A new algorithm for dual-rate systems frequency response computation in discrete control systems

Abstract

ElsevierSalt Llobregat, JJ.; Sala Piqueras, A. (2014) AbstractThis paper addresses an easy computation of the multiple components of the response to a sinusoidal input of a dual-rate linear time-invariant discrete system from the Bode diagram of LTI systems arising from a lifted representation. Based on those results, a generalized Bode diagram is suggested. Some new conclusions derived from this conceptual interpretation are introduced. This diagram provides a better insight in the frequency-response issues in multivariable control than the standard Singular Value Decomposition of the lifted model. As an application, the output ripple suppression in a multirate control scheme is presented.

A QFT approach to robust dual‐rate control systems

“…The GBD technique 23 allows the computation of the frequency response from r T s to y Tf (see Figure 1) by using only one Bode plot, and even for a more general case in which N f and N s are coprime integers (being N s T s = N f T f ). It is understood that this "frequency response" does not give a single sinusoidal output for a sinusoidal input, in fact for a input r T s (k) = e j𝜔T s k the output is a sum of components y r (k) = ŷr e j𝜔 r T f k with frequencies 𝜔 r = 𝜔 + r 2𝜋…”

“…In recent years, some contributions allow to make easier those purposes. [20][21][22][23] In this work, the quantitative feedback theory (QFT) 24 is postulated as an efficient technique for analysis and design of DR control systems, including system with potentially large uncertainty. Being a sound and well-developed frequency domain technique, it is believed that QFT will be a unique framework for understanding how slow and fast sampling from the DR controller interact with the plant continuous dynamics, being a goal the efficient characterization of ripples and their removal with a proper controller design.…”

A QFT approach to robust dual-rate control systems

“…There was an inherent difficulty due to the complexity of the MR frequency response. In recent years, some contributions allow to make easier those purposes [4,3,58,55].…”

Diophantine equation based model of data transmission errors caused by interference generated by DC-DC converters with deterministic modulation

“…7 shows the pro mission error for d The solid curve sho ). The equation 4 is known as Diophantine equation [21][22][23][24]. …”

“…Elaboration of the presented mathematical model has enabled explanation of significant differences in experimentally obtained distributions of awaiting times for data transmission errors caused by interference generated by a DC-DC converter with random [9][10][11] and deterministic modulation. The evaluated probability of the appearance of data transmission error may become a useful factor supporting the development of data transmission systems.…”