Signal Transformation Approach to Tracking Control With Arbitrary References

Abstract

Abstract-In this paper, we introduce a signal transformation (ST) methodology for tracking control of a large class of arbitrary references. The method can improve tracking performance of ordinary one-degree-of-freedom (1-DoF) feedback control structure, while keeping robustness against unmodeled dynamics and limiting the projected measurement noise by ensuring a low closed-loop bandwidth. Using singular perturbation theory, sufficient conditions for stability and convergence of the tracking error are derived. Effectiveness of the proposed method is demonstrated by simulations. It is shown how ST method can provide a better control performance compared to ordinary 2-DoF feedback control systems having similar projected noise power, and maintain robustness against uncertainties, disturbances, and unmodeled dynamics.

Improvement of Transient Response in Signal Transformation Approach by Proper Compensator Initialization

“…Although the connection between ISM and the conventional STA was studied for triangular references and zero initial conditions in [12] and [14], the effect of nonzero initial conditions in the compensator was not addressed. In addition, in contrast to ISM, which only deals with affine references, ISTA and STA are also applicable to a more general class of references (Section V and [23]). The following theorem reveals the connection between ISTA and ISM for triangular references.…”

“…In addition to triangular references, the STA method can also be developed to handle arbitrarily shaped reference signals [23]. In this section, we demonstrate how a proper initialization of compensator can considerably improve the transient performance of STA system for a nonaffine reference.…”

“…Contrary to repetitive controllers [29], repetition is not necessary in STA and ISTA systems, as shown by the example in [23], where the reference period is long and the steady state almost starts before the end of the first period. Compared with the slope of a triangular waveform having similar amplitude and period, the slope of the selected reference changes considerably (from 0.05 to 5.37 times the triangle's slope).…”

“…We also show that the proposed ISTA can equally improve the transient performance of a recently developed STA for reference signals with arbitrary shapes [23], where ISM is not applicable. Simulations and experiments are presented to investigate the robustness of the proposed method against disturbances and measurement noise.…”

“…1(b), the resulting system remains stable and approximates the slow dynamics of the twotime-scale system. More details on this condition were presented in [23], where a zero feedthrough term was used for the compensator. 5) The triangular reference signal has a sufficiently large fundamental period so that stability condition γ = λ max A < 1 is satisfied.…”