Controle de sistemas nebulosos Takagi-Sugeno baseado em observador de entradas desconhecidas

Abstract

Understanding the dynamics of systems is essential in engineering design. In real contexts, control systems present nonlinear dynamics, which results in an increase in complexity in design, both for stability analysis and for the development of monitoring and control techniques. Another important characteristic to be considered in control applications is the fact that part of the state vector of the system may be inaccessible to measurement, due to technical or economic limitations, which compromises the design of the state feedback controller. These characteristics of real applications motivate the use of effective techniques to properly describe the nonlinear dynamics of systems, as well as to estimate the unmeasured states. Takagi-Sugeno fuzzy systems stand out as a powerful technique in the design of nonlinear systems, because they allow the representation of the nonlinear dynamics of the plant through a convex combination of local linear models. In turn, state observers are devices based on the system dynamics and represent an appropriate alternative to solve the problem of estimating unmeasured states, which enables the design of observer based state feedback controllers. In this context, this dissertation presents the design of observer based control with unknown inputs for discrete Takagi–Sugeno systems. For this purpose, the nonlinear system is represented by a Takagi–Sugeno fuzzy system, and an unknown input observer is used to estimate the unmeasured states of the system. In this way, the state feedback control is designed through a parallel distributed compensation controller, which uses the states estimated by the observer to obtain the control law for the closed loop system. In nonlinear systems, such designs become challenging, since the nonlinearities may be associated with the unmeasured states of the system. To deal with this complexity, the Mean Value Theorem is used to treat the mismatch of the membership functions and to deal with this uncertainty in the design. Finally, the proposed methodology is applied to nonlinear models of real systems, specifically, a twin rotor MIMO system and a four coupled tank system. The obtained results demonstrate the effectiveness of the technique for the estimation of unmeasured states of the system, as well as for observer based control applied to stability and reference tracking.