Variable Structure Adaptive Pole Placement Control for Suppression of Chaos in the Lorenz System
Adaptive Pole Placement Control, Variable Structure Systems, Lorenz System
There are two main methods 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 control, presenting a design methodology for the controller and adaptation law quite flexible, besides not involving plant zero-pole cancellations. The combination of the conventional adaptive methods, that use integral adaptive laws, with variable structure systems (VSC) based in switching laws, allows to aggregate fast transient and robustness to disturbances and parametric uncertainties. In this work is proposed, based on the variable structure adaptive pole placement control (VS-APPC) theory, a new control system able to control the chaos phenomenon in Lorenz system, using only the measured plant’s output and input variables in design. The parameters of system are considered unknown and is considered the disturbance presence in input system. It is shown 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 input plant.