On Actuator Weighting in Adaptive Control Systems

Active control of noise and vibration in large dimensional complex systems is often accomplished with adaptive feedforward control algorithms based on the steepest descent optimization approach. This paper examines the effects of incorporating actuator weighting terms into the cost function which is minimized by the 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 actuator signals can drift with no change in performance. Small amounts of uniform actuator weighting can enforce a unique solution at the expense of decreased performance. To overcome this, a non-uniform form of actuator weighting is introduced which yields a unique solution without a performance penalty. Furthermore, with ill-conditioned systems, small amounts of actuator weighting can provide significant reductions in actuator signals with only a very small increase in residual error. We introduce a form of non-uniform actuator weighting for ill-conditioned systems based on the results of the rank-deficient case. Stability and robustness issues are examined for each form of actuator weighting. It is shown that the non-uniform forms of actuator weighting can significantly diminish the tradeoff between performance and robustness in the presence of plant model error.