Adaptive Least-Mean Square Feed-Forward Control With Actuator Saturation by Direct Minimization

The least-mean squares (LMS) adaptive feedforward algorithm is used widely for vibration and noise cancellation. If reference signals become large enough to saturate that actuators, the filter coefficients in such algorithms can diverge. The leaky LMS method limits the controller effort by augmenting the objective function by a weighted control effort, and is known to attain good performance and avoid growth of filter coefficients for well-chosen weights. We propose an algorithm that seeks to directly minimize the mean-square cost in the presence of saturation. We derive the true stochastic gradient of the cost for systems with saturation with respect to the filter coefficients and obtain an adaptation rule very close to that of the filtered-x algorithm, but in the proposed algorithm, the reference filter is a time-varying modification of the secondary channel. In simulations of an active vibration isolation system with actuator limits subject to random ground vibration, the leaky LMS algorithm attains its best performance with actuation weights small enough to allow significant actuator saturation but large enough to prevent divergence. The proposed algorithm attains performance better that attained by the leaky LMS algorithm, and does not require the selection of weights.