If you don't want to identify parameters of the process model then you need to use so-called non-parametric methods of tuning. Two well-known non-parametric methods are the closed-loop Ziegler-Nichols tuning method and the relay feedback test-based tuning by Astrom and Hagglund. A review of methods and the theory of non-parametric is given in I. Boiko "Non-parametric Tuning of PID Controllers," Springer, 2013. Some sections are available for download from http://www.springer.com/engineering/control/book/978-1-4471-4464-9

Did yo try to apply Ziegler-Nichols method ?

http://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method

IF u have transfer function of the plant and u also know ur desire response then , u may use Ziegler & Nichls, Tyreus-Luyben, and Cohen-Coon tuning methods.

You have to find the plant transfer function. This can be done by using classical Laplace calculations or by taking the advantage of state-space technique, and from the parameters A, B, C and D you can write the transfer function.

If the transfer function becomes very large and very complex, then you may think about the minimal realization technique to simplify that transfer function without changing the plant behavior.

Also, if the obtained transfer function (any one, the simplified or non-simplified) is unstable, then by using poles placement, you can make it stable.

Once you construct it, then you have to choices to tune the plant:

1- By using conventional technique (Ziegler-Nicholas, Cohen-Coon, etc):

A- Open loop approach

B- Closed loop approach

2- Or, simply, by using numerical technique (optimization)

Regards and best wishes,

In this case, I suggest to use gain scheduling and the optimal values of Kp, Ki, and Kd can be easily found for both simulation and experimental cases. Good luck.

hello,

1- I think you can estimate your system with a simple transfer function and then design controller, you can use matlab identification GUI and estimate your system and then try to PID controller.

2- and I am agree with Ali's offer , you can use numerical optimization technique, PSO,GA, or ....

best regards ...

The beauty of PID is that there are only 3 parameters that are pretty intuitive to tune. If you are not an experienced PID user, then the Ziegler-Nichols closed loop tuning method may be useful to you. The open loop methods based on step responses may also be easy to apply. Good luck.

(1) A typical PID tuning procedure: (1) Use relay control to estimate the control model (or control plant); (2) Use Ziegler-Nichols formula to initialize Kp and Ki; (3) use trial and error method to adjust Kp and Ki or other method such as gain scheduling suggested by Ibrahim Jasim, iterative feedback tuning (IFT), internal model control (IMC), etc.

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 the 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.

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 from 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 from 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?ev=prf_pub

(2) 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

(3) 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, as indicated by Marada Naveen Kumar's comment "But the transfer function of the process is complex to derive."

The basic procedure of tuning PID controller using IFT proposed by the Automatica 2003 paper can be summarized as follows:

(I) Use relay control to estimate the control model (or control plant) for a water tank (a real-world control system);

(II) Apply Ziegler-Nichols method suggested by Kazuya Tada, Syed Faiz Ahmed, and Ali Alroomi to calculate PID controller parameter. However, there is a great deviation between the estimated control plant and the water tank. The system performance of the water tank controlled by the PID controller based on Ziegler-Nichols formula was unsatisfactory.

(III) Apply Iterative feedback tuning (IFT) method to tune PID controller and achieve a satisfactory performance of the real-world water tank.

(4) In summary, although "the transfer function of the process is complex to derive" (quote from Marada Naveen Kumar's comment),

(4a) Ziegler-Nichols, Tyreus-Luyben, and Cohen-Coon tuning methods suggested by Kazuya Tada, Syed Faiz Ahmed, and Ali Alroomi are effective for many control systems. The most advantage of these three methods is the low implementation cost in the industrial application.

(4b) In the case that Ziegler-Nichols, Tyreus-Luyben, and Cohen-Coon tuning methods are ineffective for a desired system response, the gain scheduling method suggested by Ibrahim Jasim is a good choice of control engineering practice.

(5) Discussions on control system design approaches

"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 Self-tuning IMC-PID control with interval gain and phase mar...

