Abstract
In this paper, a novel repetitive control scheme is presented and discussed, based on the so-called B-spline filters. These dynamic filters are able to generate a B-spline trajectory if they are fed with the sequence of control points defining the curve. Therefore, they are ideal tools for generating online reference signals with the prescribed level of smoothness for driving dynamic systems, possibly together with a feedforward compensator. In particular, a continuous zero phase error tracking controller (ZPETC) can be used for tracking control of nonminimum phase systems but because of its open-loop nature it cannot guarantee the robustness with respect to modeling errors and exogenous disturbances. For this reason, ZPETC and trajectory generator have been embedded in a repetitive control scheme that allows to nullify interpolation errors even in nonideal conditions, provided that the desired reference trajectory and the disturbances are periodic. This paper is based on the results presented in the conference paper [L. Biagiotti, F. Califano, and C. Melchiorri, “Repetitive control of non-minimum phase systems along b-spline trajectories,” in Proc. IEEE 55th Conf. Decis. Control , 2016, pp. 5496–5501.], where asymptotic stability of the overall control scheme has been proved mathematically, but extends such results with an experimental validation based on a nonminimum phase system. Different models of the same physical system have been identified and used in the implementation of this model-based control scheme, allowing a real evaluation of the relationship between control system performance and model accuracy.
Highlights
Q UITE often, in industrial applications, the given tasks present a cyclic or repetitive nature
The basis functions are forward filtered using the dynamics of the plant, the name Filtered Basis Function (FBF) method, and the control points defining the B-spline curve are computed by solving an optimization problem which minimizes the tracking error with respect to the desired trajectory
It can be applied to all those systems, like servo-motors or robotic manipulators, that equipped with an off-the-shelf controller, only admit an external reference signal
Summary
Q UITE often, in industrial applications, the given tasks present a cyclic or repetitive nature. The integration of the CZPETC into the RC scheme, represents an important step forward with respect to the results reported in previous papers [6], [13] since, at least in nominal conditions, it allows to achieve the asymptotic stability of the RC scheme for any value of the time period T between via-points to be interpolated, even in case of non-minimum phase plants This means that the stability of the control scheme does not depend anymore on the duration of the reference trajectory, like in [6], [13].
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