Uncertainty Block Research Articles

Analysis of robust performance with multiple objectives

Performance robustness with multiple objectives of linear control systems having structured norm-bounded uncertainty is considered. In order to deal with any two objective functions Ψ 1 and Ψ 2 associated with a single feedback control system, the combined criterion Ψ[Ψ 1 ψ 2]Ψ ⪕S 1 is often used. The paper, however, considers Ψ ψ 1 Ψ ⩽ 1 and Ψ W, 11 ⩽ 1 directly. It is shown that it is possible to assess robust performance of two objectives by a single μ test if repeated nonscalar blocks are adequately introduced in the structure of μ. In other words, a performance robustness problem with multiple objectives is proved to be equivalent to a stability robustness problem with extra repeated uncertainty blocks. This equivalence theorem is applicable to various system and norm setups including sampled-data systems.

A Study on Design Techniques for Control System of an Electrohydraulic Servo Mechanism Based on .MU. Synthesis.

Design techniques for a control system of an electrohydraulic servo mechanism are discussed with emphasis on modeling error and structure of an uncertainty block. As a typical modeling error, compressibility of hydraulic oil, servo valve dynamics and linearized parameters are considered. Classification of the modeling errors is proposed, where errors are classified into those caused by order-reduction and those caused by linearization. Techniques for building an uncertainty block which represents the errors are discussed. Robust controllers which are designed based on μ synthesis using the techniques are examined experimentally.

Robust stability with time-varying structured uncertainty

Considers the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. It is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Small gain versus positive real modeling of real parameter uncertainty

The authors shown by means of a lightly damped oscillator example with uncertain stiffness that small gain modeling of constant real parameter uncertainty can be extremely conservative. This example was chosen to highlight inherent drawbacks of small-gain principles applied to the analysis of robust controllers for lightly damped flexible structures. If, for this class of problems, uncertainty in the stiffness operator, which may be relatively large, is modeled as a small gain H/sub infinity / block, then the arbitrary phase characteristics of the uncertainty block can contribute to a significant perturbation of the damping operator, which may be relatively small. An alternative uncertainty modeling approach involving positive real transfer functions and the positivity theorem is shown to be significantly less conservative. >

An M-matrix and majorant approach to robust stability and performance analysis for systems with structured uncertainty

Uncertain multiinput multioutput systems described in the frequency domain are discussed. The theory of nonnegative matrices and M-matrices is used along with majorant bounding techniques to develop robust stability and performance results for two types of uncertainty. The first type is uncertainty with norm-bounded subblocks. The second type is uncertainty that has subblocks with known patterns but unknown gains. This latter uncertainty representation allows the elements of a given uncertainty block to be correlated. For uncertainties of this type a recursive analysis methodology is developed which yields increasingly nonconservative results. Throughout this paper the performance analysis determines norm bounds on the deviations of the outputs from their nominal values. The results are illustrated by a numerical example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>