On Multi-Input Multi-Output Repetitive Control Design Methods

Repetitive control (RC) can address the common spacecraft jitter problem for fine pointing equipment resulting from small imbalance in reaction wheels or control momentum gyros (CMG). This problem requires multi-input, multi-output (MIMO) RC design methods. Previous papers by the authors developed a rather comprehensive stability theory for MIMO repetitive control, and suggest design methods whose performance is studied here. One approach stays on the MIMO level and minimizes a Frobenius norm summed over frequencies from zero to Nyquist. And it produces a matrix compensator composed of finite impose response (FIR) filters. The second approach reduces the problem to a set of SISO design problems, one for each input-output pair. The latter approach allows one to make use of experience gained in SISO designs. Both approaches are seen here to be able to create RC designs with fast monotonic decay of the tracking error. Choice of the FIR filter order and the choice of the number of non-causal gains, although critical in some SISO low order designs, does not appear to be an important issue in MIMO designs using reasonably large order.