The ARX modeling of the robot-beam system is achieved with the use of measurements obtained from the robot’s force sensor under nor- mal production conditions without necessitating knowledge or determi- nation of the beam’s and/or the robot’s physical parameters. This type of stochastic modeling accounts also for external uncertainty sources included in the data (i.e. measurement noise, modeling error, etc.)  that may affect the actual robot-beam system dynamics leading thus to a more realistic representation than a physical model. The necessary data measurements may be obtained when the robot performs a typical ma- nipulation of the flexible beam without interrupting its normal opera- tion or stopping the production line.

The method’s control system design includes the determination of the PID-type controller gains via typical approaches, two of which are employed in this study, and it may be completed autonomously based on the ARX model obtained previously without using the actual robot-beam system. It is also important to note that this is an outer, software-wise, controller that does not intervene in the robot’s internal controller and it is activated once the robot has completed its main motion and stands in front of the final target – presently it is a slot where the beam should be inserted – allowing thus any speed and trajectory of the robot’s end- effector until that point.

The method’s synthetic environment may be optionally used for fur- ther assessment and fine-tuning of the developed control system perfor- mance under realistic production conditions without interrupting the robot from its industrial activity. Yet, for this part of the method a fur- ther measurement of the vibration acceleration at the free-end of the manipulated beam is needed. This may be achieved with the use of a typical accelerometer that is placed at the free-end of the beam for a limited period of time of some seconds during a single experiment with the actual robot-beam system. The synthetic environment allows also for further testing of the developed control system using various exter- nal disturbances that may affect its performance under normal operating conditions as well as different inputs and trajectories to the  robot.

The method’s performance is experimentally assessed through the vibration control of a flexible metallic beam that is rapidly inserted into a slot by an industrial robot. Apart from the specific manipulation for which the control system has been designed to deal with, its effec- tiveness is also investigated under other, unknown, operating conditions including: (i) significant industrial noise that affects the robot’s force sensor measurements, (ii) different robot trajectories, (iii) various dis- turbance scenarios to the beam and (iv) additional mass on the beam, without re-design or fine-tuning of the control system parameters.

It is noted that an early version of the method and some prelimi- nary results have been presented in [16]. This study includes the formal presentation of the method’s final form where the synthetic environ- ment is disengaged from the controller design and it may be optionally used, as well as the thorough experimental assessment of the method’s performance based on numerous comparisons and different operating conditions.

The rest of the article is organized as follows: The problem state- ment and the general concept of the method is presented in Section 2. The ARX-based vibration control method is presented in Section 3. The experimental assessment of the vibration control method and its sensi- tivity to unknown operating conditions are presented in Sections 4 and 5, respectively. A general discussion on the method as well as future plans are presented in Section 6 and the conclusions of the study are finally summarized in Section 7.

2. Problem statement and general concept of the    method

The manipulation of flexible objects is a common task in the indus- trial production of various sectors such as aerospace, automotive, shoe leather, garment and others [17], as well as it constitutes a challenging industrial automation problem. The flexible objects may be categorized to flexible sheets and linear flexible objects, the latter being character- ized by significantly greater length than their other dimensions, and they may be handled by a robot in various phases of an industrial pro- duction, from raw material until final product. The focus of the present study is on linear flexible beams for which the fast suppression of the vibration at their free-end is critical for various peg-in-hole type actions [18,19] that often constitute pre-stages of major assembly tasks. More specifically, the investigated problem of this study is the rapid  vertical