Even Intelligent PID control is not model free control, since you need the an accurate model of the system to design the controller, however intelligent methods such as GA could be used for fine tuning. A good example of model free controllers is Fuzzy Logic Control, where as exact model of the system is not required for design stage.

Actuallty it is not one of artificial intelligence controllers, and it depends on estimation of system dynamics to be cancelled out out later, so in principal it does not need accurate model.

you cans see it in the attached paper.

Article Model-free control

Both issues (windup and sensitivity of ther derivative term) are not related to the way you select the parameters but to the algorithm you use to calculate the controller-output. Thus the answer to your first question is "yes".

Hitting upper / lower limitations of your control- and / or measurement signal means, your loop is opened (control signal does not depend on the control error any longer). This results in loss of performance, when compared to a limitless system. No algorithm can change this

If your controller hits limitations infrequently, you'll have to add an anti-windup scheme to the implementation and live with the reduced performance

If this happens frequently, you'll have to reconsider the choice of your sensor and / or actuator.

I think that if the dynamic estimation is "good" and it is realized on-line, it gives some degree of adaptation to the controller under dynamics changes in the plant. However, this adaptation does not disappear the integral and derivative actions of the controller. So, I agree with Marc Enzmann in that iPID still has control saturations or noise amplification as the classical PID.

(1) A quick answer for the question is Yes.

Model Free Control (intelligent PID) has the same classical PID drawbacks, like integral windup, sensitivity of derivative term to noisy data.

(2) According to the paper [FJ13] suggested by Taghreed Mohammadridha, the key idea of Model-free control is that

"The unknown 'complex' mathematical model is replaced by an ultra-local model".

In other words, model-free control simplifies a nonlinear system to a system with a single control variable u and a single output variable y.

The system model can be expressed as

y^(v) = F + au

y^(v) is the derivative of order v of y (v>=1). The integer v is selected by the practitioner. The existing examples show that v may always be chosen quite low, i.e., 1, or, only seldom, 2.

a is a non-physical constant parameter.

F can be approximated by a piecewise constant function. How to estimate F is the key of the model-free control.

In the mean time, intelligent PID control is proposed to incorporate with model-free control for a nonlinear system which is difficult to be identified relatively accurately.

[FJ13] Michel Fliess and Cedric Join, "Model-free control," International Journal of Control, Volume 86, Issue 12, 2013.

http://www.tandfonline.com/doi/abs/10.1080/00207179.2013.810345?journalCode=tcon20#.U2rFx43D_oY

The paper [FJ13] has also cited the landmark paper [AHPH92] on Intelligent PID controller.

Quote from [FJ13] "Remark 1.4 Intelligent PID controllers may already be found in the literature but with a different meaning (see, e.g., Astrom, Hang, Persson & Ho (1992))."

K.J. Astrom, 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

Only PID Control and Smith Predictor were listed in the “Leaders of the Pack” InTech’s 50 most influential industry innovators since the year 1774. Available from 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 Astrom and modern PID Control (IEEE Medal of Honor, 1993)

http://en.wikipedia.org/wiki/IEEE_Medal_of_Honor

(3) Date back to 1990s, H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin proposed Iterative feedback tuning (IFT) approach to tune controller parameters for those control model (or control plant) whose parameters are difficult to be identified relatively accurately using system identification approach.

Both Model-free control proposed by [FJ13] and Iterative feedback tuning (IFT) approach proposed by [HGGL98] aim at tuning controller parameters for the nonlinear system whose model/plant is difficult to be identified/estimated relatively accurately using different types of system identification approaches.

[HGGL98] 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

 Discussions on system identification approaches can be found in the following RG link.

"What is the best reference for system identification?"

https://www.researchgate.net/post/What_is_the_best_reference_for_system_identification

By cooperating with his peer researchers including Stanford University researcher, H. Hjalmarsson integrated iterative feedback tuning with the 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 due to his fundamental contribution to iterative feedback tuning.

