SPR Design using Feedback

Abstract

In this paper we derive necessary and sufficient oonditions for a square transfer matrix to be rendered Strictly-Positive-Real (SPR) using output feedback. These conditions are then related to the existence of stable inverse systems.

Laminar–Turbulent Transition Control Using Passivity Analysis of the Orr–Sommerfeld Equation

“…where Dϕ ≡ ∂ϕ∕∂y. The boundary conditions are ϕ y a; t ϕb; t ϕ y b; t 0, and the (real) control inputs are νt Refϕa; tgJ mfϕa; tg T ν r tν i t T ; the vector ν should not be confused with the scalar velocity components u and v. Noting that the velocity components satisfy ux; y; t R efDϕy; t expiαxg (23) vx; y; t −R efiαϕy; t expiαxg (24) we see that the control input ν can ultimately be related to the wall velocity v w x; t vx; a; t αJ mfϕa; tg cos αx α R efϕa; tg sin αx. This will be done in more detail in the following section.…”

“…(58) and (59) is rendered passive by the output feedback. For systems with nonzero high-frequency gain (D ≠ 0), the necessary and sufficient condition for this to be possible are Det D ≠ 0 and A − BD −1 C having eigenvalues with negativereal parts (i.e., the system is minimum-phase [23]).…”

“…x; y; t using expression (23), where y −0.975 for the Poiseuille example and y 0.344 for the Blasius example. These locations are chosen because they produce the largest velocity magnitudes.…”

Static output feedback—A survey

“…In fact, The minimum-phase and the relative-degree conditions are necessary and su cient to make square i.e. same number of inputs and outputs systems Strictly-Positive-Real SPR using static output feedback as described for example in Gu, 1990b andAbdallah et al, 1991.…”

Passification-Based Adaptive Control with Implicit Reference Model*

“…Solution of the problems of passification and passifiability AL, BL were formulated in (Fradkov, 2003) for the linear rectangle (l = m) systems. For the special case of quadratic (l = m) linear multidimensional systems, similar problems were considered in (Gu, 1990;Abdallah et al, 1990;Weiss et al, 1994;Huang et al, 1999). Namely, theA special case of L = K was studied in (Gu, 1990;Abdallah et al, 1990), while the results of (Weiss et al, 1994;Huang et al, 1999) apply to the special case of L = I.…”