Precise path tracking in Cartesian overhead cranes through an improved non-colocated Wave Based Control
Wave Based Control (WBC) has been proven to be very effective in combining position and oscillation control of underactuated flexible multibody systems [1]. This paper proposes an extension of the method aimed at ensuring accurate path tracking of a load suspended by a planar Cartesian crane, even in the presence of non ideal actuators and sensors. The basic configuration of WBC [1] uses the measured mechanical wave coming back from the flexible system to the actuator, the so called returning wave, to accomplish both position control and active swing damping. In Cartesian cranes, two independent controllers for the X and Y axis set the trolley position references, q T , to be the sum of two components (q denotes both the X and Y motion). The first component is set to half the load displacement reference, q L , and is the launch wave. The second component is the measured returning wave, denoted bq . The addition of this second component performs active vibration damping while moving the system the remaining second half of the target displacement. This achieves exact steady state final positioning in rest-to-rest motion. When WBC is instead employed in path tracking in the presence of delay or noise in sensor measurements, or of delay between the trolley reference and actual position, correct tracking of the spatial trajectory during transients is not always ensured. Indeed, the measured return wave will have inaccuracies in amplitude and in time delay (phase) with respect to the launch wave. To deal with this, two improvements of WBC are suggested in this paper. First, a new term, γ ( ) q s , is added to q T , leading to the following relation in the Laplace domain: 1 q ( ) q ( ) b ( ) γ ( ) 2 ref ref T L q q s s s s = + + (1) Second, a model based estimation of the return wave is computed using an Extended Kalman Filter. Such a state observer is based on an augmented dynamic model of the system, including a simplified model of the delay. The feedback and non-colocated correction γ ( ) C( ) ( ) q q s s s = ε is computed through the convolution between the contour error ( ) q s ε (i.e. the distance between the desired spatial contour to the actual position, regardless of the time required to reach such a position) and a linear regulator, C( ) s , which can be a PID regulator. In effect, an outer non-colocated loop is closed. Indeed, whenever the aim of the control is to ensure accurate load path tracking even in the presence of sensor disturbances or external excitations on the load, non-colocated actuator/sensor pairs can be effectively adopted to increase the external disturbance rejection. Besides being more suitable than tracking error in trajectory following tasks, the use of the contour error makes the controller get rid of the unavoidable delay introduced to perform swing control, which is due to the nature of the physical coupling between the trolley and the load. A numerical method suitable for the estimating ( ) q s ε in load swing control is also developed, by taking advantage of the general technique proposed in [3]. The reduced computational effort of the formulation proposed, ensures easy and effective real-time control. Finally, in order to decouple the return wave from the corrective term, γ ( ) q s , the computation of b ( ) q s is modified by removing the effect of γ ( ) q s as follows: ( ) ( ) ˆ b ( ) G( ) q G( ) γ ( ) a ( ) q L q q s s s s s = − + , with a ( ) q ( ) b ( ) q T q s s s = − (2) In Eq. (2) G( ) s is the wave transfer function, q̂ L is the output of the Kalman Filter and q T is the actual trolley position. Experimental results assessing the effectiveness of proposed method have been obtained through an Adept Quattro robot mimicking a Cartesian crane and driving a load suspended by a 1 meter cable. The non-colocated WBC has been implemented by closing an outer loop computing q T , and sending it to the robot inner position controller through using an Ethernet connection. The robot is also instrumented with two CCD cameras sensing the swing angles at a low sample rate, i.e. introducing delay in the loop. Some results are shown in Figure 1 with reference to three different paths: circular, 8-shaped and square. The plots in the first column show the path tracking in the case of no swing control, i.e. when only the native robot position controller is adopted in the inner loop. Considerable and persistent load oscillations prevent acceptable tracking of the suspended load. The second column shows the same tests performed using WBC [2]: effective swing damping is ensured, but the issues discussed above prevent exact tracking. Finally a great improvement is obtained with the noncolocated WBC here proposed: desired and actual load trajectories are much closer. No swing control WBC Non-colocated WBC Figure 1: Path tracking: experimental results. References [1] W. J. O’Connor. Wave-echo control of lumped flexible systems. Journal of sound and vibration, Vol. 298, No.4, pp. 1001-1018, 2006. [2] G. Boschetti, R. Caracciolo, D. Richiedei, A. Trevisani. Moving the suspended load of an overhead crane along a pre-specified path: A non-time based approach. Robotics and ComputerIntegrated Manufacturing, Vol. 30, No. 3, pp. 256-264, 2014. [3] M.A. El Khalick, N.Uchiyama. Contouring controller design based on iterative contour error estimation for three-dimensional machining. Robotics and Computer-Integrated Manufacturing, Vol. 27, No. 4, pp. 802-807, 2011.
Contouring controller design based on iterative contour error estimation for three-dimensional machining
Recently, there has been a growth of interest in high precision machining in multi-axis feed drive systems, subjected to problems such as friction, cutting force and incompatibility of individual driving axis dynamics. To guarantee high precision machining in modern computer numerical controlled (CNC) machines, CNC's controllers do its control efforts to reduce contour error. One of the common approaches is to design a controller based on the estimation of contour error in real time. However, for complex contours with severe curvatures, there is a lack of effective algorithms to calculate contour errors accurately. To address this problem, this paper proposes an accurate contour error estimation procedure for three-dimensional machining tasks. The proposed method is based on an iterative estimation of the instantaneous curvature of the reference trajectory and coordinates transformation approach, and hence, it is effective for complex reference trajectories with high curvatures. In addition, contour error controller is presented to reduce the estimated contour error. The feasibility and superiority of the proposed model as well as contour error controller are demonstrated through experimental system using a desk-top three-axis CNC machine.
Relationship between level of internet addiction and time management skills among nursing students.
PURPOSE
This study investigated nursing students' levels of internet addiction (IA) and time management (TM) skills.


DESIGN AND METHODS
This cross-sectional descriptive study was conducted with 400 nursing students of a university in Turkey. The data were collected using the Personal Information Form, IA Scale, and TM Inventory.


FINDINGS
The IA scale and TM inventory mean scores were 40.83 ± 14.81 and 81.34 ± 11.91, respectively. A significantly negative relationship between students' level of IA and TM skills was found (p <0.05).


PRACTICE IMPLICATIONS
The concept of effective time management should be used in interventions for promoting students' conscious internet use.