Control effort weighting in feedforward adaptive control systems

Abstract

Active control of noise and vibration in large dimensional complex systems is generally accomplished with adaptive feedforward control algorithms based on the steepest descent optimization approach. This paper examines the effects of incorporating control effort weighting into the cost function that is minimized by an adaptive control algorithm. When the plant matrix is rank-deficient, the least-squares solution to which the control algorithm converges is nonunique. In such situations, the control signals can drift with no change in performance. Small amounts of uniform control effort weighting can enforce a unique solution at the expense of decreased performance. A nonuniform form of control effort weighting is introduced that yields a unique solution without a performance penalty. With ill-conditioned systems, small amounts of effort weighting can provide significant reductions in the control signals with only a very small increase in residual error. A form of effort weighting is introduced for ill-conditioned systems based on the results for the rank-deficient case. Stability and robustness issues are examined for each form of weighting. It is shown that the nonuniform forms of control effort weighting can significantly diminish the trade-off between performance and robustness in the presence of plant model error.