Model Predictive Control of Vibration in a Two Flexible Link Manipulator — Part I

Abstract

A model predictive controller (MPC) in the form of dynamic matrix control (DMC) is implemented for attenuating in-plane vibrations of a two flexible link planar manipulator. The rotation of the joints and inertia effect of both the joints and links induce vibration. Piezoelectric actuators, mounted in a bimorph configuration, provide the control actions to reduce vibrations. Implementation of this control scheme is shown to provide appreciable attenuation of vibration over the uncontrolled case, increasing the damping ratio for the first and second link by a factor of 5.99 and 3.40, respectively. DMC control is further shown to reduce the mean amplitude of dominant vibrations from the uncontrolled case by 90.0% and 87.4%, respectively, for the first and second links. Furthermore, for the two link setup, this control is shown to outperform the more conventional ProportionalIntegral-Derivative (PID) control and is sufficiently robust to handle an unknown payload.

Nonlinear Control of Multibody Flexible Mechanisms: A Model-Free Approach

“…A direct comparison between (20) and (21) shows that the equivalence between the two controllers happens when k p = Jk 3 , k d = Jk 1 , k n = 3Jk 2 . Such equivalence shows that the proposed strategy can be used for both torque-controlled systems and speed-controlled systems, retaining the same level of performance in both cases.…”

“…In this sense, model-based control strategies can be very effective, as testified in several papers. In particular, predictive control have proven to be very effective in terms of performance [20][21][22], and have shown sufficient robustness to be a proper choice for flexible multibody mechanisms. It should also be considered that control practitioners often rely on simple models as the basis for model-based controls [1], such as modal systems with a limited number of state variable.…”

Active predictive vibration suppression algorithm for structural stability and tracking control of nonlinear multivariable continuum‐mechanics mobile systems

“…According to the discussed overview, the following notes can be cited as the major motivations of this research: It was discussed that the majority of investigations in control of flexible systems are limited to addressing the problem of reducing undesired vibrations. This is also the case when application of optimal control theories is concerned 23‐26 The issue of addressing the control problem in an optimal sense is addressed in several works.…”