Evaluar la eficiencia de un controlador robusto de orden no entero usando la función de costo del criterio integral del valor absoluto del error.

Abstract

The objetive was to compare the efficiency of a non-integer order controller with respect to the efficiency of a classical robust PID control. In order that evaluations of these control algorithms are under the same conditions, they were implemented on an experimental plant model. Also, control algorithms were designed using the Ziegler-Nichols method for the whole control, the method of numerical approximations that used the Euler series in the time and the method based in the state space for the development of the non-integer controller, cementing in convolution two causal signals to generate states and non-integer control equations. The research focused on obtaining non-integer control algorithm and the results for the numerical approximation method introduced an error in steady state to completely invalidate the approximation. However, at the moment of implementing the algorithm developed based on the state spaces, it was observed that the efficiency, with a cost function generates based on the absolute integral of error, is increased. Consequently, the procedure for developing a non-integer controller based on state space is similar to that of the whole controller, except that the concept of integral and fractal derivative of Riemman and Louville; the disadvantage introduced in a convolution of causal signals is that a large amount of storage space is required in the buffer to store the value of the previous spaces, another no-integer control algorithm can be developed using a third numerical approximation method to eliminate the steady state error.