INDEPENDENT HARMONIC CONTROL FOR STRUCTURAL ENGINEERING

In a previous paper [Baratta and Corbi, 1999] one has defined a procedure allowing to identify a closed-ioop control algorithm with feedback based on the whole record of the response time-history rather than on instantaneous response parameters. The control force results from control of each harmonic component of the forcing function, simply integrated over the frequency domain. Every harmonic is controlled, independently of each other, by a classical linear control whose coefficients are calibrated in way to make the relevant response component a minimum compatibly with the control effort one wants to apply at the corresponding frequency. The distribution of this control intensity over the frequency range remains a arbitrary choice; such a choice however lends itself to be effectively assisted by intuition, much more than similar choices in other procedures (e.g.: the coefficients of the quadratic norms in the J-index optimization). The result is that every harmonic remains controlled by a different couple of optimal coefficients (corresponding to the proportional and to the derivative terms in the linear control law), and the overall control force for an arbitrary disturbance, after Fourier inverse transformation, is produced by feedback integration over the whole response time-history.

The procedure, tested with reference to simple and composed harmonic excitations incoming a s.d.o.f. structural system, has proved a good agreement of the numerical results with the theoretical treatment; furthermore it has shown that the main limit of such an approach consists of referring the dynamic equilibrium solution to a particular solution, that, neglecting the initial conditions, may introduce some unstable components in the oscillation. In the paper the effects induced in the controlled structural system response by the adoption of the proposed procedure are deepened and an improved strategy is presented, able to overcome the detrimental transient effects determined by the original algorithm. The final adopted control law is shown to achieve an improved time response, both in the transient and in the steady-state field, in comparison to a control strategy based on classical linear control minimizing the response norm conditioned by a bounded control.