Question about ueq in the smc.m

[lienguang0624]

I repeated the implementation in function [u, s, ueq, usw] = smc(e,edot,xddot_d,f,b,lambda,kappa,eta, switch_fun) according to formulas (3.61) and (3.62). In my understanding, ueq is the first two items of the above fractions (3.61 and 3.62), and usw is the last two items of the fractions. But in the process of manual calculation, it was found that lambda.*edot in ueq did not appear in the fractions (3.61 and 3.62). Please help me.

[mateus-amarante]

In the code, I split the input into "equivalent" and "switch" parts.

• u_eq is the ideal input to drive the system on the sliding modes, i.e. s = s_dot = 0

We have that:

s_dot = xddot_d - xddot + lambda*(xdot_d - xdot)
0 = xddot_d - fx - bx*ueq + lambda*(xdot_d - xdot)
ueq = (lambda*(xdot_d - xdot) + xddot_d - fx) / bx

• u_sw is the input to drive the system towards the sliding mode, shaping s_dot when s != 0

[mateus-amarante]

In the paper, I recommend some books:

• QIAN, D.; YI, J. Hierarchical Sliding Mode Control for Under-actuated Cranes: Design,
  Analysis and Simulation. Berlin Heidelberg: Springer-Verlag, 2015.
  https://doi.org/10.1007/978-3-662-48417-3.

• SHTESSEL, Y. et al. Sliding Mode Control and Observation. 2013 edition ed. New York:
  Birkhäuser, 2013. https://doi.org/10.1007/978-0-8176-4893-0.

• UTKIN, V.; GULDNER, J.; SHI, J. Sliding Mode Control in Electro-Mechanical Systems. [s.l.]
  CRC Press, 2009. https://doi.org/10.1201/9781420065619.

[mateus-amarante]

@lienguang0624, how is going your study? I'm sorry I took more time to answer you last time. I think I've might have broken your pace. I just want to let you know that I'm still open to supporting you in understanding this work if you desire. Best regards.

[lienguang0624]

It's very kind of you. You've done me a lot of help. Due to the traditional Chinese festivals, my work has been suspended for a period of time. I will continue the unfinished work when life returns to normal. I am looking forward to our friendly communication.Wish you success in your work and good health. 获取 Outlook for iOS<https://aka.ms/o0ukef>

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