Application of Multivariable Virtual Reference Feedback Tuning with Anti-Windup to the Benchmark PID 2018 ⁎ ⁎This work has been supported by CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico.

Abstract This work presents an application of the Virtual Reference Feedback Tuning (VRFT) method to a multivariable refrigeration system benchmark. For the Benchmark PID 2018 problem, two approaches are developed: decentralized and centralized multivariable PID controllers are designed using only open-loop collected data. In order to cope with the saturation of the process’ input variables, an anti-windup strategy is associated with the PID controllers. Finally, the closed-loop behavior achieved with VRFT is compared with the reference controller originally provided by the problem, where it can be noted that the performance is considerably enhanced by both proposed designs, with obtained combined indexes of 0.4134 and 0.3635 for the decentralized and centralized controller, respectively.

[1]  A. Karimi,et al.  Iterative correlation‐based controller tuning , 2004 .

[2]  Jeffrey Q. Chambers,et al.  Tree damage, allometric relationships, and above-ground net primary production in central Amazon forest , 2001 .

[3]  Radu-Emil Precup,et al.  Three-level hierarchical model-free learning approach to trajectory tracking control , 2016, Eng. Appl. Artif. Intell..

[4]  David Patiño Rodríguez,et al.  Parameter identification of a multi-stage, multi-load-demand experimental refrigeration plant , 2017 .

[5]  Stephen P. Hubbell,et al.  Drought sensitivity shapes species distribution patterns in tropical forests , 2007, Nature.

[6]  F. Luizão,et al.  RAPELD: A MODIFICATION OF THE GENTRY METHOD FOR BIODIVERSITY SURVEYS IN LONG-TERM ECOLOGICAL RESEARCH SITES. , 2005 .

[7]  J. Zuanon,et al.  Comparação da eficiência de dois métodos de coleta de peixes em igarapés de terra firme da Amazônia Central , 2006 .

[8]  Jean-Marc Hero,et al.  A Program for Monitoring Biological Diversity in the Amazon: An Alternative Perspective to Threat‐based Monitoring , 2008 .

[9]  Sergio M. Savaresi,et al.  Noniterative data-driven design of multivariable controllers , 2011, IEEE Conference on Decision and Control and European Control Conference.

[10]  J. Zuanon,et al.  Seasonal variation in the composition of fish assemblages in small Amazonian forest streams: evidence for predictable changes. , 2009 .

[11]  W. Magnusson,et al.  Leaf litter fungi in a Central Amazonian forest: the influence of rainfall, soil and topography on the distribution of fruiting bodies , 2008, Biodiversity and Conservation.

[12]  L. Ferreira,et al.  Effects of Forest Fragmentation on Mortality and Damage of Selected Trees in Central Amazonia , 1997 .

[13]  R. Q. Thomas,et al.  Clustered disturbances lead to bias in large-scale estimates based on forest sample plots. , 2008, Ecology letters.

[14]  William F. Laurance,et al.  Total aboveground biomass in central Amazonian rainforests: a landscape-scale study , 2002 .

[15]  Matteo Corno,et al.  Data-Driven Design of Braking Control Systems , 2013, IEEE Transactions on Control Systems Technology.

[16]  Diego Eckhard,et al.  Data-Driven Controller Design: The H2 Approach , 2011 .

[17]  Sergio M. Savaresi,et al.  Virtual reference feedback tuning: a direct method for the design of feedback controllers , 2002, Autom..

[18]  Flávio Vasconcelos da Silva,et al.  Dynamic linear modeling of a refrigeration process with electronic expansion valve actuator , 2017 .

[19]  J. Zuanon,et al.  Relationships between Habitat Characteristics and Fish Assemblages in Small Streams of Central Amazonia , 2005, Copeia.

[20]  J. Marengo,et al.  Future change of temperature and precipitation extremes in South America as derived from the PRECIS regional climate modeling system , 2009 .

[21]  D. Clark,et al.  Detecting Tropical Forests' Responses to Global Climatic and Atmospheric Change: Current Challenges and a Way Forward , 2007 .

[22]  D. P. Atherton,et al.  An analysis package comparing PID anti-windup strategies , 1995 .

[23]  Jansen Zuanon,et al.  Fallen leaves on the water-bed: diurnal camouflage of three night active fish species in an Amazonian streamlet , 2006 .

[24]  F. Luizão,et al.  Short‐Term Temporal Changes in Tree Live Biomass in a Central Amazonian Forest, Brazil , 2010 .

[25]  A. Lima,et al.  Gradients within gradients: The mesoscale distribution patterns of palms in a central Amazonian forest , 2009 .

[26]  Variação da densidade, área basal e biomassa de lianas em 64 km2 de floresta de terra-firme na Amazônia Central , 2006 .

[27]  W. Magnusson,et al.  Spatial patterns in the understorey shrub genus Psychotria in central Amazonia: effects of distance and topography , 2005, Journal of Tropical Ecology.

[28]  Wenjian Cai,et al.  Energy-efficiency-oriented cascade control for vapor compression refrigeration cycle systems , 2016 .

[29]  B. Ahrens,et al.  Regional Climate Projections , 2015 .

[30]  J. Chambers,et al.  Relationship between soils and Amazon forest biomass: a landscape-scale study , 1999 .

[31]  Bart Kruijt,et al.  Variation of carbon and nitrogen cycling processes along a topographic gradient in a central Amazonian forest , 2004 .

