Using Kalman filter to attenuate noise in learning and repetitive control can easily degrade performance

Abstract

Repetitive control (RC) and iterative learning control (ILC) can eliminate deterministic tracking errors of a control system in executing a periodic command or a repeating tracking command. In addition they can cancel errors resulting from a periodic disturbance (RC) or a repeated disturbance (ILC). When there is substantial plant and measurement noise it is natural to consider employing a Kalman filter to improve the error signals used by the RC/ILC law, and the performance is analyzed here. Introducing a Kalman filter to RC or ILC can substantially decrease the steady state error due to noise. However, there are several competing issues. First, when the model used in the filter design is inaccurate, deterministic error is introduced in the response that can be more important than the decrease in error variance from random noise. Second, deterministic steady state errors are also introduced when there are unmodeled repeating external disturbances. Use of a Kalman filter actually requires you to know the time history of the disturbance, not just the period. Hence, one should carefully analyze the situation before deciding to use a Kalman filter. And one should examine model free alternatives to the use of a Kalman filter, such as reducing the learning gain. All of these comments also apply when using a Kalman filter running in time steps in the ILC problem. In third, under appropriate conditions, both ILC and RC are capable of reducing the error level in hardware below the error level in ones model of the system. This very desirable property is lost when one introduces Kalman filtering in the time domain for RC and ILC.