Bounded Error Tracking Control for Contouring Systems with End Effector Measurements

Abstract

Many industrial applications of machining require a bounded tracking error during transient and steady processes. Traditional control architectures in machining are unable to explicitly bound tracking errors, and therefore conservative operation is required to ensure satisfactory performance. In this paper, we propose a model-predictive-based approach to guarantee bounded error tracking for the family of systems with available end effector position measurements. The state and input constraints and the bounded error requirements are satisfied by a model predictive controller (MPC) that enforces the system and reference states to remain in a polyhedral robust control invariant (RCI) set. We propose an algorithm for calculating this RCI set in a finite number of computation steps and give the formulation of the MPC. The superiority of the proposed control approach over a conventional tracking controller is demonstrated via simulation of a laboratory machine.

Modelling and Contouring Error Bounded Control of a Biaxial Industrial Gantry Machine

“…An tracking error bounded control method for a single axis machine described as a LTI system with disturbance has been proposed in [9]. We now extend this work to allow bounds to be imposed on contouring error in biaxial systems.…”

“…The parameters of the proposed model are identified for a commercial industrial laser machine. To guarantee that the contour error is not violated during the entire process, we extend the single-axis bounded tracking error control methods in [9] to the two-axes scenario. The structure of the problem is exploited to partially decouple the controllers between axes and reduce the computational load in calculating the control outputs.…”

Robust Funnel MPC for nonlinear systems with relative degree one

“…The calculation of these robust control invariant sets, however, requires a lot of computational effort and, more important, in general it cannot be ensured that the algorithm proposed in [13] terminates in finite time. In [35] the aforementioned approach was extended to systems with external disturbances. A close relative of funnel MPC is barrier-function-based MPC, cf.…”

Novel Gaussian Acceleration Profile for Smooth Jerk-Bounded Trajectories

“…A machine motion dynamics is defined by its position, velocity, acceleration, and jerk profiles [4]- [7]. It is well known that high jerk values produce high amplitude vibrations in a machine component.…”