David,

I may suggest three reasons for the popularity of SM control despite the chattering (which can be a proper pain in many problems):

-Sanjay

There are many advantages of using SMC

i) The system under sliding mode is independent of matched uncertainty 

ii) We do not require a precise value of the system parameters, rather we need to know their bounds only

iii)  During sliding mode, the system behaviour is ideally independent of system's original dynamics

iv) It effectively reduces the order of the system under sliding motion

v) Chattering is definitely  an issue in SMC but there are convenient ways like (Continuous approximation, Assymototic SMC or HOSMC etc) to reduce chattering considerably.

Moreover I partially agree with this statement "simple high-gain feedback control provides better results than latest results on adaptive sliding mode control (super-twisting, high order SMC" because effectiveness of high-gain feedback control typically depends on the modelling accuracy and many a times it results poor transient and also demands more control energy. And for a MIMO system in presence of internal loop ensuring stability using high-gain feedback control is very difficult. 

For reference you may see this book

The mirage of high Gain is evedently with the peaking phenomenon . thas why SMC is better that high Gain control

Many people here tell you that SMC is all you need and they are right, and can show you many examples.

Other people will tell you that PID is all you need and is even simpler and they are also right, and can also show you many examples.

As there is no General Solution for the General Problem, if a solution fits your problem, then all is good.

I happen to work with difficult systems, where a PID is not sufficiently good and any switching may only excite oscillatory modes.

However, as the uncertainty did not allow me to count on fixed controllers either, I had to use adaptive controllers, a methodology that I ended calling Simple Adaptive Control (SAC). It may remind what is called here “high-gain output feedback”, only I don’t believe in high gain either (it may work with your model and in simulations, yet in real world it may excite oscillations and nonlinearities that you would not even know they were there, if not for the high gain.)

So, we (my Colleagues and myself) had to work for more than a couple of decades, yet I think we finally ended with a simple adaptive procedure, which does not use high gains and does not need chattering.

(If you write Simple Adaptive Control (SAC) on Google, you may find quite a bit.)

Thank you very much for your answers!

I agree that there is no general solution for general problems. However, I said I preferred high-gain feedback control because of a few numerical examples. 

With your answers, I realize why SMC has many advantages over other control methods. Also, other recent control algorithms (eg. SAC) intrigue me and I would really like to study them in detail.

Thanks again for your valuable answers!

I'd say that there are two main reasons (some other are dependent of the following in my opinion):

a) People like to use sliding mode control (SMC) as a result of being a powerful robust control design. Even in the presence of chattering, you can also design your controller with bounds for this chattering, roughly speaking you limit the switching nature of the states of the system. In the field of adaptive control this is more or less straightforward.

b) It is very useful to analyze non-linear systems and to endow them of stability and performance. Constructing Lyapunov functions in terms of the SMC is very useful because you can select the gains of , say, an additional PID controller which combined with the SMC regime does the work, Even fuzzy logic ontrollers (FLC) can be designed and studied with this (which is a hit because a FLCs deficiency is lacking of theory which ensure performance and stability. Fuzzy logic is a multivalued logic which is misunderstood and despised most of the times.

For both cases, an additional (and implied) advantage of SMC is that you can use it for SISO (single input-single output)  or MIMO (multiple input-multiple output) systems.

I'd recommend the book written by Slotine and Li (Applied Nonlinear Control) to start with for case (a) and the book written by Driankov, Hellendorn et al (An Introduction to Fuzzy Control) for (b),

I will still add that in practical control system design, there is no fit-all solution to control problems. Generally, the word "best solution" can not be generalized because a complex problem may require an elegant PID controller while a comparably simple problem may require an intelligent controller. That is why in spite of the advances in intelligent controller techniques, the industries are still awashed with PID controlled systems. Sliding mode control has chattering problem. Other types of control strategies also have their inherent problems. Mastering how to circumvent the chattering problem during the modelling and analysis is the key.

To reduce chatter use 'sat'  function instead of 'sign'  function

I did a lot of work in sliding mode, so I can tell you when linear controller is better and when SMC is better.

• Speed : Linear is faster in (∞,a), SMC is faster in (a,0) and ensure finite time convergence.
• you can use high gain in linear and in SMC, it's just a time rescaling.
• if you have \dot z = u + phi (phi lipshitz), linear PI can not stabilise it; but supertwisting can do.
• the previous point remain in PID, Researcher are developping the so called Higher Order supertwisting to solve it (including me with coworkers)
• In the case of perturbation with unknown bound linear and non linear have the same advantage and inconvénient.

with differenciation,

• exact linear deifferenciator did not exist, in SMC you can do this. also yo can get fixed time exact differenciation.

Regards

Sliding mode control (SMC)  is one type of robust control. This means that that allows you to deal with uncertainties in the plant's model. The latter can be nonlinear so, you are not restricted to work in the linear world. SMC is very useful to design SMC-based controllers for complex nonlinear plants as serial, parallel, mobile robots as well as other hybrid systems. SMC permits to design with stability and performance easier than with other control schemes (considering as I said above, possible uncertainties in the model). On the other hand, it can be "mixed" with fuzzy logic control (FLC)  to create a SM-FLC which can improve the alone-SMC characteristics. SMC makes easier (and endows!) a way to analyze theoretically the FLC stability and performance. Yes, chattering is a disadvantage but the bounds of such chatttering can also be minimized. Best regards.

The more important issue in sliding mode control is determining a switching function, that produces a desirable response, from which a suitable sliding mode controller can be defined. What is left is to drive its value to zero. Rapid discontinuous switching does that fantastically well, leading to chattering, but it isn't the only option.

I don't see chattering as an issue nowadays for a significant number of applications. For one, you might find that using a sigmoidal approximation such as $tanh(.)$ or $s/(s+ \epsilon)$ satisfies your performance specifications. Secondly, if this is not sufficient, you may use the 'supertwisting' sliding mode control algorithm or one of a similar structure. Thirdly, if the above options seem artificial, then the method of 'higher-order sliding mode' control might meet your needs.

Control of friction might appear to demand discontinuous switching, but that does not detract from the fact that good performance can still result from using approximations (There's a paper by Prof. Stanislaw H. Zak related to this).

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

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