The LQG/LTR procedure for multivariable feedback control design

Abstract

Abstract-This paper provides a tutorial overview of the LQG/LTR design procedure for linear multivariable feedback systems. LQWLTR is interpreted as the solution of a specific weighted H*-tradeoff hetween transfer functions in the frequency domain. Properties of this solution are examined for both minimum-phase and nonminimum-phase systems. This leads to a formal weight augmentation procedure for the miuimumphase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights. While such arbitrary specifications are not possible for nonminimum-phase problems, a direct relationship between weights and sensitivities is developed for nonminimum-phase SlSO and certain nonminimum-phase MIMO cases which guides the weight selection process.

Loop transfer recovery designs with an unknown input reduced‐order observer‐based controller

“…With cost functions J ∞ or J r∞ we minimize the recovery error E(s) or a frequency weigthing recovery error E(s) R(s) [7]. We obtain an approximate LTR, but not an exact (or asymptotic) LTR, with any state feedback control law u = F x, because the transfer matrix [ ] G 21 (s) G 22 (s) is non-minimum phase [19], [20].…”

Understanding Sensorimotor Feedback through Optimal Control

“…Briefly, the application of LQ control requires three types of input: The LQ method (Stein and Athans 1987) involves two assumptions: (1) that for small enough perturbations, the system is locally linear, and (2) that the appropriate measure of error to be minimized is quadratic, i.e., the sum of the squares of the deviations from the nominal trajectory in all of the state variables. The combination of a linear plant plus quadratic criterion implies linear state feedback control (Athans and Falb 1969); see Discussion.…”

LQG/LTR-PID based Controller Design of UAV Slung-Load Transportation System

“…여러 대의 무인기가 화물의 각기 다른 부위에 체결될 때 정적 안정성에 대한 분석은 진행되었지 만, 경로 추종 제어는 필요성만 언급 되었다 [11,12]. 제어 기법으로는 PID제어와 LQG/LTR (Linear Quadratic Gaussian / Loop Transfer Recovery) 방법이 고려된다 [13][14][15] …”