Robust output feedback control against disturbance filter uncertainty described by dynamic integral quadratic constraints

Abstract

SUMMARYMotivated by a robust disturbance rejection problem, in which disturbances are described by an uncertain filter at the plant input, a convex solution is presented for the robust output feedback controller synthesis problem for a particularly structured plant. The uncertainties are characterized by an integral quadratic constraint (IQC) with general frequency-dependent multipliers. By exploiting the structure of the generalized plant, linear matrix inequality (LMI)-synthesis conditions are derived in order to guarantee a specified L 2 -gain or H 2 -norm performance level, provided that the IQC multipliers are described by LMI constraints. Moreover, it is shown that part of the controller variables can be eliminated. Finally, the rejection of non-stationary sinusoidal disturbance signals is considered. In a numerical example, it is shown that specifying a bound on the rate-of-variation of the time-varying frequency can improve the performance if compared with the static IQC multipliers.

Robust estimation with dynamic integral quadratic constraints: the discrete‐time case

“…Then all eigenvalues of are strictly inside the unit circle if where is partitioned according to the dimensions of A ϕ , A ψ 1 , A ψ 3 and . Proof The equivalence between (4) and LMI (9) follows the well‐known Kalman–Yakubovich–Popov lemma, and so does the equivalence between (3) and LMI (10). The spectrum characterisation of is the discrete‐time counterpart of Theorem 4 of [27], the proof of which follows exactly the same line of arguments. □…”

“…The spectrum characterisation of A is the discrete-time counterpart of Theorem 4 of [27], the proof of which follows exactly the same line of arguments.…”

A Novel Actuator Controller: Delivering a Practical Solution to Realization of Active-Truss-Based Morphing Wings

“…A common practice is to maximize the inherited robustness of a controller by careful parameter design and tuning [5], [6]. Further robustness improvement can be achieved via advanced techniques such as nonlinear control [7]- [9], H ∞ or optimized loop-shaping robust control [10]- [12], and adaptive intelligent control [13], [14]. A more attractive approach distinguished from the aforementioned comes with the concept of unknown-input estimation, which brings disturbance rejection to a higher level, as demonstrated by various industrial applications [15]- [22].…”

Joint Synthesis of Robust Dynamic State Feedback and Dynamic Disturbance Feed-Forward for Uncertain Systems

“…Luckily though, robust controller synthesis (in the presence of unmeasurable parameters) can be rendered convex in a number of specific cases and typically by admitting to some unknown degree of conservatism. In particular, one can perform robust syntheses based on LMI optimization in the cases of static state feedback [19], dynamic disturbance feedforward [7], [23], [5], [3], [12], output filtering/estimation [13], [6], [1], [25], [22] and dynamic output feedback with uncertainty solely in the disturbance filter [4], [11]. From a technical point of view, it is the specific structure that makes robust synthesis possible for a particular problem.…”