By Naira Hovakimyan
This publication provides a entire review of the lately built L1 adaptive keep watch over concept, together with targeted proofs of the most effects. the foremost characteristic of the L1 adaptive keep an eye on idea is the decoupling of edition from robustness. The architectures of L1 adaptive regulate conception have assured brief functionality and robustness within the presence of quickly model, with out implementing chronic excitation, using gain-scheduling, or resorting to high-gain feedback.
The ebook covers specific proofs of the most effects and likewise provides the flight attempt effects that experience used this thought and includes effects now not but released in technical journals and convention proceedings.
the cloth is equipped into six chapters and concludes with an appendix that summarizes the mathematical effects used to help the proofs. software program is out there on a supplementary net page.
Audience: L1 Adaptive keep an eye on Theory is meant for graduate scholars; researchers; and aerospace, mechanical, chemical, business, and electric engineers attracted to pursuing new instructions in examine and constructing know-how at diminished charges.
Contents: Foreword; Preface; bankruptcy 1: creation; bankruptcy 2: kingdom suggestions within the Presence of Matched Uncertainties; bankruptcy three: nation suggestions within the Presence of unrivaled Uncertainties; bankruptcy four: Output suggestions; bankruptcy five: L1 Adaptive Controller for Time-Varying Reference structures; bankruptcy 6: purposes, Conclusions, and Open difficulties; Appendix A: structures conception; Appendix B: Projection Operator for edition legislation; Appendix C: simple proof on Linear Matrix Inequalities; Bibliography
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Additional resources for L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation (Advances in Design and Control)
2t) without any retuning of the controller. Next, consider the following design: = 400 , C2 (s) = 3ωc2 s + ωc3 . (s + ωc )3 ✐ ✐ ✐ ✐ ✐ ✐ ✐ 30 L1book 2010/7/22 page 30 ✐ Chapter 2. 5: λ1 and λ2 with respect to ωc . 6: Performance of L1 adaptive controller with C1 (s) = inputs. 5(b) shows λ2 = G2 (s) L1 L = H (s)(1 − C2 (s)) L1 L as a function of ωc . Notice that for ωc > 40, we have λ2 < 1. 71. 8(b) for constant reference inputs r = 25, 100, 400, which are again scaled accordingly. 7 The example above illustrates that high-order filters C(s) may give the opportunity to use relatively small adaptive gains.
13) will be modified in two ways. 15) ˆ − θ . 13), is where x(t) ˜ x(t) ˆ − x(t) and θ˜ (t) θ(t) thus replaced by > 0. 16) ˆ are the Laplace transforms of u(t) and θˆ (t), respectively, and C(s) is where u(s) and θ(s) a bounded-input bounded-output (BIBO) stable strictly proper transfer function subject to C(0) = 1 with zero initialization for its state-space realization. 5. 17) C(s) = s + ωc however, similar results can be obtained using more complex filters. The loop transfer function of this system (with negative feedback) is L2 (s) = C(s) .
4 − 1. 31) where x(t) ∈ Rn is the system state vector (measured); u(t) ∈ R is the control input; y(t) ∈ R is the regulated output; b, c ∈ Rn are known constant vectors; Am is a known Hurwitz n × n matrix specifying the desired closed-loop dynamics; ω ∈ R is an unknown constant with known sign; θ (t) ∈ Rn is a vector of time-varying unknown parameters; and σ (t) ∈ R models input disturbances. 2. 1 (Uniform boundedness of unknown parameters) Let θ (t) ∈ where σ (t). 2 (Uniform boundedness of the rate of variation of parameters) Let θ (t) and σ (t) be continuously differentiable with uniformly bounded derivatives: ˙ θ(t) ≤ dθ < ∞ , |σ˙ (t)| ≤ dσ < ∞ , ∀ t ≥ 0.