New approach using flatness-based control in high speed positioning: Experimental results

Abstract

This paper discusses flatness-based control approaches to reduce oscillations on the load side of mechanical motion systems. Choosing a suitable trajectory is one essential step in implementing a flatness-based control. Existing approaches use slow polynomials or mathematically complex Gevrey-functions to achieve the necessary differentiability. Our approach combines the oscillation reduction of flatness-based control and the dynamic and simplicity of higher order Scurve trajectories generated by a convolution based algorithm. The performance and robustness of the presented methods is experimentally validated with a linear flexible motion system.978-1-4799-7800-7/15/$31.00 ©2015 IEEE

Trajectory Optimization for the Handling of Elastically Coupled Objects via Reinforcement Learning and Flatness-Based Control

“…While no general method for finding a flat output of a nonlinear dynamic system exists, in the case of linear controllable systems the controllable canonical form allows determining the flat output directly [6]. After a flat output is found, one can use (1) to calculate an input signal u(t) that leads to the desired output trajectory y(t) for the system.…”

“…The implementation for high-speed positioning is e.g. presented in [1] for a linear flexible motion system using trapezoidal motion profiles. The concept of adaptive input shaping from [14] allows a more robust parameterization than the feedforward control by using frequency parameters instead of specific physical parameters, which can be difficult to obtain.…”

Flatness-Based Feedforward Control of a Stacker Crane with Online Trajectory Generation

“…In [8] convolution is applied repeatedly to increase the differentiability of a trajectory, starting with a rectangular velocity profile. Convolution requires knowledge of the entire trajectory and repeated use entails a significant computational cost, which hinders once again an online implementation.…”

“…The flatness-based approach has also proven effective in reducing load side vibrations of any number of different flexible motion systems (see e.g. [4], [7], [8]). But of these only [4] includes simultaneous motion of two axis similar to the motion of platform and LHD.…”

“…Many different types of trajectories have been explored in the literature, such as polynomial functions ( [7]) and Gevrey functions ([2], [5]). Newer approaches include the use of classical s-curve trajectories, whose differentiability is increased through various means ( [4], [6], [8]). This will be expanded upon in section III.…”