GENERALIZED HOLDS, RIPPLE ATTENUATION, AND TRACKING ADDITIONAL OUTPUTS IN LEARNING CONTROL

Iterative discrete-time learning control can be very effective at impr oving the tracking performance of control systems, Three different lim itations or potential difficulties of discrete-time learning control a re addressed. 1) The number of output variables for which zero trackin g 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 mea sured variable. 3) Because the control action is digital, the intersam ple behavior may have undesirable error from ripple. The first issue i s addressed by two approaches, either by seeking zero error for differ ent output variables at alternating time steps or by skipping time ste ps, The latter corresponds to using a generalized hold device, To addr ess the second issue, it is shown how these techniques can be combined with an observer when one wishes to have improved tracking of not onl y measured outputs but also unmeasured output variables. To improve ri pple, one can ask for good tracking of the output, and in addition goo d tracking of its derivative or derivatives, and it is shown how metho ds developed here can accomplish this, These generalizations are made for three different effective learning control laws: integral control- based learning with zero phase filtering, which is particularly simple ; a contraction mapping learning control, which Is particularly robust ; and a phase cancellation learning control, which is particularly eff ective at producing small final error levels in experiments.