Tuning and auto-tuning of fractional order controllers for industry applications
TL;DR: In this article, a method for tuning the PI λ D μ controller is proposed to fulfill five different design specifications, including gain crossover frequency, phase margin, and iso-damping property of the system.
About: This article is published in Control Engineering Practice.The article was published on 2008-07-01 and is currently open access. It has received 881 citations till now. The article focuses on the topics: Phase margin & Fractional calculus.
Summary (1 min read)
Jump to: [ARTICLE IN PRESS] – [2.1. A review] – [3.2. Experimental results by using the tuning method] – [4.5. Experimental results by using the auto-tuning method] and [5. Conclusions]
ARTICLE IN PRESS
- As commented before, nowadays many research efforts related to the applications of fractional order controllers have concentrated on various aspects of control analysis and synthesis.
- Section 4 presents an auto-tuning method for this kind of controller, whose experimental results are also shown in the section.
- By choosing the minimum value m min ; the distance between the zero and the pole of the compensator will be the maximum possible (minimum value of parameter x; a positive value very close to zero).
- For that purpose the slope of the phase of the plant, u, is estimated by using the expression (18).
2.1. A review
- To sum all this up, it is clear that FOC and its applications are becoming an important issue.
- Of course, there are other published texts related to fractional calculus.
- The main reason why they are not cited here is that their subjects are not relevant for the purpose of this work.
3.2. Experimental results by using the tuning method
- From these results, the potential of the fractional order controllers in practical industrial settings, regarding performance and robustness aspects, is clear.
- The design method proposed here involves complex equations relating ., ""'".
4.5. Experimental results by using the auto-tuning method
- For the implementation of the auto-tuning method proposed the following devices have been used, showing a connection scheme in Fig. 13 : Data acquisition board AD 512, by Humusoft, running on Matlab 5.3 and using the real time toolbox ''Real-Time Windows Target''.
- The mechanical unit has a brake whose position changes the gain of the system, that is, the break acts like a load to the motor.
- Specifications of gain crossover frequency, phase margin and robustness to plant gain variations are given.
- After several iterations the output signal shown in Fig. 15 is obtained.
5. Conclusions
- Besides, an auto-tuning method for the fractional order PI l D m controller using the relay test has been proposed.
- This method allows a flexible and direct selection of the parameters of the controller through the knowledge of the magnitude and phase of the plant at the frequency of interest, obtained with the relay test.
- Again, the experimental results illustrate the effectiveness of this method.
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Citations
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10 Jun 2009
TL;DR: A tutorial on fractional calculus in controls is offered which may make fractional order controllers ubiquitous in industry and several typical known fractional orders controllers are introduced and commented.
Abstract: Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. In this paper, we offer a tutorial on fractional calculus in controls. Basic definitions of fractional calculus, fractional order dynamic systems and controls are presented first. Then, fractional order PID controllers are introduced which may make fractional order controllers ubiquitous in industry. Additionally, several typical known fractional order controllers are introduced and commented. Numerical methods for simulating fractional order systems are given in detail so that a beginner can get started quickly. Discretization techniques for fractional order operators are introduced in some details too. Both digital and analog realization methods of fractional order operators are introduced. Finally, remarks on future research efforts in fractional order control are given.
809 citations
Cites background from "Tuning and auto-tuning of fractiona..."
...For the latest developments, we refer to [7], [47], [60], [51], [52]....
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...It has also been answered in the literature why to consider fractional order control even when integer (high) order control works comparatively well [49], [52]....
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Book•
10 Feb 2010
TL;DR: Fractional Order Systems Fractional order PID Controller Chaotic fractional order systems Field Programmable Gate Array, Microcontroller and Field Pmable Analog Array Implementation Switched Capacitor and Integrated Circuit Design Modeling of Ionic Polymeric Metal Composite as discussed by the authors.
Abstract: Fractional Order Systems Fractional Order PID Controller Chaotic Fractional Order Systems Field Programmable Gate Array, Microcontroller and Field Programmable Analog Array Implementation Switched Capacitor and Integrated Circuit Design Modeling of Ionic Polymeric Metal Composite
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TL;DR: A recent article published in this magazine has labeled fractional-order continuous-time systems as the "21st century systems" and highlighted specific problems which need to be addressed particularly by electrical engineers.
Abstract: A recent article published in this magazine has labeled fractional-order continuous-time systems as the "21st century systems". Indeed, this emerging research area is slowly gaining momentum among electrical engineers while its deeply rooted mathematical concepts also slowly migrate to various engineering disciplines. A very important aspect of research in fractional-order circuits and systems is that it is an interdisciplinary subject. Specifically, it is an area where biochemistry, medicine and electrical engineering over-lap giving rise to many new potential applications. This article aims to provide an overview of the current status of research in this area, highlighting specific problems which need to be addressed particularly by electrical engineers.
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TL;DR: This review investigates its progress since the first reported use of control systems, covering the fractional PID proposed by Podlubny in 1994, and is presenting a state-of-the-art fractionalpid controller, incorporating the latest contributions in this field.
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References
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01 Jan 1986
TL;DR: This introductory book provides an in-depth, comprehensive treatment of a collection of classical and state-space approaches to control system design and ties the methods together so that a designer is able to pick the method that best fits the problem at hand.
Abstract: From the Publisher:
This introductory book provides an in-depth, comprehensive treatment of a collection of classical and state-space approaches to control system designand ties the methods together so that a designer is able to pick the method that best fits the problem at hand. It includes case studies and comprehensive examples with close integration of MATLAB throughout the book. Chapter topics include an overview and brief history of feedback control, dynamic models, dynamic response, basic properties of feedback, the root-locus design method, the frequency-response design method, state-space design, digital control, and control-system design. A basic reference for control systems engineers.
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TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.
Abstract: Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.
2,479 citations
"Tuning and auto-tuning of fractiona..." refers background in this paper
...(RL) definition (Podlubny, 1999a)....
[...]
...Podlubny (1999b) proposed a generalization of the PID controller, namely the PIlDm controller, involving an integrator of order l and a differentiator of order m....
[...]
Book•
01 Jan 1945
2,469 citations
"Tuning and auto-tuning of fractiona..." refers background in this paper
...Maybe the first mention of the interest of considering a fractional integro-differential operator in a feedback loop, though without using the term ‘‘fractional’’, was made by Bode (1940), and next in a more comprehensive way in Bode (1945)....
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TL;DR: In this article, the state-of-the-art on generalized (or any order) derivatives in physics and engineering sciences is outlined for justifying the interest of the noninteger differentiation.
Abstract: The state-of-the-art on generalized (or any order) derivatives in physics and engineering sciences, is outlined for justifying the interest of the noninteger differentiation. The problems subsequent to its use in real-time operations are then set out so as to motivate the idea of synthesizing it by a recursive distribution of zeros and poles. An analysis of the existing work is also proposed to support this idea. A comprehensive study is given of the synthesis of differentiators with integer, noninteger, real or complex orders, and whose action is limited to any given frequency bandwidth. First, a definition, in the operational and frequency domains, of a frequency-band complex noninteger order differentiator, is given in a mathematical space with four dimensions which is a Banach algebra. Then, the determination of its synthesized form, by a recursive distribution of complex zeros and poles characterized by complex recursive factors, is presented. The complex noninteger differentiation order is expressed as a function of these recursive factors. The number of zeros and poles is calculated to be as low as possible while still ensuring the stability of the synthesized differentiator to be synthesized. A time validation is presented. Finally, guidelines are proposed for the conception of the synthesized differentiator.
1,361 citations