Article Relay auto-tuning of PID controllers using iterative feedback tuning

It might be difficulty to tune a PID controller without the transfer function. It seems that your problem is not on the PID tuning part, but on identifying the plant's transfer function.

You can use the step response method. Just apply a step input and measure the output response. Plot it in a piece of paper and derive the model. If there is no overshoot, just assume it as a first-order model G(s)=Kexp(-Ls)/(Ts+1). If there is overshoot, then assume it as a second-order model G(s)Kexp(-Ls)/((T_1.s+1)(T_2.s+1)), then compute for the PID constant using Ziegler Nichols as mentioned by our good colleagues.

experimentally .... start with step response and small Kp without Ki or Kd .... from small Kp and with gradually highing it you will note the decreasing of the steady state error ...... at the smallest steady state error you can get start to add nearly 0.1 of Kp in Ki ... it will solve the problem of the steady state error .. hope it may useful

If you don't want to identify parameters of the process model then you need to use so-called non-parametric methods of tuning. Two well-known non-parametric methods are the closed-loop Ziegler-Nichols tuning method and the relay feedback test-based tuning by Astrom and Hagglund. A review of methods and the theory of non-parametric is given in I. Boiko "Non-parametric Tuning of PID Controllers," Springer, 2013. Some sections are available for download from http://www.springer.com/engineering/control/book/978-1-4471-4464-9

try to use zigler nichols method.

approximate the plant into 3 parameter model and this can be easily done by getting the step response of the system first. For getting the basic knowledge of zigler nichols method refer page no 682 of book "Modern Control Engineering, 4th edition" Author-Katsuhiko Ogata .

I think this will work.

Just as Igor Boiko wrote, the relay method is one of the simplest and saftest in case of tuning a real time plant. I recommend you to read an article Comparing PI Tuning Methods in a Real Benchmark Temperature Control System written by Finn Haugen.

I checked a relay method in practice and it works, what wasn't strange. because this method is often implemented in industrial controllers and programmable controllers.

Consider the following steps if you want to tune the PID controller without transfer function or frequency response data of the process.

1. Roughly, guess the dominant time constant (tau) of the process. Usually, you can roughly guess how long it will take for the process to sufficiently react to a step control output. That is tau. Now, you can tune the integral time (Ti) and the derivative time (Td) of the PID controller by Ti=tau and Td=Ti/4.0.

2. Roughly, guess the static gain (K) of the process. K is delta_y/delta_u. delta_y is the process output variation corresponding to the control output variation of delta_u. For example, assume that increasing the control output as much as 2.0 results in increasing the process output as much as 4.0 at stead state. In this case, K=4.0/2.0=2.0. Now, the proportional gain (Kc) of the PID controller is tuned by Kc=1/K.

3. Now, refine the tuning parameters using the trial and error tuning method. If the control action is too aggressive, reduce Kc, vice versa. If the initial part of the control output grows too much compared to the final part, increase Ti, vice versa. For detailed descriptions on the trial and error method and various tuning methods, please, refer to the following textbook.

Process Identification and PID Control, Su Whan Sung/Jitae Lee/In-Beum Lee, John Wiley & Sons, April, 2009

*** If you have process input and process output data excited by changing setpoint or manually changing control output, send them to me. I will check if the process modeling is possible and provide the tuning parameters if the process data are sufficiently informative. Of course, you don't have to worry about money ^^. It is free.^^ My email is [email protected].

If you have a model-free tuning approach in mind, there maybe a number of ways to proceed.

1. Simplest is the Ziegler-Nichols, closed-loop, tuning. But it tends to work better with plants that have some delay.

2. You could use PID autotuning with Relay feedback [you may want to see the book by Derek Atherton from Bookboon.com, it is free to download]

3. If you want to be a but more adventurous, try Fuzzy PID techniques.

Personally, I would commence from the simplest then move to the next technique (and ideally compare what one gains from the increased complexity of the tuning method). However, I will also agree with the comment from Emmanuel Gonzalez above, you may wish to identify an approximate model for your plant (which i pressume is stable). Hence, introduce more flexibility in choosing a tuning method (i.e. you can then move towards model-based PID tuning, but beware of any uncertainty introduced by the approximation).

