Aliasing of Resonance Phenomena in Sampled-Data Feedback Control Design: Hazards, Modeling, and a Solution

Abstract

Abstract-High-performance control design for electromechanical sampled-data systems with aliased plant dynamics is investigated. Though from a theoretical viewpoint the aliasing phenomenon is automatically handled by direct sampled-data control, such an approach cannot be used in conjunction with models derived through system identification. From a practical viewpoint, aliasing is often considered as an undesirable phenomenon and a typical remedy is the increase of the sampling frequency. However, the sampling frequency is upper bounded due to physical and economical constraints and aliasing may be inevitable. Control design for plants with aliased dynamics has not received explicit attention in the literature and it is not clear how to handle this situation. In this paper, it is shown that aliased resonance phenomena can effectively be suppressed in sampled-data feedback control design without the need for increasing the sampling frequency. Furthermore, it is shown experimentally on an industrial wafer stage that ignoring aliasing during control design can have a disastrous effect on closed-loop performance. Additionally, a novel, practically feasible procedure for identification of (possibly aliased) resonance phenomena based on multirate system theory is proposed.

Suppressing intersample behavior in Iterative Learning Control

“…Multirate ILC deals with both these phenomena appropriately by balancing the error at the low sampling frequency and the intersample behavior. The presented approach also handles the case of aliased disturbances [2] and aliased poles [10].…”

“…In the zero-order-hold case, a low F , e.g., 2 ≤ F ≤ 5 typically suffices due to the low-pass character of the interpolator [2], [10]. In the next section, the multirate setup in Figure 2 is analyzed in detail.…”

“…In all cases, the considered exogenous variables are trial invariant, except for the command signal 47th IEEE CDC, Cancun, Mexico, Dec. [9][10][11]2008 WeA15.6 In addition, the parameter r e = 1 in J MR and r e = 4 in J DT , see Section IV-C. To compare the presented multirate ILC approach with standard discrete time ILC, both multirate and discrete time ILC are applied, which is indicated by the subscripts DT and MR, respectively. For instance, the resulting error at sampling frequency f l after 10 iterations of the discrete time ILC algorithm is denoted by e l DT<10> .…”

“…• aliased poles [10], [1]; and • aliased disturbances [2]. These aspects should be appropriately dealt with in sampleddata control design, including ILC for sampled-data systems.…”