If there is, how do we smooth these sharp variations?
I mean how can we reduce the chattering?
You can use the modified filtered error in the derivation of the control strategy instead of the filtered error along with replacing the sgn function with sat or tanh.
The chattering can be reduced or even removed by a number of methods:
1. Accurate modeling of the process can yield in smaller value of discontinuous gain in first order sliding mode.
2. by using sat(.) instead of sign(.) in first order sliding mode
2. By using higher order sliding modes
3. using smooth higher order sling modes
4
A linear system is usually applied in a region around the crossover point to avoid chatter. I have had great success in numerical tests of an equivalent control over rate-of-change of acceleration. It is easy to apply this control as feedback and it doesn't succumb to chatter. It also performed better in my tests than ordinary sliding mode. This is I think the higher-order sliding mode that Ali mentioned.
Are you using higher-order sliding mode in any of your resaerch Ali?
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