Active disturbance rejection control for nonlinear systems : by Bao-Zhu Guo, Zhi-Liang Zhao

By Bao-Zhu Guo, Zhi-Liang Zhao

A concise, in-depth advent to energetic disturbance rejection keep an eye on thought for nonlinear platforms, with numerical simulations and obviously labored out equations

  • Provides the basic, theoretical starting place for functions of lively disturbance rejection control
  • Features numerical simulations and obviously labored out equations
  • Highlights the benefits of lively disturbance rejection keep an eye on, together with small overshooting, speedy convergence, and effort savings

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Additional resources for Active disturbance rejection control for nonlinear systems : an introduction

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83) . ⎪ ⎪ ⎪ ⎪ ⎪ x˙ n (t) = xn+1 (t) − kn [x1 (t)]nθ−(n−1) , ⎪ ⎪ ⎪ ⎩ x˙ n+1 (t) = −kn+1 [x1 (t)](n+1)θ−n . Proof. 83) is (θ − 1) degree homogeneous with weights {(i − n 1)θ − (i − 2)}n+1 i=1 . Let q = Πi=1 ((i − 1)θ − (i − 2)). Then ⎞ ⎛ 1 [x1 ] q ⎟ ⎜ 1 ⎟ ⎜ [x2 ] θq ⎟ ⎜ ⎟ ⎜ .. 84) y(x) = ⎜ ⎟ . 85) where P is the positive definite matrix solution to the Lyapunov equation K P + P K = −I(n+1)×(n+1) . Let S = {x ∈ Rn+1 : V (1, x) = 1}. 86) It is easy to verify that S is a compact set. Let θ = 1. 83) becomes x(t) ˙ = Kx(t), which is asymptotically stable and dV (1, x(t)) =− dt x(t) 2 < −a < 0, a > 0, ∀ x ∈ S.

In addition, if Ω = Rn then the Lyapunov function V (x) is radially unbounded. Proof. We only need to prove (ii). For the sake of simplicity and without loss of generality, we may assume that Ω = Rn . 87) is finite-time stable, it is asymptotically stable. 3, there exists a positive definite Lyapunov function V˜ : Rn → R such that LF V˜ is negative definite on Rn . 88) 1, s ∈ [2, +∞), and ⎧ ⎪ ⎨ V (x) = +∞ 0 ⎪ ⎩0, 1 μk+1 (α ◦ V˜ )(μr1 x1 , . . 89) x = 0. Apparently, V (x) is positive definite. For any λ > 0, x = 0, +∞ V (λr1 x1 , .

1) is convergent in the sense that, for any a > 0, ˙ =0 lim |z1R (t) − v(t)| = 0, lim |z2R (t) − v(t)| R→∞ R→∞ uniformly for t ∈ [a, ∞). Proof. 13). Let t = s/R.

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