Deterministic robust control design for an iron core linear drive including second-order electrical dynamics

Abstract

This work proposes a deterministic robust controller to improve tracking performance for a linear motor, taking into account the electrical dynamics imposed by a commercial current controller. The design is split in two parts by means of the backstepping technique, in which the first part corresponds to a typical deterministic robust controller, neglecting the electrical dynamics. In the second part, a second-order electrical dynamics is considered using a particular state transformation. There, the proposed control law is composed of a term to compensate the known part of the model and a robust control term to impose a bound on the effect of uncertainties on tracking error. Stability and boundedness results for the complete controller are given. To this effect, a general result on boundedness and stability of nonlinear systems with conditionally bounded state variables is derived first. Finally, experimental results for the complete controller show an improvement on tracking error of up to 31.7% when compared with the results from the typical controller that neglects the electrical dynamics.

Modified integral action with time-varying forgetting function for tracking control

“…As for the practical relevance, the type of dynamics in equation (3) is frequently found in positioning systems, for instance as a model subsystem in a linear direct drive 7,12 or in a ball-screw drive. 13 In such cases, e 1 would represent the difference between measured and reference position (or position error) while e 2 would stand for the velocity error.…”

“…For instance, in the work by Yao and Xu 14 an adaptive robust controller is set in order to make as small as possible a similar variable regarding just a part of the system. Another example, which will be considered later in more detail, is the deterministic robust control in the work by Villegas et al 7 where a controller is set for a similar purpose. Obviously, the controller in each case is designed taking the whole system in consideration, but the aim of the whole design is to reach a bound on the magnitude of such a variable.…”

“…One particular form for K ( x ) is shown in the following section, where the proposed augmented state has been implemented in the controller from the work by Villegas et al 7 In fact, it can be proven that the conclusions about stability obtained in that work remain unchanged after introducing the proposed modification to the integral action. For completeness, the updated result, controller and the most important aspects of the system are displayed next, beginning with the following recollection of the assumptions about the system given in Villegas et al 7…”

“…As a means to see the performance of the proposed integrator in an experimental setup, this modification is introduced in the deterministic robust controller from the work by Villegas et al 7 The controller is tested on the experimental setup described in the study by Villegas et al 8 for a series of reference trajectories, where it is shown the improvement attained in tracking error for a particular implementation of the forgetting function.…”

Force ripple compensation of the directly-driven linear motors via iterative tuning feed-forward controller

“…One is driven by the rotatory motor through a ball screw and the other is driven directly by the linear motor. 2,3 Since the linear-motor-driving axis eliminates the flexible coupling and thus increases the bandwidth greatly, it is promising for developing the higher-performance equipments. 4 However, for the same reason, any disturbance from the motor will affect the motion precision.…”