By An-chyau Huang
This ebook introduces an unified functionality approximation method of the keep watch over of doubtful robotic manipulators containing common uncertainties. it really works at no cost area monitoring keep an eye on in addition to compliant movement keep watch over. it truly is acceptable to the inflexible robotic and the versatile joint robotic. regardless of actuator dynamics, the unified strategy continues to be possible. a majority of these good points make the publication stick out from different latest guides.
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Additional info for Adaptive Control of Robot Manipulators: A Unified Regressor-free Approach
The pair (ap, bp) is controllable. The problem is to design a control u and an update law so that all signals in the closed loop plant are bounded and the system output xp tracks the output xm of the reference model xɺ m = a m xm + bm r (2) asymptotically, where am and bm are known constants with a m < 0, and r is a bounded reference signal. If plant parameters ap and bp are available, the model reference control (MRC) rule can be designed as 46 Chapter 2 Preliminaries u = ax p + br (3) am − a p bm and b = are perfect gains for transforming dynamics in bp bp (1) into (2).
In addition, we can only conclude convergence of Vɺ , not the states. In this book, we would like to use the other form of Barbalat’s lemma to prove closed loop stability. If we can prove that a time function e is bounded and square integrable, and its time derivative is also bounded, then e is going to converge to zero asymptotically. It can be restated as: if e ∈ L∞ ∩ L2 and eɺ ∈ L∞ , then e → 0 as t → ∞ . 9 Sliding Control A practical control system should be designed to ensure system stability and performance to be invariant under perturbations from internal parameter variation, unmodeled dynamics excitation and external disturbances.
An identity matrix is a diagonal matrix with a11 = ⋯ = a nn = 1. A matrix A ∈ℜ n × n is nonsingular if ∃B ∈ℜ n × n such that AB = BA = I where I is an n × n identity matrix. If B exists, then it is known as the inverse of A and is denoted by A −1 . The inverse operation has the following properties: ( A −1 ) −1 = A (2a) ( A T ) −1 = ( A −1 )T (2b) (α A) −1 = 1 α A −1 ∀α ∈ℜ, α ≠ 0 ( AB) −1 = B −1A −1 ∀B ∈ℜ n × n with valid inverse (2c) (2d) A matrix A ∈ℜ n × n is said to be positive semi-definite (denoted by A ≥ 0 ) if x Ax ≥ 0 ∀x ∈ℜ n .
Adaptive Control of Robot Manipulators: A Unified Regressor-free Approach by An-chyau Huang