I suggest to control the PID parameters by Mulyi Layer Perceptrons (back propagation algorithm)

all you need is an open-loop step-response of the control system to proper tune the PID. with more information on that response I could give you hints on papers etc...

regards

[EDIT] p.s. I am just wondering how many of the people suggesting Ziegler-Nichols ever tried this in practice... ;-)

That's it. In practice an original Ziegler - Nichols method based on closed loop response isn't a safe solution, because of the fact that it is possible to make a system non stable. Just as Martin wrote at the beginning we can use a step response of the controlled plant in the selected working point and estimate parameters of the PID. The problem is that a set point can vary between minimal and maximal technological value, what usually causes some changes in the dynamics of the plant, precisely dynamical parameters are changeable due to changes of the working point. According to that a well tuned controlled should provide some robustness, but often it doesn't and a re-tuning process should be done.

But I agree that tuning a PID controller manually without understanding a dynamic of the plant i.e. without even a simple model e.g. transition function, is a dangerous process if we take into account a possibility of making a control system not stable.

From my own experience with real time plants controlled using plc, a relay method is effective and safe.

> Just as Martin wrote at the beginning we can use a step response of the controlled plant

ähm... no, sorry. I talked about an OPEN-loop response. that is, switch your PID to MANUAL, not AUTO, and step the output manually. (hint: start with small steps :- )

if you suspect strong nonlinearities, you need to step the manipulated variable (the "input") over the whole range or at least as far as possible (more theoretically spoken: move your working point over the whole possible range).

i have to read through the paper about the relay method as i have no experience with it; but i am tuning control loops in large chemical plants every day (really big ones - controlled by a DCS, not by PLCs), and a step response is always the first step towards a good model of the loop. if you have a good model, deriving the PID parameters is the easy part and there are always more than one method that will give good results (if, contrary, you have optimal parameters derived from a bad model, they won't make your real-world loop behaving nice)... so, this relay method could work, but is definitely not the only method around...

regards

martin

Beware of Ziegler-Nichols tuning method!

As a closed loop tuning method, it is safe for the whole process as long as the system is intrinsically stable in a wide range of conditions, e.g thermal systems but NOT chemocal process systems

Also consider the Cohen.Coon process reaction method (it's open loop and reliable).

Regard

Vito

Hi, there are a few papers in this area, i.e., to use the I/O data directly to design and meet the control performance requirements:

https://www.researchgate.net/publication/3732785_Direct_design_of_uniform_LTI_controllers_from_plant_IO_data_using_a_parallel_evolutionary_algorithm?ev=prf_pub

https://www.researchgate.net/publication/2596266_Evolving_Generic_Feedforward_Path_Nonlinear_Controllers_From_Open-Loop_Plant_Response_Data?ev=prf_pub

Performance Based Linear Control System Design By Genetic Evolution With Simulated Annealing http://eprints.gla.ac.uk/67115/

https://www.researchgate.net/publication/222678827_Performance-based_control_system_design_automation_via_evolutionary_computing?ev=prf_pub

https://www.researchgate.net/publication/2641778_Physical_Parametric_Modelling_for_Nonlinear_Systems?ev=prf_pub

PID control system analysis, design, and technology, IEEE Transactions on Control Systems Technology 08/2005; https://www.researchgate.net/publication/3332664_PID_control_system_analysis_design_and_technology?ev=prf_pub

Conference Paper Direct design of uniform LTI controllers from plant I/O data...

Article Evolving Generic Feedforward Path Nonlinear Controllers From...

Article Performance-based control system design automation via evolu...

Article Physical Parametric Modelling for Nonlinear Systems

Article PID Control System Analysis, Design, and Technology

My favourite PID tuning is by "Extremum Seeking" control methods, see for example

[Killingworth and Krstic] PID tuning using extremum seeking: online, model-free performance optimisation, or other pubs by Krstic and co-workers. Fool-proof !

