H2 Guaranteed Cost Control in Track-Following Servos

A Separation Principle for Output Feedback Discrete-Time H2 Guaranteed Cost Control

“…In turn, this simplified SDP for optimizing the closed-loop τ-specific guaranteed cost can be exploited in a heuristic to design output feedback controllers that optimize the closed-loop H 2 guaranteed cost. For example, in [1], exploiting the separation principle in the controller design for a hard disk drive reduced the required computation from over an hour to less than 40 seconds.…”

“…It is possible to go one step further and transform this output estimation problem into a full control problem, which corresponds to choosing filter gains in an estimator. Moreover, this full control problem can be solved using an SDP [1]. Since the focus of this paper is on just the separation principle, we omit the details here.…”

“…Equations (8)-(9) are proved similarly. Equation (10) follows trivially from the factorization (1). Note that the left-hand side of (11) is given by…”

“…Finally, the output feedback control problem was considered in [1]. Two heuristics were given in that work for finding the optimal controller.…”

“…For the sake of brevity, [1] states but does not explicitly prove the separation principle. In this paper, we first review the necessary material for H 2 guaranteed cost analysis and optimal full information H 2 guaranteed cost control and then proceed to prove the separation principle.…”