Reduced-Order Iterative Learning Control and a Design Strategy for Optimal Performance Tradeoffs

Abstract

Abstract-When iterative learning control (ILC) is applied to improve a system's tracking performance, the trial-invariant reference input is typically known or contained in a prescribed set of signals. To account for this knowledge, we propose a novel ILC structure that only responds to a given set of trial-invariant inputs. The controllers are called reduced-order ILCs as their order is less than the discrete-time trial length.Exploiting all knowledge available on the input signals is instrumental in facing the fundamental performance limitations in ILC: an ILC is bound to amplify trial-varying inputs and reducing this trial-varying performance degradation invokes a slower learning transient. We present a novel optimal ILC design strategy that allows for a quantitative and systematic analysis of this trade-off. The merit of reduced-order ILCs in view of this tradeoff is demonstrated by numerical results.

Design and control of a hydraulic composite actuator for vibration simulation

“…15 ILC is also a low-complexity and robust controller for identification, model reduction, and controller reduction of higher order systems, which can meet real-time control requirement of motion control systems. 12 Therefore, ILC has provided a feasible solution for the control issues of vibration simulation.…”

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

“…In (7), W e 1 0, and W f ; W Df # 0 are user-defined weighting matrices to specify performance and robustness objectives [28], namely, robustness with respect to model uncertainty (W f ) and convergence speed and sensitivity to trial varying disturbances (W Df ). The tracking error at the paper for trial j þ 1, i.e., e z jþ1 , is used in cost function (7), and is given by:…”

Optimal behaviour prediction using a primitive-based data-driven model-free iterative learning control approach

“…In addition, the 100 centres of the copies of the output primitives used for approximation are known. Following the recommendations given in [30][31][32], a reduction of the dimension of the learned reference input primitives is achieved. For each reference input corresponding to a SISO channel which has a dimension of 400, only 50 parameters are learned by employing the RBFs approximation.…”