[HHHHD03] 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

The paper [SLY17] extends iterative feedback tuning PID controller proposed by [HHHHD03] to enhance the handling and stability performance of an in-wheel motor-driven electric vehicle.

[SLY17] Y. Shi, Q. Liu, and F. Yu, "Design of an Adaptive FO-PID Controller for an In-Wheel-Motor Driven Electric Vehicle," SAE  International Journal of Commercial Vehicles, 10(1), March 2017, pp. 265-274.

http://papers.sae.org/2017-01-0427/

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

(4) Quote Amin Noshadi's comment "Even Intelligent PID control is not model free control, since you need the an accurate model of the system to design the controller."

Note that "model free control" mentioned by Amin Noshadi is more general than "model free control" proposed by the paper [FJ13].

I agree with Amin Noshadi's comment "A good example of model free controllers is Fuzzy Logic Control, where as exact model of the system is not required for design stage."

Quote MATLAB's website "Fuzzy logic can model nonlinear functions of arbitrary complexity."

http://www.mathworks.com/help/fuzzy/what-is-fuzzy-logic.html

However, the real-world implementation cost of fuzzy logic is much more expensive than both intelligent PID control and classical PID control.

Due to its cheap implementation cost and high reliability, "The PID controller is probably the most widely-used type of feedback controller." "PID controllers are the most well-established class of control system." (quote from ABB's white paper [ABB11])

[ABB11] ABB, "PID control theory made easy: Optimising plant performance with modern process controllers," Technical White Paper, ABB, 2011.

ABB is one of the largest engineering companies as well as one of the largest conglomerates in the world.

http://en.wikipedia.org/wiki/ABB_Group

(5) I agree with the comments by Marc Enzmann and Rene Galindo.

Quote Marc Enzmann's comment "Both issues (windup and sensitivity of the derivative term) are not related to the way you select the parameters but to the algorithm you use to calculate the controller-output."

Quote Rene Galindo's comment "However, this adaptation does not disappear the integral and derivative actions of the controller. So, I agree with Marc Enzmann in that iPID still has control saturations or noise amplification as the classical PID."

Let us look at an application of PID control for SIP overload control and TCP congestion control.

(A) SIP(Session Initiation Protocol) is a dominant signalling protocol for Voice over IP in the Internet.

For Round-Trip Delay Control (RTDC, implicit SIP overload control) algorithm, each overloaded downstream SIP server has buffer size (constraint of queue length), leading to the constraint of queuing delay (the output constraint of the system model/plant). where queuing delay=queue length/server capacity; each upstream SIP server has limited server capacity, the constraint of allowed SIP retransmission rate (the input constraint of the system model/plant) .

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)

For Redundant Retransmission Ratio Control (RRRC, implicit SIP overload control) algorithm, each overloaded downstream SIP server has limited service capacity, generating the constraint of the response message rate to corresponding redundant retransmissions (the output constraint of the system model/plant); each upstream SIP server also has limited server capacity, the constraint of allowed SIP retransmission rate (the input constraint of the system model/plant).

Redundant Retransmission Ratio Control (RRRC, implicit SIP overload control) algorithm: [HHY10] 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 RRRC (implicit SIP overload control) algorithm by the former IEEE TAC Associate Editor S. Mascolo (Google Faculty Award 2014 ) with reference to three papers [HHY10], [HHY12], and [HHY13]:

L. De Cicco, G. Cofano, and S. Mascolo,"Local SIP Overload Control: Controller Design and Optimization by Extremum Seeking", IEEE Transactions on Control of Network Systems, Vol. 2, Issue 3, September 2015, pp. 267-277.

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7035079

http://c3lab.poliba.it/images/f/f4/Dcm-tcns15.pdf

http://services.google.com/fh/files/blogs/googlefras-aug2014.pdf 

Journal paper (implicit 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).

