Experimentally supported 2D systems based iterative learning control law design for error convergence and performance

Pass profile exponential and asymptotic stability of nonlinear repetitive processes

“…In the control and systems theory developed for linear repetitive processes, the stability along the pass property has formed the basis for control law design and experimental verification (Rogers et al, 2007;Hladowski et al, 2010;Paszke et al, 2013Paszke et al, , 2016, but there are examples for which a weaker property is all that can be achieved or is required. Stability along the pass demands that a bounded initial pass profile produces a bounded sequence of pass profiles for all possible values of the pass length and is based on linear operator theory in a Banach space setting.…”

“…In several particular cases, the abstract model based stability conditions have been converted into tests that can be completed using standard methods, such as Nyquist or Bode plots. This progress has, in turn, led to the application of repetitive process control theory to the design of iterative learning control laws that have been experimentally validated (Hladowski et al, 2010). This validation has used a gantry robot executing a pick and place operation that replicates a common use for such robots in the industrial setting, with further results in, e.g., (Paszke et al, 2013).…”

KYP lemma based stability and control law design for differential linear repetitive processes with applications

“…Examples include classes of iterative learning control schemes [2,3] and iterative algorithms for solving nonlinear dynamic optimal control problems based on the maximum principle [4]. Iterative learning control algorithms designed using a repetitive process setting have been experimentally tested [5,6]. Also, there has been recent work on the use of this setting for the analysis of OL-Nash games with a gas pipeline application [7].…”

Iterative learning control laws with full dynamics

“…This fact allows the application of the stability and control law design algorithms for discrete linear repetitive processes in ILC design, see, e.g., [6].…”

“…Given the finite pass length, repetitive processes are a more natural setting for ILC design and such designs have also seen experimental benchmarking [6], [7], [8]. These results were based on the use of a static state feedback and pass profile feed forward controller with the extensive application of Linear Matrix Inequalities (LMIs) as a numerical to calculate the required controller parameters.…”