Non-uniform sampling strategies for digital control

Abstract

Most conventional control algorithms cause numerical problems where data is collected at sampling rates that are substantially higher than the dynamics of the equivalent continuous-time operation that is being implemented. This is of relevant interest in applications of digital control, in which high sample rates are routinely dictated by the system stability requirements rather than the signal processing needs. Digital control systems exhibit bandwidth limitations enforced by their closed-loop frequency requirements that demand very high sample rates. Considerable recent progress in reducing sample frequency requirements has been made through the use of nonuniform sampling schemes, so called alias-free signal processing. The approach prompts the simplification of complex systems and consequently enhances the numerical conditioning of the implementation algorithms that otherwise would require very high uniform sample rates. However, the control communities have not yet investigated the use of intentional non-uniform sampling. The purpose of this article is to address some algorithmic issues when using such regimes for digital control.

Studying the impact of intermittent variations using sensitivity analysis

“…With R = 1ω, L = 0.1H and C = 0.01F, Figure 3 illustrates that any variations in L and C will have the most impact on the output response, whereas the circuit is less responsive at the deviation of R in the vicinity of the cut-off frequency. This hypothesis can be verified by making use of the Fourier transform and studying the impact of parameter variations [17] .…”

“…Phase φ ( ) = ∠H output − ∠H input ..................... (17) The frequency response parameters for f = 0.1, 0.5, 1, 2, 3, 4 and 5 Hz is illustrated in Figure 4. Here, the Fourier result reaches a steadystate value after an initial transient stage; however, this preliminary stage dies out once the Fourier coefficients reach a steady state 2 .…”

Piecewise-continuous observers for linear systems with sampled and delayed output

“…Email: hp.wang@njust.edu.cn In this paper, we focus on the compensation of the delay T sc which is introduced by sensor sampling effect and information coding, decoding, processing and transmitting induced delay. This compensation is particularly important for VSS (Hutchinson, Hager, & Corke, 1996;Monroy, Kelly, Arteage, & Bugarin, 2007;Wang, Lin, & Li, 2010;Xu & Ritz, 2009) with low cost cameras because in this case the application of the standard sampled-data control techniques (Aström & Haglund, 1995;Aström & Wittenmark, 1997;Chen & Francis, 1995;Findersen & Allgöwer, 2005;Khan, Goodall, & Dixonand, 2013) runs into serious difficulties due to the important sampling periods and delays of these systems.…”

Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems

“…Furthermore, it can overcome the restriction of the Nyquist limit and enable a much lower average sampling frequency. Therefore, intentional non-uniform sampling has the potential to reduce the hardware cost in control applications [29]. Due to the complexity of arbitrary non-uniform sampling, most of the literature works have focused on periodically non-uniformly sampled-data systems [30,31].…”