Cross-Coupled Control of Biaxial Feed Drive Servomechanisms

1990 ◽  
Vol 112 (2) ◽  
pp. 225-232 ◽  
Author(s):  
K. Srinivasan ◽  
P. K. Kulkarni
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
Tracking Error ◽  
Time Varying ◽  
Tracking Accuracy ◽  
Contouring Error ◽  
Feed Drive ◽  
Straight Line ◽  
Controller Performance ◽  
Contouring Accuracy

A cross-coupled controller, designed to improve high-speed contouring accuracy independently of tracking accuracy in biaxial machine tool feed drive servomechanisms, is presented here. The controller parameters depend on the instantaneous slope of the desired contour and hence vary with time for curved contours, resulting in a time-varying controller. An approximate stability analysis of the controller is presented. The proposed controller is evaluated experimentally on a microcomputer controlled two-axis positioning table and compared to a more traditional uncoupled controller. Controller performance is evaluated for straight line, cornering and circular contours at feed rates varying from 2.25 m/min to 7.2 m/min. The experimental results show that the proposed controller reduces contouring error as compared to the uncoupled controller and leaves the tracking error practically unchanged. The cross-coupled controller is simple to implement and is practical.

Integrated optimal design of a high-speed planar parallel manipulator

2018 ◽  
Vol 233 (9) ◽  
pp. 2976-2990 ◽  
Author(s):  
Zhengsheng Chen ◽  
Minxiu Kong
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
High Speed ◽  
Design Method ◽  
Tracking Error ◽  
Dimensional Synthesis ◽  
Tracking Accuracy ◽  
Nsga Ii ◽  
Parameters Tuning ◽  
Planar Parallel Manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

Perfectly Matched Feedback Control and Its Integrated Design for Multiaxis Motion Systems

2004 ◽  
Vol 126 (3) ◽  
pp. 547-557 ◽  
Author(s):  
Syh-Shiuh Yeh ◽  
Pau-Lo Hsu
Keyword(s):  
Feedback Control ◽  
High Speed ◽  
Feedforward Control ◽  
Phase Error ◽  
Integrated Design ◽  
Cnc Machining ◽  
Dynamic Responses ◽  
Tracking Accuracy ◽  
Control Loops ◽  
Contouring Accuracy

For motion systems with multiple axes, the approach of matched direct current gains has been generally adopted to improve contouring accuracy under low-speed operations. To achieve high-speed and high-precision motion in modern manufacturing, a perfectly matched feedback control (PMFBC) design for multiaxis motion systems is proposed in this paper. By applying stable pole-zero cancellation and including complementary zeros for uncancelled zeros for all axes, matched dynamic responses across the whole frequency range for all axes are achieved. Thus, contouring accuracy for multiaxis systems is guaranteed for the basic feedback loops. In real applications, the modeling error is unavoidable and the degradation and limitations of the model-based PMFBC exist. Therefore, a newly designed digital disturbance observer is proposed to be included in the proposed PMFBC structure for each axis to compensate for undesirable nonlinearity and disturbances to maintain the matched dynamics among all axes for the PMFBC design. Furthermore, the feedforward control loops zero phase error tracking controller are employed to reduce tracking errors. Experimental results on a three-axis CNC machining center indicate that both contouring accuracy and tracking accuracy are achieved by applying the present PMFBC design.

Optimal Contouring Control of Multi-Axial Feed Drive Servomechanisms

1989 ◽  
Vol 111 (2) ◽  
pp. 140-148 ◽  
Author(s):  
P. K. Kulkarni ◽  
K. Srinivasan
Keyword(s):  
Controller Design ◽  
Contour Error ◽  
Loop Control ◽  
Feed Drive ◽  
Feed Drives ◽  
Straight Line ◽  
Contouring Control ◽  
Contouring Accuracy ◽  
Closed Position ◽  
The Individual

The capability of multi-axial machine tool feed drives to follow specified trajectories accurately is an important requirement for precision machining and especially so in applications involving high contouring speeds. In current generation machine tools, contouring is achieved by coordinating the commands to the individual feed drives, and implementing closed position loop control for each axis. The present paper deals with the evaluation of a cross-coupled compensator aimed specifically at improving contouring accuracy in multi-axial feed drives. The controller design is formulated as an optimal control problem. The performance index to be minimized weights the contour error explicitly. The controller is evaluated experimentally on a microcomputer controlled two-axis positioning table. Controller performance is evaluated for straight line, cornering and circular contours at feed rates varying from 2.25 m/min to 5.63 m/min. Measures of the steady state and transient contour errors are considered. The experimental results show that the proposed controllers reduce contouring errors considerably as compared to conventional uncoupled control of the multiple axes. The control action of the optimal controller is compared with that of more conventional uncoupled controllers.

