In some literature of sliding mode control, the control law is proposed as follows,
u=u_eq +u1
Where u_eq is the equivalent control, as they named it, and u1 is the discontinuous control term.
Is u_eq, mentioned above, the equivalent control as defined in the Utkin's sense? (see for example "Sliding Modes in Control and Optimization"). Also, how is computed especially when considering the uncertainty and disturbances in the system model?
u_eq is the result of low pass filter applied to the discontinuous control.
the equivalent control part can be defined from the system model when s=s'=0
I think,following paper is helpfull for your question.
https://www.researchgate.net/publication/270507240_Experimental_Evaluation_of_Novel_High_Order_Sliding_Mode_Controllers_for_High_Performance_Direct_Drive_Systems
Article Experimental Evaluation of Novel High Order Sliding Mode Con...
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