Adaptive Repetitive Control With Two Nonsynchronized Sampling

Abstract

Repetitive controllers have been shown to be effective for tracking periodic reference commands with known period. For a reference with fixed period, its implementation can be done with time fixed sampling where an integer number of samples in each period can be required. With variable periodic signal tracking with real-time realization, the number of samples per period may be a noninteger with a fixed sample rate. This paper presents an adaptive repetitive control scheme for reducing tracking errors due to variable periodic reference signals with two nonsynchronized sampling. Aside from time sampling, a position pulse signal generated by optical encoder is used to produce another fixed sampling. This technique can accommodate the variable periodic signal and variable samples per period for synchronization can be achieved by the position sampling. Experimental studies of a twin linear motor control system which comes up with variable periodic references are given. The experimental results illustrate the validity of the proposed implementation method in that adaptive repetitive control with two nonsynchronized sampling can effectively eliminate steady-state errors within a few cycles that are caused by variable periodic references.

Laplace-type integral transform for time-varying periodic repetitive controller design

“…Referring to the design requirement of the repetitive control, assuming the closed-loop control system of G 0 1 + G 0 is stable without repetitive control. 20 The control parameters of K q (s) = K(s)e X q s ,…”

“…, and K b (s) = e X b s are introduced to improve the stability and performance of Figure 2 and v q , X q , and X b can be designed by Na et al 20 As shown in Figure 2, the repetitive controller can be given as…”

Modeling and stabilization of eccentric gravity machinery

“…Based on the design rule 8,9 of K q (s) and K b (s), the magnitude of the sensitivity function in Figure 13 can be reduced at the harmonic frequencies of the reference signal within the designed frequency range v n of K q (s).…”

“…Based on the analysis results of Yao and colleagues, 8,9 if the main harmonics of r and T l are all within the designed bandwidth, the steady-state tracking error will be attenuated significantly. Assume that the regeneration spectrum 8,9 satisfies K qŜ0 (jv)…”

“…For a controlled plant of G(s) and a pre-determined controller of C(s), an unity feedback system G p (s)=1 + G p (s) is internally stable where G p (s) = C(s)G(s). The repetitive controller of K q (s) and K b (s) can be designed by Yao and colleagues, 8,9 where…”