Fractional methods for design of controller appear as the latest problems to solved in control. These methods are developed for systems described by integer and non integer order differential equations.
Thank you both for the answers.....waiting for more suggessions
Literature of fractional methods will be found in mathematical literature.
I worked on control systems in the past but of late it dawn on me that PID is still the best in the practical industry. But for academic purposes, there are still some bottlenecks that had yet to be solved. I faced some problems dealing with stability proofs of constrained dual adaptation predictive control.
Hello Deep,
You Can think of solving some of the existing benchmark Control problems with 'Fractional Order Sliding Mode Control' to get improved control
Continuous- and Discrete-Time Inverse Optimal Control for Nonlinear Systems and Games Theory.
Optimization-based control; Inverse control; Vibration rejection; Delay compensation;
Repetitive and iterative learning control; Hybrid control
I agree with Yong Kuen Ho's comment "PID is still the best in the practical industry. But for academic purposes, there are still some bottlenecks that had yet to be solved."
I also agree that Fractional order controllers can achieve better performance for complex control system (including nonlinear system).
(1) By cooperating with his peer researchers including Stanford University researcher, H. Hjalmarsson integrated iterative feedback tuning with PID controller to solve controller tuning issues caused by plant uncertainty of nonlinear system. H. Hjalmarsson was elected to the Class of 2013 IEEE fellow last year due to his fundamental contribution to iterative feedback tuning.
"Relay auto-tuning of PID controllers using iterative feedback tuning," Automatica 39 (1), January 2003, pp. 149-157.
Iterative feedback tuning (IFT) was proposed to tune controller parameters for system with unknown parameters. A linear control model can be used to approximate nonlinear system with unknown parameters roughly, and such control plant approximation may exist large deviation from the real non-linear system. IFT was proposed to solve controller tuning issues caused by plant uncertainty. The goal of IFT is similar to Quantitative Feedback Theory proposed by Isaac Horowitz.
http://en.wikipedia.org/wiki/Isaac_Horowitz
H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin, "Iterative feedback tuning: theory and applications," IEEE Control Systems Magazine, vol.18, no.4, Aug 1998, pp .26-41,
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=710876
The key contribution of Iterative feedback tuning (IFT) is tuning controller parameters for those control model (or control plant) whose parameters are difficult to be identified relatively accurately,
(2) For industrial control community,
Only PID Control and Smith Predictor were listed in the “Leaders of the Pack” InTech’s 50 most influential industry innovators since 1774. Available in the following link.
http://archive.today/2RoSK
PID Control was listed twice (the dominant control method in the industrial application -- (1) John G. Ziegler and Nathaniel B. Nichols and classical PID Control; (2) Karl Johan Åström and modern PID Control (IEEE Medal of Honor, 1993)
http://en.wikipedia.org/wiki/IEEE_Medal_of_Honor
The next popular method is Smith Predictor: Otto J.M. Smith and Smith Predictor.
http://en.wikipedia.org/wiki/Otto_J._M._Smith
A typical PID tuning procedure: (1) Use relay control to estimate the control model (or control plant); (2) Use Z-N formula to initialize Kp and Ki; (3) use trial and error to adjust Kp and Ki or other method such as iterative feedback tuning (IFT), internal model control (IMC), etc.
WK Ho, Y Hong, A Hansson, H Hjalmarsson, and JW Deng, "Relay auto-tuning of PID controllers using iterative feedback tuning," Automatica 39 (1), January 2003, pp. 149-157. Available in the following RG Link.
https://www.researchgate.net/publication/223504459_Relay_auto-tuning_of_PID_controllers_using_iterative_feedback_tuning
W.K. Ho, T.H. Lee, H.P. Han, and Y. Hong, "Self-Tuning IMC-PID Control with Interval Gain and Phase Margin Assignment," IEEE Transactions on Control Systems Technology, 9(3), May 2001, pp. 535-541. Available in the following RG Link.
H. Nyquist (Sweden) --> K.J. Astrom (Sweden) --> W.K. Ho (Sweden)
| Nyquist plot (published in 1932)
| Bell Labs
V Bode plot (published in 1940)
H.W. Bode (Harvard) --> K.S. Narendra (Harvard, Yale) --> T.H. Lee (Yale)
https://www.researchgate.net/publication/3332273_Self-tuning_IMC-PID_control_with_interval_gain_and_phase_marginsassignment
C.C. Hang, K.J. Astrom, and W.K. Ho, "Refinements of the Ziegler-Nichols tuning formula," IEE Proceedings on Control Theory and Applications, 138(2), March 1991, pp.111-118.
