Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition

Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition

This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward a...

Robust adaptive control using a fractional feedforward based on SPR condition

Robust Strict Positive Realness: Characterization and Construction

Let 9 be a convex set of real polynomials. This paper considers the question of when there exists a real polynomial b(s), or more generally, a real transfer function b(s), such that p ( s ) / b ( s ) is strictly positive real for all p ( s ) E 9. Necessary and sufficient conditions are found for the transfer function b(s ) case, and when the degree of the polynomials in 9 is restricted, such co...

New Extreme Point Results on Robust Strict Positive Realness

This paper considers the robust strict positive real (SPR) problem for a family of plants of the form G(s; q) = N(s; q n)D ?1 (s; q d)?, where N(s; q n) and D(s; q d) are multiaane in uncertain parameters q n and q d , respectively , and > 0. In the discrete-time setting, this problem plays an important role in digital quantiza-tion. Several results are presented. First, we prove that this plan...

Fractional Hold Circuits versus Positive Realness of Discrete Transfer Functions

The appropriate use of fractional-order holds (β-FROH) of correcting gains β ∈ [−1,1] as an alternative to the classical zero-and first-order holds (ZOHs, FOHs) is discussed related to the positive realness of the associate discrete transfer functions obtained from a given continuous transfer function. It is proved that the minimum direct input/output gain (i.e., the quotient of the leading coe...