Sep 16, 2013 - be used to design a discrete-time con- trol system using any ... sampled-data system is to design a ... the IEEE Control Systems Society (CSS).
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Sampling
T
he vast majority of control systems periodically sample continuous-time sensor signals to produce a discrete-time signal that is used by the control algorithm to calculate the next control action, which is then converted into a continuoustime signal that is input to the process. The overall system that couples a continuous-time plant with a discrete-time control system is called a sampled-data system. Digital Object Identifier 10.1109/MCS.2013.2270399 Date of publication: 16 September 2013
One approach to approximately model the dynamics of a sampled-data system is to replace a continuous-time model for the process being controlled with a discrete-time model. A variety of methods are available for the construction of discrete-time models, with one method to replace the time derivatives in the continuous-time process model with finite-difference approximations. The resulting discrete-time model can be used to design a discrete-time control system using any of a large number of methods. A well-known drawback of this purely discrete-time approach is
that it does not capture the dynamics of the closed-loop system between the sampling instances, and oscillations or other undesirable dynamics can occur between the sampling instances if sufficient care is not taken to avoid such problems. Another approach to approximately model the dynamics of the sampled-data system is to design a continuous-time control system based on a continuous-time process model, in which case the large suite of methods available for continuous-time systems can be applied. The resulting controller
Contributors
Juan C. Agüero in his office at The University of Newcastle, Australia.
Graham C. Goodwin in his office at The University of Newcastle, Australia.
8 IEEE CONTROL SYSTEMS MAGAZINE » OCTOBER 2013
Mauricio Cea Garrido in his office at The University of Newcastle, Australia.
Mario Salgado at the front of the Universidad Técnica Federico Santa María, Valparaiso, Chile.
is then approximated by a discrete-time system, for instance, by using finite differences to approximate the time derivatives. This purely continuoustime approach for the controller design does not really take the sampling aspect into account, and care must be taken to avoid having a large discrepancy between the closed-loop dynamics of the sampled-data system and its continuous-time approximation. A third approach is to analyze the sampled-data system directly, by explicitly addressing both the continuous- and discretetime elements within the closed-loop system. The mathematics are more complicated for this approach, but the approximations of both the pure discrete-time and the pure continuoustime approaches are avoided. The feature article “Sampling and Sampled-Data Models: The Interface
Between the Continuous World and Digital Algorithms” by Graham C. Goodwin, Juan C. Agüero, Mauricio E. Cea Garrido, Mario E. Salgado, and Juan I. Yuz provides a tutorial on both exact and approximate sampleddata models. Interesting dynamics can occur when the sampling rate is fast relative to the process dynamics, and connections are drawn between the sampled-data model and its underlying continuous-time system under such conditions. The dynamic behavior of the states in between the sampling instances—that is, the intersample behavior—is also considered. The “President’s Message” discusses the IEEE Control Systems Society (CSS) awards and honors, its Executive Committee, and its relationship with IEEE. “CSS News” announces the elected members of the 2014 CSS Board of Gov-
Juan Yuz (left) and colleague Cesar Silva at the Power Electronics Laboratory at Universidad Técnica Federico Santa María, Valparaiso, Chile.
Linda Bushnell at Pike Place Market, Seattle, Washington.
Günther Schmidt.
ernors and encourages nominations for the next round of CSS awards. In “Member Activities,” Linda Bushnell describes activities of IEEE Women in Engineering (WIE). “Technical Activities” covers the recent activities of the CSS Technical Committee on Systems Biology and a name change for another technical committee. In “Publication Activities,” we speak with Yannis Paschalidis, who is founding editor-in-chief of the CSS’s new journal, IEEE Transactions on Control of Network Systems. The column describes the journal’s scope and plans for its inaugural issue. “People in Control” has interviews with IEEE Fellows Ben M. Chen, Daizhan Cheng, Ratnesh Kumar, Carsten W. Scherer, R. Srikant, and Bo Wahlberg. “Focus on Education” provides an example of a distributed parameter system where stability analysis based on an analytical expression for the state given by a textbook produces an incorrect conclusion. The column recommends that control engineering
Ioannis (Yannis) Paschalidis with his students at Boston University.
Zoltan K. Nagy controlling particle size distributions in his laboratory.
Dongyin Erin Shen.
OCTOBER 2013 « IEEE CONTROL SYSTEMS MAGAZINE 9
Christopher Bissell in a forest in the rain.
Kwang Ki Kim at a café during the 2011 IFAC World Congress in Milan, Italy.
Michael Rasche in the wilderness.
M. Vidyasagar at the IEEE Multiconference on Systems and Control held in Dubrovnik, Croatia, in October 3–5, 2012.
students are taught stability within the context of specific physical systems rather than as purely mathematical exercises and that they are encouraged to think critically about the dynamics of the physical system while analyzing stability by formal methods. One purpose of the “Historical Perspectives” column is to look back at work by pioneers in control that was neglected for many years and later revived in the control literature. In this issue, “Historical Perspectives” is the second column in a series that commemorates the life and work of Norbert Wiener. An introduction is provided on polynomial chaos expansions, which are methods for quantifying the effects of probabilistic parametric uncertainties on states and outputs of nonlinear dynamical systems, and was the topic of Norbert’s most cited paper. The column provides an overview of the control literature that has utilized this tool for robustness analysis and controller synthesis and considers the question of why polynomial
chaos expansions have only appeared in the control literature rather recently. Winfried Oppelt was a pioneering German control engineer who recognized the importance of educating the general public on control engineering principles and their applications. In another contribution to “Historical Perspectives,” Günther Schmidt and Christopher C. Bissell describe Winfried Oppelt’s proposal in 1972 for a special permanent exhibition on control engineering at the Deutsches Museum in Munich, Germany. The proposal was accompanied by numerous hand-drawn images of such concepts as hands-on experiences of controlling dynamical systems and physical manifestations of proportional-integral-derivative control. The column ends with a discussion of the underrepresentation of control engineering in major international museums of science and technology. Control theory is founded on mathematics, and much of the developments in mathematics were stimulated by
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efforts to solve mathematical problems that had been posed centuries ago. For example, Fermat’s last theorem was stated in the early 1600s by Pierre de Fermat, who claimed to have a simple proof but did not publish it. Mathematicians worked for over three centuries attempting to prove the result, which was only published about 20 years ago. In “On the Lighter Side,” M. Vidyasagar makes some observations obtained while reading the paper that proposed another famous open problem in mathematics, the Riemann hypothesis. “Book Announcements” provides summaries of recently published books in the control field. “Random Inputs” considers a possible analogy to a phenomenon commonly observed in sliding mode control. The “25 Years Ago” column revisits an article by Davorin Hrovat and William F. Powers on control systems for automotive power trains. Richard D. Braatz
