Performance enhancing adaptive friction compensation for uncertain systems

Abstract

A regulator design technique for uncertain motor drive systems severely affected by nonlinear friction is presented in this paper. The regulator includes an internal adaptive loop to compensate for the nonlinear friction torque. The adaptive loop is based on a simple friction model, and is adapted with respect to the measure of performance. A new, simple search algorithm for the adaptation is proposed. The friction compensation allows the design of a lower gain robust linear controller for prescribed performance specifications. The closed loop is analyzed with respect to stability and performance. A quantitative comparison is made between robust control with and without friction compensation. Experimental results are presented.

Back Matter

“…Note that if the matrix P satisfies the algebraic Riccati equation (9.3-11), then P satisfies (A. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. This completes the proof.…”

Large bursts do not cause instability

“…Let b = j + (I + P T )j; c = jj, and fix > 0 and with 0 < < 1: By Lemma 1 and the assumption that (C; P; m) is not totally stable for DC(; ) traffic, given a > 0 a solution S a = (E a ; Q a ; q a ; T a ; I a ) to (1)- (7) exists such that f a defined by f a (t) = jQ a (t)j violates either (8) or (9). Examination of the constraints (1), (2), (5), and (6) satisfied by S a shows that f a satisfies (9), so it must violate (8), meaning f a (t a + f a (t a )) > f a (t a ) and f(ta) > a for some ta 0: By shifting the functions of S a to the left if necessary, it can be assumed without loss of generality that ta = 0 for all a: Hence, S a = (E a ; Q a ; q a ; T a ; I a ) satisfies (1)- (7) and the additional constraints jQ a ( jq a j)j > jq a j and jq a j a: Next, a space-time rescaling is used.…”

A novel robust tracking controller based on hierarchical perturbation compensation

“…As a solution to the friction problem, there have been three kinds of approaches: the first method is the sophisticated friction modeling and compensation based on the identified model [l], the second method is the adaptive technique where a few parameters of the simple friction model are updated on-line [2], and the third method is to use a perturbation observer involved in two degrees of frdom(TD0F) controllers, e.g., disturbance observers in [3,4]. Unlike the first and the second method, the third is an indirect compensation technique without a direct friction model.…”