Generalized Iterative Learning Control Using Successive Projection: Algorithm, Convergence, and Experimental Verification

Abstract

Iterative learning control (ILC) is a high performance control design method for systems working in a repetitive manner. ILC has traditionally focused on tracking a reference defined at all points over a finite time interval; recent developments have begun to exploit the design freedom unlocked by tracking only a finite number of distinct time instants driven by the needs of e.g. robotic pick-and-place tasks. This paper proposes a generalized ILC paradigm which extends and unifies the scope of existing design frameworks by amalgamating previous task descriptions and embedding system constraints on the input and output. A novel solution is then derived using a successive projection method which provides well defined convergence properties. The proposed design framework is illustrated by applying it to a spatial reference tracking problem with experimental results on a gantry robot testing platform demonstrating its effectiveness.

Generalized iterative learning control with mixed system constraints: A gantry robot based verification

“…Due to the continuous time system problem setup, the signals u k and e s k are defined in infinite dimensional Hilbert spaces and input signal update (30) of Step One cannot be directly implemented as that in [48] using matrix computation with finite elements. Instead of that, this step 305 is suggested to be implemented using the state feedback and feedforward action with differential equations, which is illustrated in the next proposition.…”

“…The authors' recent work in [48] considered a similar problem for linear discrete time systems, where all the signals (e.g. input and output) are finite dimensional.…”

“…continuous linear time 140 invariant systems, continuous linear time varying systems, linear differential systems and linear deferential delay systems. Therefore, it is a substantial generalization to [48] and so can be used on much broader application classes. The Hilbert space theoretical deviation also has substan-145 tial difference.…”

“…Remark 2. Note that the work in [48] focused on discrete time systems, whose signals were all finite dimensional.…”

Constrained Iterative Learning Control for Linear Time-Varying Systems With Experimental Validation on a High-Speed Rack Feeder

“…Point-to-point ILC relaxes the requirement to one where the reference trajectory is specified only at specified sample instants. This form of ILC has been developed, based on linear time-invariant dynamics, to the stage of experimental validation, see, e.g., [18]- [20]. Terminal ILC is a particular case of point-to-point where only the starting and final values of the trajectory are specified, for a recent application with experimental support see [21].…”