Study on torsional stiffness of transmission employed in a rotary table

2016 ◽  
Vol 230 (19) ◽  
pp. 3541-3555 ◽  
Author(s):  
Lin Han ◽  
Lixin Xu ◽  
Fujun Wang
Keyword(s):  
High Speed ◽  
Torsional Stiffness ◽  
Design Stage ◽  
Time Varying ◽  
Rotary Table ◽  
Mesh Stiffness ◽  
Feed Drive ◽  
Number Of Teeth ◽  
Stiffness Model ◽  
Feed Drive System

Torsional stiffness of a rotary table plays an important role in the static and dynamic characteristics of a rotary feed drive system. This paper proposes an effective approach to estimate the torsional stiffness of a worm geared transmission usually employed in rotary table. First, the stiffness models of each component used in the transmission are extracted. Then, an expression for the coefficient relating angular displacements is derived and a general torsional stiffness model for the rotary feed drive is developed, taking the time-varying mesh stiffness into account. Finally, a stiffness test scheme is presented and conducted to verify the proposed stiffness model. Furthermore, the influences of the gear’s parameters on the resultant torsional stiffness are investigated based on the developed model. Results indicate the necessity to incorporate a time-varying mesh stiffness when the torsional stiffness of the rotary table is under estimation. Also, a high-frequency variation in profile of torsional stiffness is induced by the mesh stiffness of gear pairs at the high-speed stage. Parametric studies show that tooth width and number of teeth of the driven gear at low-speed stage are more sensitive to stiffness than those at high-speed stage. However, the number of teeth of the driving gears introduces different effects onto the torsional stiffness. The presented model can be used to estimate the torsional stiffness of a rotary feed system efficiently, especially during the preliminary design stage.

A Robust Delay Compensator for Uncertain Nonlinear Systems With Unknown Time-Varying Input Delay

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Ashish Kumar Jain ◽  
Shubhendu Bhasin
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Tracking Error ◽  
Input Delay ◽  
Control Law ◽  
Time Varying ◽  
Uncertain Nonlinear Systems ◽  
Uniformly Ultimately Bounded ◽  
Simulation Results

This paper proposes a robust compensator for a class of uncertain nonlinear systems subjected to unknown time-varying input delay. The proposed control law is based on the integral of past values of control and a novel filtered tracking error. Sufficient gain conditions dependent on the known bound of the delay are derived using a Lyapunov-based stability analysis, where Lyapunov–Krasovskii (LK) functionals are used to achieve a global uniformly ultimately bounded (GUUB) tracking result. Simulation results for a nonlinear system are used to evaluate the performance and robustness of the controller for different values of time-varying input delay.

Modified integral action with time-varying forgetting function for tracking control

2019 ◽  
Vol 234 (6) ◽  
pp. 715-725
Author(s):  
Fernando Villegas ◽  
Rogelio Hecker ◽  
Miguel Peña
Keyword(s):  
Stability Analysis ◽  
Tracking Error ◽  
Control Law ◽  
Time Varying ◽  
Forgetting Factor ◽  
Robust Controller ◽  
Integral Action ◽  
Abrupt Changes ◽  
New Type ◽  
And Control

While the use of integral action in control is quite common, in part due to its benefits for output regulation, it can also be counterproductive when abrupt changes in disturbance occur during tracking. In order to mitigate its counterproductive effect while at the same time maintaining its advantages for regulation, this work proposes a new type of integral action, including a time-varying forgetting factor suited to the expected behavior of the disturbance during tracking. Also, Lyapunov stability techniques are used to derive general results aiming to reduce the complexity of stability analysis and control design when the proposed integral action is included in a control law. In particular, these results are used for stability analysis when the proposed integral action is implemented in a deterministic robust controller for a linear motor system. Furthermore, the controller is implemented in the corresponding experimental setup, resulting in an improvement on maximum tracking error of up to 32%.

Control System for Suppressing Tracking Error Offset and Multiharmonic Disturbance in High-Speed Optical Disk Systems

2012 ◽  
Vol 132 (3) ◽  
pp. 347-356 ◽  
Author(s):  
Yuta Nabata ◽  
Tatsuya Nakazaki ◽  
Tokoku Ogata ◽  
Kiyoshi Ohishi ◽  
Toshimasa Miyazaki ◽  
...  
Keyword(s):  
Control System ◽  
High Speed ◽  
Tracking Error ◽  
Optical Disk
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