[HHY13] 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: [HHY12] 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

 (B) TCP/IP (Transmission Control Protocol/Internet Protocol) is the basic communication protocol of the Internet.

For API-RCP (Adaptive PI rate control protocol for explicit TCP congestion control), each congested router has buffer size (constraint of queue length, the output constraint of the system model/plant); each TCP source has limited transmission rate (the input constraint of the system model/plant).

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

(6) Discussions on control system design

"What are trends in control theory and its applications in physical systems (from a research point of view)?"

https://www.researchgate.net/post/What_are_trends_in_control_theory_and_its_applications_in_physical_systems_from_a_research_point_of_view2

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

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 ...

Thank you all for your valuable answers .. and special thanks for Yang Hong for your rich survey..

Now I'm more convinced that even if we estimate system dynamics to be cancelled out later we are still benefiting from PID control that has same classical PID characteristics to deal with error dynamics that surely has some remaining non modeled system dynamics.

Actually my work is on Artificial Pancreas design, and my first control strategy was model-free control, during my simulations on clinical data I did not have the expected good performance of iPID and rather I ended up by same classical PID drawbacks.

Medical Control problems are very complex, and in the most cases are strongly non-linear.

Maybe you can try a non-linear controler for it.

I suggested a Robust Fixed Point Transformation. It needs just an aproximate model.

The current version is using “precursor oscillations”,

https://www.researchgate.net/publication/261381178_Improvement_of_the_stability_of_RFPT-based_adaptive_controllers_by_observing_precursor_oscillations?ev=prf_pub

You can use fractional derivatives to Increase cycle time:

https://www.researchgate.net/publication/260738956_Increased_cycle_time_achieved_by_fractional_derivatives_in_the_adaptive_control_of_the_Brusselator_model?ev=prf_pub

Conference Paper Improvement of the stability of RFPT-based adaptive controll...

Conference Paper Increased cycle time achieved by fractional derivatives in t...

if we want to discuss about linear PID controller and PID like fuzzy controller, we should to compare them. linear PID controller is a controller which depend to only three coefficients but in  PID like fuzzy  we must to compensate system dynamic based on rule base of fuzzy logic controller.

So for the first question, your answer is yes but you know in practical application we can not said exactly.

If you want to tuning PID controller, you have only three coefficients but to tuning PID like fuzzy controller some parameters have important role; universe of discourse, membership function, linguistic variable, gain updating factor and ............

if you want to design controller you must to know that, the type of input is not important.

overally I think some time they are the same and some times they are different

you also can follow my papers related to nonlinear control. 

Thanks Mr. Farzan, but the iPID in question is not of artificial intelligent one , I refered a paper previously you can see it.

thank you very much you any way!

I'm currently working on model free control of a magnetic levitation system. I'm using y^(2) = F + au . The controller performance strongly depends on the parameter "a", wich has to be tuned manually.

I didn't test it myself, but it seems that iPID can handle control effort limits very well. I saw this on the following article:

Thanks Matheus, actually I agree with you that "a" has a grand role, but I noticed that iPID gains have a good impact also especially with relatively slow system dynamics.

With regards to 'F_est', many of Fliess's papers mention the notation of 'sigma' in the 'F_est' equation. Does anyone know what that refers to?

@ Richard Chang:

'sigma' is just an integration variable that is supposed to represent time.

I propose a PID well-balanced, it is a good baseline to start a problem of control without effort :

Data datasheet appedge hal v1

I did implement these controllers for automotive application. You may handle the saturation like you do with an observer. The estimation of the unknown signal F is a form of unknown input observer (somehow). In order to avoid drift of the implicit integral action, you just need to feedback the saturated control in the estimation of the unknown signal F.

Can somebody please explain the proceeses of going from equation (1) at the top to equation (2) the bottom in this picture. I know there is convolution occuring but I do not undertsnad how -6/L^3 is coming up in this equation.