ESTABILIZACIÓN DEL CARRO PÉNDULO INVERTIDO APLICANDO CONTROL ÓPTIMO NO LINEAL VARIANTE EN TIEMPO (STABILIZATION OF A CART INVERTED PENDULUM APPLYING NONLINEAR TIME-VARYING OPTIMAL CONTROL)
Resumen
El control óptimo LQR es una opción adecuada para la obtención de las ganancias de control realimentado, sin embargo, en sistemas dinámicos no lineales su aplicación se ve limitada a una región local. En este trabajo se propone resolver el problema de control óptimo del tipo LQR, utilizando un sistema equivalente lineal en vez de llevar a cabo la linealización, esto permite extender la región donde el controlador LQR puede funcionar adecuadamente. Para probar el método propuesto, se realizan simulaciones donde se aplica el control LQR de los sistemas linealizado y equivalente lineal al sistema carro péndulo invertido. Los resultados muestran que el sistema equivalente lineal tiene un mejor índice de desempeño que el sistema linealizado.
Palabras Clave: carro péndulo invertido, control óptimo, linealización, LQR.
Abstract
Optimal control, based in LQR, is a suitable option for obtaining feedback control gains, however, in non-linear dynamic systems its application is limited to a local region. In this work, it is proposed to solve the optimal control problem (based in LQR) using a linear equivalent system. To evaluate the proposed method, the LQR control of the linearized and linear equivalent systems is applied in a simulation environment to a cart inverted pendulum system. The results show that the linear equivalent system has a better performance index than the linearized system.
Keywords: cart inverted pendulum, linearization, LQR, optimal control.
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