Dear Biswajit,

I do not think that adaptive SOSM will add improvement in terms of chattering. But you may pay attention to you sign function definition (sometimes it is a source of problems).

PS. We have successfully used SOSM for wind and marine turbine applications (you can have a look on our papers in researchgate).

Regards,

Mohamed

Thanks for your attention, Mohamed. I have used the normal sign function in the SOSMC. I have figured that in my case, there is a significant amount of white noise being added at the DAQ and this might as well be a reason behind the high amount of chattering at the control output. So I am thinking of mitigating this noise first. What do you say? I have gone through your paper where you have used the error as the sliding surface. In my case I have used S=c*e1+e1_dot as the sliding surface.

Biswajit,

There could be many reasons for the chattering, and it is difficult to claim that either will be better without knowing the specific plant parameters and controller settings.

Why not simulate and see for yourself ?

-Sanjay

shalom,

We have also used Fuzzy Logic to reduce chattering in a speed regulation of DC Motor with Permanent Magnet by using a first order SMC.

Sanjoy, 

Thanks for your reply. I have simulated as well as practically implemented the SOSMC on the coupled tank system using LabVIEW. Actually I am doing this to compare an intelligent controller called BELBIC with SOSMC in terms of disturbance rejection, set-point changes and parameter uncertainties. With SOSMC I found that the real time results showed a considerable amount of chattering when compared with simulation results and I figured that there is a significant amount of white noise being added at the DAQ interface and so I am looking towards filtering this noise first rather than modifying the SOSMC. How does that sound? Your expert advice is highly solicited.

Biswajit

Hello,

The main drawback for (actual) adaptive sliding mode controller is the neighborhood of convergence. you can refer to the work of Levant Shtessel Plestan for fist order Fridman , Plestan for second order and my work fo arbitrary order. we can not yet ensure the practical convergence, we only ensure the onvergence fo some neighborhood of zero.

In your case, The best way is to use a Robust non linear form of PID contrroller. It's not yet formulate clearly, you can see it in one paper called , continuous twisting , continuous terminal sliding mode for relative degree 2, Higher order supertwisting.

you can refer to the work of mexican team (Moreno, Fridman ...) or our work under review (online version on research page).

Regards.

Biswajit,

I still don't have enough data to exactly tell you why the chattering is there. But since you have a good simulation in place, I can suggest a bypass route !

Assuming that the chattering is due to noise in some part of the system, simply introduce a noise source (deliberately !) at the same point in the simulation that you suspect to be the source in the practical realisation, until the degree of chattering you observe in simulation is same as that you observe in practice.

Next, tune the control in simulation until the chattering reduces, or is entirely eliminated.

Thereafter, make exactly the same modifications in the experimental controller, and test.

If you get an improvement identical to the simulation, your initial guess regarding the position and strength of noise was correct. If not, you may have to redo the simulation after locating the noise source at a new point.

Hope that helps.

-Sanjay 

Sanjoy,

Your idea is a nice one but I am at a dichotomy at this point. Will it be better to first suppress the sensor noise with the help of signal conditioning elements and then tune the controller or to tune the controller in presence of noise ??

Biswajit

Biswajit,

To get you out of this, won't you love a controller that gives chatter-free control regardless of the source and strength of the noise ? I Think you get the answer !!

-Sanjay

We have used almost all versions including terminal sliding mode control. However, I felt the nonlinear PID based on second order sliding mode vector based gives better results in real-time. You can refer the following paper (few other papers are also available but in different domain) for more information

http://www.sciencedirect.com/science/article/pii/S0094114X09001530

Hi Biswajit,

whenver you are working with real systems take care that, in practical implementation of SMC the chattering effect cannot be completely removed. The reasons of that are: the presence of unmodeled dynamics in your plant, and, of course, the fact that discrete SMC always introduce a chattering whose amplitude is related with the step-size of your algorithm. This is what people call "boundary layer" around the sliding surface, that is true also for HOSM. With refence with SMC with adaptive gains, I'm agree with Mohamed it will not improve your system's perfomancin in terms of chattering, maybe just a bit, nothing more! ;)

However there are some trick that can be done for alleviating the chattering effect:

1- Reduce the sampling time Ts of your DAQ+Control system as you can

2-Minimimize the discontinuous control effort by adding to the your SMC control rule, e.g. uSM(t) a further contribute continuous contibute uc that consist in the filtered version of your discontuous control action, i.e. what people call equivalent control so that your control becames u=uSM+uc, alternatively add in place of the equivalent control some other continuous control.

3- Replace your discontinuous sign function with sigmoidal approximation, e.g. sign(x)=x/(|x|+e) with e close to zero, or by using saturation function. So that, you lose the robusteness properties of your system while remooving the undesired chattering

4- Use "oversized" HOSM for example if your plant has relative degree R, you can simply use an integral control, where the argument of your integral action is an R+1 - SMC algorithm. In this way your control rule will be continuous.

Note, in order to understand the reason of chattering it is helpful to know which is the relative degree between of your control and the output of your plant! So that you will be able to distinguish between chattering (that depends from Ts) and self-sustained oscillation in your control systems (that depends on your plant's transfer function) 

As an example if you use the superstisting algorithm and your plant consist in a simple Tank+Actuator, self-sustained oscillations cannot be avoided since the system has relative degree greater than one. 

However in the literature there several solution to reduce these oscillations. The price you have to pay is that you will reduce the performances of your control system while preserving the robustness. As an example If you are working with the STW SMC take a look to these works.

[1] Oscillation shaping in uncertain linear plants with nonlinear PI control: analysis

and experimental results.

[2] Observer-Based Air Excess Ratio Control of a PEM Fuel Cell System via High-Order Sliding Mode

Hope to be helpfull,

Alex.

If you use the adaptive SMC proposed in my paper below, you can eliminated the chattering completely while robustness and performance are preserved. Method is simple and effective. And there is no need to design boundary layer and to use saturation function. The control input (Eq. 35 in the paper) is a continuous adaptive SMC and un-modeled dynamics in your plant is estimated based on the behaviour of sliding function. You can implement this controller without any knowledge of bound of uncertainties and with basic information of the plant model.

Adaptive sliding mode control with uncertainty estimator for robot manipulators, M Zeinali, and L Notash, Mechanism and Machine Theory 45 (1), 80-90