Designing effective feedback controllers for non-minimum phase (NMP) systems can be challenging. Applying Iterative Learning Control (ILC) to NMP systems is particularly problematic. ILC aims for zero tracking error, solving an unstable inverse problem. Some literature incorporates stable inverse theory, implying one no longer asks for zero tracking error. Other ILC literature characterizes the problem, showing that ILC of NMP systems can appear to converge, but to a disappointing non-zero error level. ILC must be digital to use previous run data to improve the tracking error in the current run. There are two kinds of NMP digital systems, ones having intrinsic NMP zeros as images of continuous time NMP zeros, and NMP sampling zeros introduced by discretization. Previous work by the authors and co-workers developed ILC design methods to handle NMP sampling zeros, producing zero tracking error at addressed sample times by two methods: (1) One can simply start asking for zero error after the second or third time step, like using a generalized hold for the first addressed time step only (2) Or double the sample rate, ask for zero error at the original rate, making two zero order holds per addressed time step, and then deleting a few initial time steps if needed. This paper extends the use of these methods to NMP systems having intrinsic NMP zeros. By modifying ILC laws to perform pole-zero cancellation inside the unit circle, we observe that all of the rules for sampling zeros are effective for intrinsic zeros. Hence, one can now achieve convergence to zero tracking error at addressed time steps in ILC of NMP systems with a well behaved control action.
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