Problem. Consider the standard feedback control system with the plant
05] and define
(i) Find an uncertainty weight in the form
such that |Wa(jω)| |δ(jω)| for all ω, and |Wa(jω)| is as small as possible for each ω.
(ii) Now consider the class of uncertain plants
P = {P∆ = P + ∆ : P∆ has one pole in C+ , |∆(jω)| < |Wa(jω)| ∀ ω}
and find the allowable interval for β 0 so that the controller
Problem. Consider the standard feedback control system with the plant
05] and define
(i) Find an uncertainty weight in the form
such that |Wa(jω)| |δ(jω)| for all ω, and |Wa(jω)| is as small as possible for each ω.
(ii) Now consider the class of uncertain plants
P = {P∆ = P + ∆ : P∆ has one pole in C+ , |∆(jω)| < |Wa(jω)| ∀ ω}
and find the allowable interval for β 0 so that the controller
is robustly stabilizing (C,P), for all P∆ ∈ P.
(iii) Now pick a value of β in the interval determined above and verify that the feedback system formed by the controller C and the plant is stable.
(iv) Let = 10; determine if there exists β values in the interval determined in part (ii), satisfying the robust performance condition
where S = (1 + PC)−1.
What is the smallest value of γr 0 such that there exists a feasible β satisfying the robust performance condition? Find the corresponding optimal value of β.
is robustly stabilizing (C,P), for all P∆ ∈ P.
(iii) Now pick a value of β in the interval determined above and verify that the feedback system formed by the controller C and the plant is stable.
(iv) Let = 10; determine if there exists β values in the interval determined in part (ii), satisfying the robust performance condition
where S = (1 + PC)−1.
What is the smallest value of γr 0 such that there exists a feasible β satisfying the robust performance condition? Find the corresponding optimal value of β.
