| Volterra feedback synthesis (VFS) is an algorithm that uses a finite consecutive number of the Volterra kernels of the plant and the desired closed-loop input-output map to incorporate higher-order information about the plant into a systematic non-linear controller design and realization. A striking feature of this method is that it permits the specification of a nonlinear desired closed-loop behavior. The control design takes place in the frequency domain and is realized as an interconnected set of linear systems. By exploiting the inherent recursive structures present in VFS controllers, the number of linear systems required for realization is significantly reduced, and the linear systems comprising the controller kernels can be organized in a parallel fashion that readily lends itself to a multiprocessor implementation. A collection of general control models for hysteresis obtained from an extensive literature search are presented in a tutorial. Of particular note are the Chua-Stromsmoe, Bouc, Preisach and certain hysteron models, which are shown to possess inverses or inverse-like systems. A number of these models can be incorporated into linear analytic plant descriptions, a class of systems to which VFS regulator and servomechanism designs are readily applied. Particular attention is given to the Bouc model, which is used in the field of structural control to model hysteretic behavior present in magnetorheological dampers and certain base isolation systems. A study is made of the stability properties of the Bouc model. VFS control designs are presented for a single-degree of freedom base-isolated structure with an active hydraulic control system, and a three-degree of freedom structure with semi-active magnetorheological damping. |
