normalized linear quadratic Gaussian control; optimal performance index; parametric H∞ loopshaping; parametrically weighted H∞ norm-bounded perturbations; quadratically convergent algorithm; robust stability condition; state-space solution; suboptimal controllers; uncertain system stabilization; weighted mixed sensitivity minimization; Automatic control; Control system analysis; Control systems; Feedback; Least squares approximation; Riccati equations; Robust stability; Robustness; Time varying systems; Uncertainty;
Journal_Title :
Automatic Control, IEEE Transactions on