[32]  N. Higuchi,et al.  Decomposition and carbon cycling of dead trees in tropical forests of the central Amazon , 2000, Oecologia.

[33]  G. B. Williamson,et al.  Positive Feedbacks among Forest Fragmentation, Drought, and Climate Change in the Amazon , 2001 .

[34]  J. Powers,et al.  Variation in small sapling density, understory cover, and resource availability in four neotropical forests , 2004 .

[35]  William F. Laurance,et al.  RAIN FOREST FRAGMENTATION AND THE DYNAMICS OF AMAZONIAN TREE COMMUNITIES , 1998 .

[36]  Larry B. Crowder,et al.  A Stage‐Based Population Model for Loggerhead Sea Turtles and Implications for Conservation , 1987 .

[37]  W. Magnusson,et al.  Reserva Ducke: A biodiversidade amazônica através de uma grade , 2008 .

[38]  Alexandre S. Bazanella,et al.  Multivariable VRFT: an approach for systems with non-minimum phase transmission zeros , 2016, 2016 IEEE Conference on Control Applications (CCA).

[39]  A. Dunham,et al.  Demographics of Common Snapping Turtles (Chelydra serpentina): Implications for Conservation and Management of Long-lived Organisms , 1994 .

[40]  Robert R. Bitmead,et al.  Direct iterative tuning via spectral analysis , 2000, Autom..

[41]  Karen L. Waddell,et al.  Sampling coarse woody debris for multiple attributes in extensive resource inventories , 2002 .

[42]  Diego Eckhard,et al.  Data-driven model reference control design by prediction error identification , 2017, J. Frankl. Inst..

[43]  W. Magnusson,et al.  Mesoscale distribution patterns of Amazonian understorey herbs in relation to topography, soil and watersheds , 2005 .

[44]  F. Baccaro,et al.  Ant species distribution along a topographic gradient in a "terra-firme" forest reserve in Central Amazonia. , 2009 .

[45]  William F. Laurance,et al.  Effects of a strong drought on Amazonian forest fragments and edges , 2001, Journal of Tropical Ecology.

[46]  Jochen Schöngart,et al.  INSTITUTO NACIONAL DE PESQUISAS DA AMAZÔNIA , 2010 .

[47]  David Patiño Rodríguez,et al.  On identifying steady-state parameters of an experimental mechanical-compression refrigeration plant , 2016 .

[48]  Diego Eckhard,et al.  Unbiased MIMO VRFT with application to process control , 2016 .

[49]  A. Andreu,et al.  Long‐term demographic fluctuations of the spur‐thighed tortoise Testudo graeca in SW Spain , 2001 .

[50]  Joaquim dos Santos,et al.  Biomassa da parte aérea da vegetação da Floresta Tropical úmida de terra-firme da Amazônia Brasileira , 1998 .

[51]  I. Swingland,et al.  Decades of Turtles. (Book Reviews: Life History and Ecology of the Slider Turtle.) , 1991 .

[52]  J. Zuanon,et al.  Fish assemblages in temporary ponds adjacent to ‘terra-firme’ streams in Central Amazonia , 2006 .

[53]  J. Zuanon,et al.  A remarkable sand-dwelling fish assemblage from central Amazonia, with comments on the evolution of psammophily in South American freshwater fishes , 2006 .

[54]  J. L. Greene,et al.  Life Tables of a Slider Turtle Population , 1990 .

[55]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

[56]  D. Burslem,et al.  The interpretation and misinterpretation of mortality rate measures , 1995 .

[57]  P. H I L I P P E C I A I S Z, W O L F G A N G C R A M,et al.  Modeled interactive effects of precipitation , temperature , and [ CO 2 ] on ecosystem carbon and water dynamics in different climatic zones , 2008 .

[58]  Ciro Aprea,et al.  Fuzzy control of the compressor speed in a refrigeration plant , 2004 .

[59]  Orhan Ekren,et al.  Comparison of different controllers for variable speed compressor and electronic expansion valve , 2010 .

[60]  Svante Gunnarsson,et al.  Iterative feedback tuning: theory and applications , 1998 .

[61]  Héctor J. Ciro-Velásquez,et al.  Identification and digital control of a household refrigeration system with a variable speed compressor. , 2014 .

[62]  Christian J.L. Hermes,et al.  A model-driven multivariable controller for vapor compression refrigeration systems , 2009 .

[63]  N. Higuchi,et al.  Variation in aboveground tree live biomass in a central Amazonian Forest: Effects of soil and topography , 2006 .

[64]  D. Bignell,et al.  A Handbook of Tropical Soil Biology: Sampling and Characterization of Below-ground Biodiversity , 2008 .

[65]  W. Magnusson,et al.  Topographic and edaphic effects on the distribution of terrestrially reproducing anurans in Central Amazonia: mesoscale spatial patterns , 2007, Journal of Tropical Ecology.

[66]  S. Solomon The Physical Science Basis : Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change , 2007 .

[67]  Lucíola Campestrini,et al.  On the Choice of an Appropriate Reference Model for Control of Multivariable Plants , 2019, IEEE Transactions on Control Systems Technology.

[68]  M. Nakamoto An application of the virtual reference feedback tuning for an MIMO process , 2004, SICE 2004 Annual Conference.

[69]  W. Magnusson,et al.  How wide is the riparian zone of small streams in tropical forests? A test with terrestrial herbs , 2008, Journal of Tropical Ecology.