Control design via TAM and H∞ approaches: a flexible beam case study

The target approximation method (TAM) and H_∞ control theory are used to design robust vibration control of a flexible beam. The beam dynamics are approximated by a few lower order vibration modes of the beam. The remaining modes are treated as a modeling error. In the closed-loop system the uncontrolled and controlled modes interact through the control and observation spillovers, which cause a degraded system performance. The TAM solves the problem in the time domain by designing gains and actuator and sensor locations such that the closed-loop system imitates a target which has no spillovers. The H_∞ approach tackles the problem in the frequency domain by designing a controller which attenuates a class of disturbing signals, including the disturbance generated by the uncontrolled modes. The TAM always gives a lower order controller than the H_∞ approach. The H_∞ approach might not be a good solution for the spillover effect minimization problem when the controller can only have a low-order estimator. The H_∞ gains are much greater than the TAM gains. This implies that the H _∞ controller consumes more power than the TAM controller