How to choose sliding variable for an interconnected non linear system?

11 June 2016 1 5K Report

If a system is expressed by several first order non linear differential equations and the relative degree is very high (say 8), and the control input appears in the eigth equation and the first state is the plant output. Then how one will choose the sliding variable for the design of simple Sliding Mode Controller?

Huiming Wang

you system model: x^(8) = u,

sliding surface: s=c1*x1 + c2*x2 + c3*x3 + c4 * x4 + c5*x5 + c6*x6 + c7*x7 + x8

control law: u = - ( c1*x2 + c2*x3 + c3*x4 + c4 * x5 + c5*x6 + c6*x7 + c7*x8 + ksign(s) )

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