Fractional order adaptive control for hydraulic differential cylinders

Hydraulic servo valve controlled differential cylinders are non-linear, strongly coupled multivariable electromechanical tools applicable for driving e.g. manipulators. Traditional PID control of such equipment have to cope with the problem of instabilities due to the friction forces between the piston and the cylinder, and the uncertainties and variation of its hydrodynamic parameters that in general makes it unrealistic to develop an accurate model for them. Brocker and Lemmen proposed two different control approaches for such systems, based on the disturbance rejection, and on the partial flatness principles, respectively. In each case it is necessary to measure the external disturbance force and its time-derivative as well as to know the exact model of the hydraulic cylinder. Later on Tar et al. proposed an alternative adaptive approach that does not require to measure the disturbance force and to know the exact parameters of the cylinder. This method rejected to use time-derivatives because of the presence of friction, and, as a consequence it resulted in a very hectic transient phase of learning. In this paper an alternative approach is presented that combines this approach with the use of calculated time-derivatives that are "rejected" by adaptively varying the order of the derivations applied. In this way the harsh initial transients can be evaded. The operation of the method is presented by simulations.