Fixed Structure Feedforward Controller Design Exploiting Iterative Trials: Application to a Wafer Stage and a Desktop Printer

Abstract

In this paper, the feedforward controller design problem for high-precision electromechanical servo systems that execute finite time tasks is addressed. The presented procedure combines the selection of the fixed structure of the feedforward controller and the optimization of the controller parameters by iterative trials. A linear parametrization of the feedforward controller in a two-degree-of-freedom control architecture is chosen, which results in a feedforward controller that is applicable to a class of motion profiles as well as in a convex optimization problem, with the objective function being a quadratic function of the tracking error. Optimization by iterative trials avoids the need for detailed knowledge of the plant, achieves the controller parameter values that are optimal with respect to the actual plant, and allows for the adaptation to possible variations that occur in the plant dynamics. Experimental results on a high-precision wafer stage and a desktop printer illustrate the procedure.

Using iterative learning control with basis functions to compensate medium deformation in a wide-format inkjet printer

“…In the present paper, Fðh j Þ is chosen linearly in h j , such that e z jþ1 is linear in h j . Consequently, the performance criterion (7) is quadratic in h jþ1 and hence an analytic solution to (8) exists [5,34]. The structure of Fðh j Þ is part of the controller design and presented in Section 5.…”

“…Norm-optimal ILC is an important class of ILC algorithms, e.g., [1,21,15,2,19], where f jþ1 is determined from the solution of an optimization problem. Norm-optimal ILC with basis functions [4,5,34,33] is an extension of the norm-optimal ILC framework, where the feed forward is generated using a set of basis functions. The optimization criterion for the present paper defined as follows.…”

“…Although ILC is known to achieve very good tracking performance, the learned command signal is optimal for a specific task only [5], extrapolation to other tasks can lead to significant performance degradation [34,18].…”

“…In [33,34,23], basis functions in ILC are introduced. In [23], the tracking errors are projected onto a basis in order to only learn the repetitive part of the tracking error.…”

“…In [23], the tracking errors are projected onto a basis in order to only learn the repetitive part of the tracking error. In [34], the ILC command signal is parameterized using basis functions, in order to achieve extrapolation capabilities. The difference between these two approaches is projecting either the measured output onto a basis, or, construct the ILC command signal from a basis; both approaches can be encompassed in the framework presented in [33].…”