Dual-rate sampled-data systems. Some interesting consequences from its frequency response analysis

ABSTRACT

The main goal of this contribution is to introduce a new procedure in order to analyse properly SISO dual-rate systems (DRS) and to provide straightforward answers to some common general questions about this kind of systems. Frequency response analysis based on DRS lifting modelling can lead to interesting results about stability margins or performance prediction. As a novelty, it is explained how to understand DRS frequency response and how to handle it for an easy computation of magnitude and phase margins keeping classical frequency domain methods. There are also some repetitive questions about DRS that can be analysed and answered properly using the results from this contribution: what the optimum relation between sampling periods is or what effects does delay have in a DRS. Every step is illustrated with examples that should clarify the understanding of the text.

KEYWORDS:

• Dual-rate systems
• frequency response
• stability
• Bode diagram

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. A more formal definition will be given in Section 2.

2. It will denoted $w_s=2\pi /T_0$.

3. Remember that in general there will be $N_y/gcd(N_u,N_y)$.

4. In this case the formula exposed in Iserman (1990).

5. It is also possible to obtain the components Bode diagram if $G\left(s\right)$ fast intersampling is required. These diagrams must be done if ripple occurence is suspected.

Additional information

Notes on contributors

Julián Salt

Julián Salt received the M.Sc. degree in industrial engineering and the Ph.D. degree in control engineering from the Technical University of Valencia, Valencia, Spain, in 1986 and 1992, respectively. He is a Full Professor with the Technical University of Valencia. He has been teaching during 32 academic years (from 1986) diverse contents in grade master and doctoral courses all related to Simulation, Automation and Systems Control. He has been advisor of different grade and master thesis and 7 PhD in the last 10 years. All of these works were related to Non-Conventional Sampling Systems. He has co-authored over 70 papers in journals and conferences. His current research interests include nonconventionally sampled control and networked control systems.

José Alcaina

José Joaquín Alcaina received his M.Sc. degree in Automation and Industrial Computing from the Technical University of Valencia, Valencia, Spain, in 2015. He is currently completing his PhD studies in Automation, Robotics and Industrial Computer Science. His current research interests include networked control systems, packet-based dual-rate control and systems with low sensing ability.