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=67610
This paper and selected classic PID tuning methods (co-invented by K.J. Astrom and his student W.K. Ho) have been implemented by Maplesoft Inc. for MapleSim Control Design Toolbox
http://www.maplesoft.com/support/help/MapleSim/view.aspx?path=ControlDesign/GainPhaseMargin
K.J. Åström, T. Hägglund, C.C. Hang, and W.K. Ho, "Automatic tuning and adaptation for PID controllers - a survey," Control Engineering Practice, 1(4), August 1993, pp.699-714.
http://www.sciencedirect.com/science/article/pii/096706619391394C
K.J. Åström, C.C. Hang, P. Persson, and W.K. Ho, "Towards intelligent PID control," Automatica, 28(1), January 1992, pp.1-9.
http://www.sciencedirect.com/science/article/pii/000510989290002W
Control theorectic approaches have been applied to model the interactions between an overloaded SIP server and its upstream servers as a feedback control system in two different scenarios - round trip delay control (IEEE ICC 2011) and redundant retransmission ratio control (IEEE Globecom 2010).
Round-Trip Delay Control (RTDC, implicit SIP overload control) algorithm: Y. Hong, C. Huang, and J. Yan, "Design Of A PI Rate Controller For Mitigating SIP Overload," Proceedings of IEEE ICC, Kyoto, Japan, June 2011.
https://www.researchgate.net/publication/224249824_Design_of_a_PI_Rate_Controller_for_Mitigating_SIP_Overload
RTDC implicit SIP overload control algorithm has been recommended as White Paper by TechRepublic (CBS Interactive)
http://www.techrepublic.com/whitepapers/design-of-a-pi-rate-controller-for-mitigating-sip-overload/25142469
IEEE ICC 2011 presentation slides for RTDC implicit SIP overload control can be downloaded from the following RG link.
https://www.researchgate.net/publication/257945199_Round-Trip_Delay_Control_(RTDC)_For_Mitigating_SIP_Overload_(IEEE_ICC_2011_Slides)
Redundant Retransmission Ratio Control (RRRC, implicit SIP overload control) algorithm: Y. Hong, C. Huang, and J. Yan, "Mitigating SIP Overload Using a Control-Theoretic Approach," Proceedings of IEEE Globecom, Miami, FL, U.S.A, December 2010.
https://www.researchgate.net/publication/221284946_Miigating_SIP_Overload_Using_a_Control-Theoretic_Approach
RRRC implicit SIP overload control algorithm has been quickly adopted by The Central Weather Bureau of Taiwan for their early earthquake warning system.
T.Y. Chi, C.H. Chen, H.C. Chao, and S.Y. Kuo, "An Efficient Earthquake Early Warning Message Delivery Algorithm Using an in Time Control-Theoretic Approach", 2011.
http://link.springer.com/chapter/10.1007%2F978-3-642-23641-9_15#
http://www.ipv6.org.tw/docu/elearning8_2011/1010004798p_3-7.pdf
Short review and comments on this implicit SIP overload control algorithm by former IEEE TAC Associate Editor S. Mascolo:
L. De Cicco, G. Cofano, and S. Mascolo,"Local SIP Overload Control", Proceedings of WWIC, June 2013.
http://link.springer.com/chapter/10.1007%2F978-3-642-38401-1_16#
http://c3lab.poliba.it/images/2/2a/SipOverload_WWIC13.pdf
IEEE GLOBECOM 2010 presentation slides for RRRC implicit SIP overload control can be downloaded from the following RG link.
https://www.researchgate.net/publication/258555827_Mitigating_SIP_Overload_Using_a_Control-Theoretic_Approach
Journal paper (SIP Overload Control) not only conducts more theoretical analysis of Round trip delay control (RTDC) and Redundant retransmission ratio control (RRRC), but also discusses how to apply RTDC algorithm to mitigate SIP overload for both SIP over UDP and SIP over TCP (with TLS).
Y. Hong, C. Huang, and J. Yan, "Applying control theoretic approach to mitigate SIP overload", Telecommunication Systems, 54(4), December 2013, pp. 387-404.
https://www.researchgate.net/publication/257667871_Applying_control_theoretic_approach_to_mitigate_SIP_overload
http://link.springer.com/article/10.1007/s11235-013-9744-8
Survey on SIP overload control algorithms: Y. Hong, C. Huang, and J. Yan, "A Comparative Study of SIP Overload Control Algorithms", IGI Global, 2012, pp. 1-20.
