ADRC precision tracking motion controller design (1)

Abstract: in order to improve non-circular turning fast servo tracking accuracy and immunity, developed a rejection controller.

Through a implementing agency modeling analysis, model of nonlinear partially due to the system of neirao, processing cutting force interference due to the system, and designed by the extended State observer, on the system, the sum of external disturbances make real-time estimation and compensation. Simulation experiments show that rejection performance over traditional PID control. Through DSP (digital signal processor) programming, ADRC applied to non-circular turning. Cutting test results show that rejection have good control of quality, rapid servo tracking accuracy control within the 5 μ m.

Keywords: non-circular turning; rejection; rapid servo

Non-circular NC turning is non-circular parts efficient, flexible, high-precision machining.

Non-circular turning, cutting tools in rapid servo (fast tool servo, FTS) driver, along with the spindle speed rotary radial along the artifacts do quick reciprocating motion. FTS of tracking accuracy is a non-circular cross section part outline precision. FTS controller design faces two difficulties: first, how to increase the rigidity of the servo FTS, to reduce the changes of cutting force effect on tracking accuracy; second, how to reduce the FTS actuator nonlinearities and parameter changes on tracking accuracy.

At present, many scholars are suitable for non-circular turning of FTS controller for in-depth study.

The text uses the PID control is a combination of feed-forward compensation approach, design feedback based on location and speed feedback both disturbance observer. Text for non-circular turning, tracking signal for regular periodic signals this characteristic, the use of repeating control algorithm, and are improving, enhancing the rapid system response. The text adopted model reference adaptive control, control on FTS, improves the system's robustness and anti-jamming ability.

Rejection (active disturbance rejectioncontroller, ADRC) is an approach based on error feedback of nonlinear control method, its principle is simple, can system unmodeled dynamics and unknown disturbance to make good estimates and compensation, with strong adaptability and robustness.

This application rejection control, according to the non-circular turning on FTS controller in tracking accuracy, response rate, resistance to disturbance of requirements developed rejection precision tracking motion controllers, and simulation analysis and cutting test.

1 charged object modeling

Non-circular turning with FTS executive body structure see the text, it uses the voice coil motor drive principle, springs and rolling guide composite bearing, can be approximated as a spring damper system, differential equations of motion for

Where: m-motion part quality, k is implementing agencies in the spring stiffness coefficient, C for damping, Fw is the process of cutting force, the electromagnetic force FA.

According to the electromagnetic force calculation formula, juice of FA (t) = nBLI (t), where n is the number of turns of the coil as magnetic flux density B and L is the length of the coil, I effectively to current intensity.

On implementing agencies for control, the input for voltage control signal, power amplifier converted to current output, the conversion of I (t) = ku (t), the motion equation can be written as follows:

However, the implementing agencies in the actual work process, because the coil magnetic flux is not uniform and reluctance thrust so that executing agencies of thrust and coil current relationship is not linear, and thus to control brought greater difficulty.

At the same time, due to the cutting force during processing is a real-time changes to the system's stability had a large impact.

2 rejection precision tracking motion controller design

Figure 1 shows the rejection controller structure.

　　

　　

Typical rejection controller including tracking differentiator (trackingdifferential, TD), extended State observer (extended stateobserveF, ESO) and nonlinear feedback controller 3 parts.

N-TD's role is to give non-differential input signal tracking signal and l-n-l order differential signal. TD signal relative to the input signal has a little lag, in addition, non-circular cross section shape parts of general use differentiable functions that the function directly: you can get the reference signal for differential values. Therefore, the controller was removed. TD. ESO real-time estimation of the charged object of the order status variables and system of total disturbance of unknown parts (including neirao and foreign interference), and compensation. Nonlinear feedback controller will TD's output signal and the ESO observed that corresponds to the state variable for the poor, through non-linear combination, does not contain a disturbance, control volume, improve system speed, decrease the amount of overshoot.

Set FTS implementing agencies in the actual work process, the thrust of FA and enter u than an unknown function b (t).

The actuator movement differential equations can be written as:

　　

　　

3 simulation analysis

In order to visit ADRC resistance to external disturbances and changes in the internal parameter, use Matlab programming, a simulation analysis, respectively.

In order to visually illustrate the problem, but also on the simulation of PID control. In the simulation programming, charged objects using second-order model. Because the actual charged objects not modeling component of the proportional factor too large will result in system instability. In order to accurately reflect the actual process of cutting force, simulation process on two control algorithm of proportional coefficient based on the actual situation. In this context, by repeatedly adjust the setting on a mission to track respectivelyError minimal control parameters, and the set of parameters for the following simulation experiment.

3.1 resistance to external perturbations of performance analysis

Non-circular turning FTS is outside disturbance mainly change of cutting force, so the simulation is interfering signal uses during processing of two typical cutting force signal.

Simulation using reference signal for non-circular turning process along the workpiece radial ideal reciprocating motion trajectory. To spindle speed 1 200 r/min, processing ellipticity 0.4 mm piston, for example, the tool motion equation y = 100 (cos (251.33t/s)-1).

Test l: from the start, join s 0.05 amplitude and frequency for 50 N, and the tool movement frequency signal same cutting force Fw/N = 50 (1-cos (251.33t/s)), this is equivalent to the circular turning into non-circular cross section of the condition.

The simulation results as shown in Figure 2, in which the ordinate e for tracking error, horizontal for time t.

　　

　　

You can see from Figure 2, PID control after joining the interference signal, clearly increase the margin of error, the error curve rules also have the obvious change.

And rejection after joining the interference signal, the impact on the fundamental error is eliminated, and not to interfere with the scope of the former is that rejection have good anti-interference characteristics, due to cutting depth changes produced by alternating the cutting force, stronger suppressing interference ability to PID control.

Test 2: from the beginning, s 0.05 joined the amplitude is 50 N, frequency and the tool movement frequency same square-wave signal cutting force, which is equivalent to processing with piston cutting hole oval cross section of the condition.

Two control method of tracking error simulation results as shown in Figure 3.

　　

　　

Visible from Figure 3, square-wave signal due to the cutting force interference with a force of nature, mutations on the impact of the control system will be more than the sine and cosine signal interference.

For the rejection, in cutting force mutation, the error occurs only on the entire range, the range has no effect. But for PID control, this kind of interference caused by error is quite drastic fluctuations. Therefore, due to factors such as the flute and the square-wave pattern change of cutting force, rejection by suppressing interference ability is also stronger than the PID control.

3.2 resistance internal parameter change performance analysis

To test control algorithm for resistance to changes in internal parameters, the reference signal from O.05 s, starting at the output of the FTS implementing agencies gain reduced 50%, the test result as shown in Figure 4.

　　

　　

Figure 4 shows that the gain reduction 50% PID control error range has a more significant change, and the rejection of the tracking results is little affected.

This test reflects the rejection of the charged object model does not depend on the characteristics of its robust strong to PID control.

4 cutting experiment

4.1 test system

Cutting test was in convex G-CNCP200 become oval-piston CNC machine tool.

The machine tools horizontal and vertical movement for open-loop control, AC servo drive. FTS mechanical structure part installed in the machine tool widthwise, driven tool to achieve precise reciprocating motion. Principal axis adopts frequency conversion control, can realize stepless speed regulation. FTS hardware including DSP (digital signal processor) dashboard, D/A converters, power amplifier and linear actuators and linear grating 5 parts. [1] [2]