Controle adaptativo por posicionamento de polos e estrutura variável para supressão do caos no sistema de Lorenz

Abstract

Two main methods highlight for the design of adaptive controllers: the model reference adaptive control (MRAC) and the adaptive pole placement control (APPC). In MRAC, a reference model is chosen to generate a trajectory, which must be followed by the output of the plant to be controlled. This type of project may involve cancellation of the plant zeros, not applicable to non-minimum phase plants. APPC, in turn, is considered the most general type of adaptive control, presenting a design methodology for the controller and adaptation law quite flexible, besides not involving plant zero-pole cancellations. The combination of the APPC structure and the VSC switched laws allows aggregation of transient speed and robustness to disturbances and parametric variations. In this context, based on a class of pole placement control schemes (PPC), the variable structure adaptive pole placement control (VS-APPC) arises. Here, such as in APPC, the control law is generated as in the case with known parameters (transfer function coefficients), replacing them by their estimates. The estimation process identifies the adaptive method used, so that APPC uses integral laws while the VS-APPC makes use of switching laws. In this work is proposed the application of VS-APPC for the control of the Lorenz system, using only the measured plant output and input variables in design. The parameters of system are considered unknown and is considered the disturbance presence in system input. It is observed that in closed-loop system, the output tracks the reference trajectory and the state vector converges to the equilibrium state, presenting good transient behavior and robustness to the parametrics uncertainties as also in presence of disturbance in plant input.