http://www.researchgate.net/publication/231609451_A_Comparative_Study_of_SIP_Overload_Control_Algorithms
http://www.igi-global.com/chapter/comparative-study-sip-overload-control/67496
Open-source SIP/VoIP project discussion archive
http://lists.sip-router.org/pipermail/sr-users/2013-April/077596.html
IETF-RFC "SIP Overload Control" discussion archive
http://www.ietf.org/mail-archive/web/sip-overload/current/msg00919.html
API-RCP(TCP Congestion Control):Y. Hong and O.W.W. Yang, "Design of Adaptive PI Rate Controller for Best-Effort Traffic in the Internet Based on Phase Margin," IEEE Transactions on Parallel and Distributed Systems, 18(4), April 2007, pp. 550-561.
http://www.researchgate.net/publication/3301176_Design_of_Adaptive_PI_Rate_Controller_for_Best-Effort_Traffic_in_the_Internet_Based_on_Phase_Margin
Review, comments, and extensive evaluation on API-RCP:
H. Zhou, C. Hu, and L. He, "Improving the Efficiency and Fairness of eXplicit Control Protocol in Multi-Bottleneck Networks", Elsevier Computer Communications, 36(10-11), June 2013, pp. 1193-1208.
http://www.sciencedirect.com/science/article/pii/S0140366413001059
Real-world Linux implementation of API-RCP: "An Implementation and Experimental Study of the Adaptive PI Rate Control Protocol," Proceedings of IEEE HPSR, Paris, France, June 2009.
https://www.researchgate.net/publication/224611517_An_implementation_and_experimental_study_of_the_Adaptive_PI_Rate_Control_Protocol
(3) For academic control community,
ACC 2012 Plenary and Semi-Plenary Lectures
Plenary: Accomplishments and Prospects of Control
Abstract: There are many success stories and major achievements in control, something remarkable for a field as young as 50 years. In this talk we will sample these accomplishments and speculate about the future prospects of control. While there are examples of feedback from ancient times, extensive use of feedback paralleled industrialization: steam, electricity, communication, transportation etc. Control was established as a field in the period 1940-1960, when the similarities of control in widely different fields were recognized. Control constituted a paradigm shift in engineering that cut across the traditional engineering disciplines: mechanical, electrical, chemical, aerospace. A holistic view of control systems with a unified theory emerged in the 1950s, triggered by military efforts during the Second World War. The International Federation of Automatic Control (IFAC) was formed in 1956. Education in control spread rapidly to practically all engineering disciplines. Conferences and journals also appeared. A second phase, driven by the space race and the emergence of computers, started around 1960. Theory developed dramatically as did industrial applications. A large number of sub-specialties appeared and perhaps due to this, the holistic view of the field was lost. In my opinion we are now entering a third phase driven by the ubiquitous use of control and a strong interest in feedback and control among fellow scientists in physics and biology. There are also new areas driven by networked systems, autonomy and safe design of large complex systems. What will happen next depends largely on how we respond to the new challenges and on how we manage to recapture the holistic view of systems. Key issues will be education and interaction with other disciplines.
Semi-Plenary Lectures also discuss promising research topics.
http://a2c2.org/conferences/acc2012/plenary.php
8 wonderful presentations in control symposium "Paths Ahead in the Science of Information and Decision Systems", Massachusetts Institute of Technology (MIT), USA, November 12 – 14, 2009.
http://paths.lids.mit.edu/papers_mitter.html
Panel on Future Directions in Control, Dynamics, and Systems, Richard M. Murray (chair), California Institute of Technology, April 2002
http://www.cds.caltech.edu/~murray/cdspanel/
R. Murray, K. Astrom, S. Boyd, R. Brockett, and G. Stein, "Future Directions in Control in an Information-Rich World," IEEE Control Systems Magazine, 23(2), April 2003, pp.20-33.
http://www.stanford.edu/~boyd/papers/cds_panel.html
Currently US National Science Foundation (NSF) funding support emphasizes the real-life applications and/or industry needs instead of pure theoretical work in control.
"The Control Systems (CS) program supports fundamental research on control theory and control technology driven by real life applications. .... that are motivated and derived from real-life applications and/or industry needs."
http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=13575
To celebrate the golden anniversary, IFAC Automatica will publish in the 50th volume throughout the year, special survey/overview papers, on selected topics, some tracing the history on some mature topics and areas, others focusing on newly emerging areas, with forecasts into the future. The survey paper published by the 1st issue provides an overview of the developments in the control field from its early days.
