Generalized Holds, Ripple Attenuation, and Tracking Additional Outputs in Learning Control

Abstract

Iterative discrete-time learning control can be very effective at improving the tracking performance of control systems. Three different limitations or potential dife culties of discrete-time learning control are addressed. 1 ) The number of output variables for which zero tracking error can be achieved is limited by the number of input variables. 2 ) Every variable for which zero tracking error is sought must be a measured variable. 3 ) Because the control action is digital, the intersample behavior may have undesirable error from ripple. The e rst issue is addressed by two approaches, either by seeking zero error for different output variables at alternating time steps or by skipping time steps. The latter corresponds to using a generalized hold device. To address the second issue, it isshown howthesetechniques can becombined with an observerwhen onewishesto haveimproved tracking ofnot only measured outputs but also unmeasured output variables. To improve ripple, one can ask for good tracking of theoutput,andinadditiongoodtrackingofitsderivativeorderivatives,anditisshownhowmethodsdevelopedhere can accomplish this. These generalizations are made for three different effective learning control laws: integral control-based learning with zero phase e ltering, which is particularly simple; a contraction mapping learning control, which is particularly robust; and a phase cancellation learning control, which is particularly effective at producing small e nal error levels in experiments.