I'd second Moshe's notion. Recently I played with some oscillator stabilising controllers concepts, and their common trouble was not recognising that integration is already present in the very oscillator you wish to stabilise, and instead you get relaxation pulses. It is only fair to approach a system as unknown and let the tuning reveal it's secrets.

Some non-invasive methods for controller tuning are described in my recent book, Chap. 14.

Jelali, M.: Control Performance Management in Industrial Automation: Assessment, Diagnosis and Improvement of Control Loop Performance. Springer-Verlag, London, 2013

You properly model the system and then simulate. You can refer to my paper

"PID Controller Tuning using Simulink for Multi Area Power Systems" which is available in ResearchGate.

1) put I=0 then select a P to make the system oscillating

2) Then little by little increase I to make the system damped

3) make a disturbance and select the D so as to adjust a min sensitivity for the system but always put a small value sometimes without D it works better

It is simple and practical and works

if it is a linear system you can find state equations by using linmod command after find transfer function. After finding TF by using sisotool u can find PID values

You can use Ziegler-Nichols tuning method, this mean is that you need to find control parameter of the system and step function is applied to system on this parameter.

Dear Moheiddine,

Very interesting methodes. I totally agree.

Dear Roger,

nice to know. Thank you.

Regards.

Mohieddine

1. if it is a single input single ouput, u can by using siso tool in matlab u can find kp,ki and kd values

2. if it is MIMO if u have differential equation u can use genetic algorithm

3. then alsoit is difficult install matlab 2013a save response in ,mat formate

In matlab 2013a pid tunner is available so u can find

1. use the control toolbox of matab.

2. Select a performance Index such as IAE, ITAE etc and optimize it using PSO, ABC, and GSA algorithm.

3. See my publication on PSS design for power system.

I agree Hossein Shayeghi, if the the control time of interest is known or can be estimated, then the easy way is to simulate the system with the controller using numerical solution of system/controller differential equations and optimize the tuning using GA or so.

Try "good gain method" or "Skogestad's" method. They both work fine.

Dear Kumar

kindly check the attached article

Which power microgrid AC or DC is more efficient with renewable energy sources?

I agree with Himour Yassine: a very practical an simple way of tuning is: first: get the máximum dynamic increassing Kp til overshooot appears. You can keep the overshoot your system admits. Second, increase Ki til the constant error dissapears (or til the system becomes instable). Third, add Kd trying to improve tracking.

Dear Naveen

Use Successive Approximation method

The PI Controller gains are Kp and Kd. First increase the Kp value by the small vale and check the response. If all the loops are fine the response will increase. Then gradually increase (Trial and error method) Kp. One instant the response of the system will be near by the reference and some steady state error will be there. If you increase Kp further the response will start to oscillatory. Hence before starting of oscillatory response, start to increase the Ki value instead of Kp. So the response will settle with reference and the speed of response will Increase.

After try this please let me know.

Thanks for reading

With thanks and Regards

Rajin M.Linus

Thanks Arshad for the article!!!

One way to tune PID controllers without transfer function is using feature based models i.e. to look for I/O step response and approximate the parameters of the plant. Then there are also many tuning rules for such process. One common example is Skogestead's Half Rule (SHR), and then you can easily design a PID controller.

If you have very small time-constant, then you can estimate it with first order or second order system response and design the controller.

I recall AEG had a very practical and handy tool called

OPTIMATOR box which consisted of Capacitors and Resistors to

be connected across operational Amplifiers in situ to optimize control of dc drives

especially in process plants . This completely eliminated need for knowing the actual values of parameters (dc drives viewed as a plant) and plants could be commissioned very fast !!

So perhaps a similar approach with microcontollers could be tried.

There are three method, first the open loop with Cohen-Coon method, second Ziegler closed loop method and third internal model control method.

This is a great opportunity for you to consider fuzzy control. If you can you describe how the process works you could easily develop a fuzzy control system.

akademi.itu.edu.tr/caliskanf/DosyaGetir/61399/C2441ch3.pdf

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...