K.J. Astrom and P.R. Kumar, "Control: A Perspective," Automatica, 50(1), January 2014, pp. 3-43.
http://www.sciencedirect.com/science/article/pii/S0005109813005037
(4) Control Theory developed in the twentieth century: 25 Seminal Papers Selected by IEEE Control Society in 2000
Control Theory: Twenty-Five Seminal Papers (1932-1981), Edited by T.S. Basar, Wiley-IEEE Press, 2000.
http://www.ebay.com/ctg/Control-Theory-Twenty-Five-Seminal-Papers-1932-1981-by-Inc-Staff-IEEE-2000-Hardcover-/1776728?_tab=1&_trksid=p2047675.l2644
http://www.amazon.ca/Control-Theory-Twenty-Five-Seminal-1932-1981/dp/0780360214
IEEE Control Systems Award
http://en.wikipedia.org/wiki/IEEE_Control_Systems_Award
IFAC Giorgio Quazza Medal
http://www.ifac-control.org/awards/major-medals
4 co-authors of 25 Seminal Papers (1932-1981) awarded IEEE Medal of Honor (the highest IEEE award): Nyquist(1960), Kalman(1974), Bellman(1979), Astrom(1993).
http://www.ieee.org/about/awards/medals/medalofhonor.html
R.E. Bellman and K.J. Astrom, "On structural identifiability," Mathematical Biosciences, 7(3-4), 1970, pp. 329–339.
http://www.sciencedirect.com/science/article/pii/002555647090132X
Richard E. Bellman Control Heritage Award for US control systems engineers and scientists (US citizenship)
http://a2c2.org/awards/richard-e-bellman-control-heritage-award
Ragazzini's notable students are Rudolf Kalman (see Kalman filters), Eliahu Ibraham Jury (see Z-transform) and Lotfi Asker Zadeh (see Fuzzy sets and Fuzzy logic).
https://en.wikipedia.org/wiki/John_Ragazzini
K. Astrom, E.I. Jury, and R. Agniel, "A numerical method for the evaluation of complex integrals," IEEE Transactions on Automatic Control, vol.15, no.4, Aug 1970, pp.468-471.
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1099492
"To control theorists, Nyquist is no doubt best known as the inventor of the Nyquist diagram, defining the conditions for stability of negative feedback systems. This has become a foundation stone for control theory the world over, applicable in a much wider range of situations than that for which it was orignally enunciated." Hendrik W. Bode, Harvard University, USA, 1977.
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1101666
Biography of Harry Nyquist, University of Cambridge, UK, 2003
"Between 1920 and 1940 he published a series of papers on research in telecommunications which are arguably the most outstanding set of scientific contributions since Newton (apart from Einstein!)."
http://babylon.acad.cai.cam.ac.uk/students/study/engineering/engineer03l/cenyquist.htm
http://babylon.acad.cai.cam.ac.uk/students/study/engineering/engineer03l/ceframes.htm
K.J. Åström, "Harry Nyquist (1889-1976): A Tribute to the Memory of an Outstanding Scientist," Royal Swedish Academy of Engineering Sciences, 2003.
American Society of Mechanical Engineers (ASME) Nyquist Lecturer Award
https://www.asme.org/about-asme/get-involved/honors-awards/unit-awards/nyquist-lecturer
Article Design of Adaptive PI Rate Controller for Best-Effort Traffi...
Article Self-tuning IMC-PID control with interval gain and phase mar...
Conference Paper Mitigating SIP Overload Using a Control-Theoretic Approach.
Article Relay auto-tuning of PID controllers using iterative feedback tuning
Conference Paper Design of a PI Rate Controller for Mitigating SIP Overload
Conference Paper An implementation and experimental study of the Adaptive PI ...
Article A Comparative Study of SIP Overload Control Algorithms
Article Applying control theoretic approach to mitigate SIP overload
Data Round-Trip Delay Control (RTDC) For Mitigating SIP Overload ...
Data Mitigating SIP Overload Using a Control-Theoretic Approach
Decentralized control and Hybrid controller is also the last issues
Domains like Fractional order controller with/without optimization algorithms and MPC in various applications could be tried.
They are quite a lot like adaptive control, robust control, fractional order systems, switched systems....etc.
Please refer to these articles:
https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller
https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance
https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design
Article From PID to Nonlinear State Error Feedback Controller
Article Improved Sliding Mode Nonlinear Extended State Observer base...
Article On the Improved Nonlinear Tracking Differentiator based Nonl...
The recursive least squares algorithm (RLS) allows for (real-time) dynamical application of least squares (LS) regression to a time series of time-stamped continuously acquired data points. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. RLS is the recursive application of the well-known LS regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. For RLS with forgetting factor (RLS-FF), acquired data is weighted according to its age, with increased weight given to the most recent data. This is often convenient for adaptive control and/or real-time optimization purposes.
Application example ― While investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...
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