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Control of Feed Drive Systems

ドキュメント内 Smooth Trajectory Generation and Control for Precision (ページ 30-35)

Literature Review

2.4 Control of Feed Drive Systems

Feed drive systems have a wide range of applications in the industrial community, in- cluding CNC machine tools and assembly robots. In machine tools, feed drives control the position and velocity of axes according to input commands to track a given reference trajectory. Tracking errors, the axial difference between the actual and the reference trajectories, occur in many industrial mechatronic systems. However, in machining appli- cations, contour errors, the orthogonal differences between actual positions and reference trajectories or contours are the best indicators of machining precision because they af- fect the geometrical shape of the machined workpiece directly[96]. Both tracking-error and contour-error based controllers are applied to enhance the performance of feed drive systems. In the tracking error approach, each axis is controlled independently such that

the load disturbance or performance variance on either axis is compensated for in indi- vidual axial control loops. However, because motion trajectories are usually complex, where axes move synchronously with respect to one another to track the desired trajectory, performance deviation in either axis leads to contour error [97]. On the contrary, under contour-error based approach, the contour error is evaluated in real-time and compensated for through the corresponding control loops.

Different control approaches have been studied in the literature to enhance the perfor- mance of feed drive systems. In this section, a brief review of basic control algorithms and iterative learning control for feed drive systems is addressed.

2.4.1 Feedback Control

Feedback control refers to a controller that considers the output signal in the control loop to adjust the system performance to meet a desired output. In machine tools, all controllers have a feedback loop [98]. Proportional-Integral-Derivative (PID) feedback controllers are widely used in industrial applications owing to their simplicity in design and implementation, and good performs in most cases. Although PID control can be applied in many control problems, it has several limitations that leads to undesirable performance. Since gains are constant and there is no direct process knowledge to the controller, PID control may lead to overshoot. Moreover, PID control tracks corners and nonlinear contours poorly owing to sudden changes in the direction of motion.

2.4.2 Feedforward Control

Feedforward controllers are customarily added to the control loop to enhance the tracking performance. A practical feedforward controller for continuous path control of a CNC machine tool was proposed in [99] to reduce trajectory error parameters, specifically, radial reduction, edge unsharpness, asymmetric error, and vibration amplitude. A feed- forward motion control design was developed in [100] for improving both the tracking and the contouring accuracies of motion control systems in CNC machine tools. By applying stable pole-zero cancellation to individual axes and by employing complementary zeros for all uncancelled zeros, the feedforward motion control design led to matched dynamics among all motion axes and thereby achieved highly accurate contouring and tracking

Reference contour

Actual position o

[

e

x1

e

x2

X

1

X

2 Reference

e

c

Actual contour

position

x

d

x

*

Figure 2.1: Definition of the contour error.

results. The main limitation of feedforward controllers is the requirement of exact knowl- edge of the model for controller design. In practice this knowledge is not known to the control designer, therefore the designed model may introduce position errors.

2.4.3 Cross-Coupling Control

Cross-coupling control considers a contour error based on feedback information from all axes and interpolates to find the best compensating law [98]. The altered signal is fed to the individual axes in real time. It was first introduced in [101] and extended to other approaches, especially contouring control [9, 96, 101–104]. The principle of this control algorithm is to directly reduce the contour error ec rather than the axial errors ex1 and ex2, that is, to position the tool at point x? instead of xd. Contouring control is an effective approach in machining because it provides performance comparable to that of non-contouring controllers with less input variance [9]. In addition, contouring control has better sharp-corners tracking and disturbance rejection capabilities than non- contouring controllers [98].

2.4.4 Iterative Learning Control

Iterative Learning Control is a particular form of feedforward control and an effective tool for improving the transient response and the tracking performance of uncertain dy- namic systems performing repetitive operations over a fixed time interval [105]. Such systems include machine tools performing batch machining and robotic manipulators in manufacturing industries. Since it is not always possible to achieve the desired tracking performance based on general control theory owing to the presence of unmodelled dy- namics and nonlinear uncertainties, ILC can be used to enhance the tracking performance of repetitive systems. In using ILC, tracking or contour errors from one iteration are used to compensate for the errors in the next iteration. Note that ILC is not independently applied because it is a feedforward controller and its application starts from the second iteration.

Although ILC has been applied widely to feed drive systems, many studies have con- sidered only tracking error, and simulations or experiments were performed on straight, circular and non-circular trajectories [6, 7, 106, 107], and only a few studies consid- ered cross-coupling control [8, 102]. However, as highlighted in the previous section, tracking-error-based controllers have poor sharp-corner tracking capability and higher in- put variance compared with contouring controllers. For this reason, it is indispensable to further enhance system performance by considering contouring control and sharp-corner trajectories.

Chapter 3

Real-Time Smooth Trajectory

ドキュメント内 Smooth Trajectory Generation and Control for Precision (ページ 30-35)

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