1. Historically twisting have been designed to substitute a discontinuous controller with Lipschitz continuous one, applying discontinous second order sliding mode controller through integrator. Such anti chattering strategy keeps the finite-time theoretically exact convergence to the sliding output for the systems with relative degree one affected by Lipschitz perturbaitons(see Levant A. IJC, 1993 https://www.tau.ac.il/~levant/slorder93.pdf).

2. The only advantage of the twisting controller is that, if this algorithm is applied to the systems with relative degree two, it ensures theoretically exact finite-time convergence of the sliding output and its derivative to zero in finite-time.

3. From the viewpoint of chattering the twisting controller is the worst one because his gains are at least twice bigger, than the upper bound of uncertainties.

Moreover, the amplitude of chattering produced by twisting controller is bigger than the amplitude of chattering produced by relay controller with a linear sliding surface (see table 1 in attached file, numbers in yellow)

Dear Pyare,

My suggestion is to better use the supertwisting algorithm, which only needs information about the sliding surface S. We have use it with high-order sliding mode successful for wind and marine turbine control (enclosed two illustrative papers). Hope you will find these helpful.

Regards,

Mohamed

Dear Prof.

Many thanks for quick response and novel papers. However, for a system with relative degree two can we apply supertwisting? In my opinion, Twisting is option.

However, I am not concerned  with \dot{s} availability. I am looking for those drawbacks which affects convergence speed, steady state precision, and presence of high frequency oscillations after sliding mode is established.

Best Regards

Pyare

Dear Viswanath,

Thanks for reply. The paper is useful. However, can u please tell me what are the differences between super twisting and twisting controllers output for a system with inherent  relative degree  one with respect to selected output sliding surface. Certainly, twisting controller demands derivative of sliding surface.

Best Regards,

P M TIWARI

Thanks for Reply.

Fully convinced with the theoretical facts mentioned. As mentioned in reply "Since STA does not depend on the derivative of s, it has an advantage over the "twisting" algorithm."                                                                                                                                        Certainly STA has advantage but how the \dot s  use may cause disadvantage in twisting controller output. I am concerned with response characteristics.

Best Regards,

p m tiwari

Dear Pyare,

The clear drawback of twisting is its discontinwity.

@Mohamed Benbouzid  : Supertwisting is not usefull at all as it's working only for system of relative degree 1.

You can take a look of the work of Fridmann about Continuos twisting, or also the so called Hiher order supertwisting. My team (Chitour, Harmouche, Laghrouche) and Moreno's Team are working to generalize Supertwisting for arbitrary Order.

Online version of our submitted work is available:

https://www.researchgate.net/publication/280590093_Higher_order_supertwisting_algorithm_for_perturbed_chains_of_integrators_of_arbitrary_order

Regards

Article Higher order supertwisting algorithm for perturbed chains of...

Dear Mohamed,

Thank you for the reply. My further request  to take my another doubt

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Relative degree depends on what we select the sliding output function. A system having relative one should be designed with supertwisting control or one should prefer for u_dot (first derivative of control input)  design with twisting control (i.e. increasing relative degree and then design twisting control)

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With Regards,

Pyare

Pyare Mohan Tiwari This an interesting you asked. I have been asking this question. Other 2-slidng mode controllers shold have advantages over STC as well. I am exploring that already.

I am a new researcher in sliding mode control. My request will be please put some light on both twisting and super twisting controller . why the name like that and what is their particular behavior. I believe we should dig the basics to answer all questions.

Mohamed Harmouche a published paper used STC (Super-Twisting for a second-order system). I am still confused as to why it was accepted because I have seen several publications and Textbooks by Yuri Shtessel where it is stated that STC is used for a system of relative degree one. However, it seems STC can also be used for arbitrary order systems.

I have used applied Twisting and Super-Twisting to the same system for comparison. I got similar results. The paper is under review presently.

1. Historically twisting have been designed to substitute a discontinuous controller with Lipschitz continuous one, applying discontinous second order sliding mode controller through integrator. Such anti chattering strategy keeps the finite-time theoretically exact convergence to the sliding output for the systems with relative degree one affected by Lipschitz perturbaitons(see Levant A. IJC, 1993 https://www.tau.ac.il/~levant/slorder93.pdf).

2. The only advantage of the twisting controller is that, if this algorithm is applied to the systems with relative degree two, it ensures theoretically exact finite-time convergence of the sliding output and its derivative to zero in finite-time.

3. From the viewpoint of chattering the twisting controller is the worst one because his gains are at least twice bigger, than the upper bound of uncertainties.

Moreover, the amplitude of chattering produced by twisting controller is bigger than the amplitude of chattering produced by relay controller with a linear sliding surface (see table 1 in attached file, numbers in yellow)

Dear Pyare Mohan Tiwari: Hope you're fine.

The main drawback of twisting is its discontinuity. You can also have a look on these research papers to understand more.

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

Article Review of sliding mode based control techniques for control ...

Article Conventional and high order sliding mode control