GB2038507A - Non-linear control system - Google Patents

Abstract

A method for the rapid, high- precision, controlled adjustment of physical values, more particularly for the controlled positioning of mechanical objects, in which the physical value is changed via an adjusting system with a wide control range and the actual values required for adjustment are obtained via a measuring system. The method is characterised in that the control deviation is non-linearly amplified in a position controller in dependence on the amplitude of the deviation. At the same time the phase position of the control deviation is non-linearly corrected in the position controller.

Description

SPECIFICATION Method for the controlled adjustment of physical values This invention relates to a method for the rapid, high-precision, controlled adjustment of physical values, more particularly for constantly repeated adjusting operations, referred to hereinafter as positioning. The invention is applicable, for example, for the positioning of mechanical objects in respect of paths or angles in precision apparatus technique.

A large number of controlled positioning systems are known in which a given position is approached by the use of incremental position adjusters (stepping motors) or other motor drives with well-defined control functions. Moreover there are various controlled positionings in which the measured value of the position is fed back via a controller to the final control element.

Methods of high-precision positioning are also known in which a changeover from coarse to fine drive (changeover transmission, special final control element control systems, two final control elements and others) is affected in the vicinity of the position value to be reached. The aim of the changeover is to extend the control zone of the adjusting system, achieve greater resolution, and enable the position to be adjusted as free from overswing as possible.

Controlled positioning is unsuitable for maximum precision demands, since: extreme demands would be made on the manufacturing tolerance of the component; the accuracy of the changeover affects the precision of positioning; disturbance variables with statistic properties occur (changes in temperature, fluctuations in frictional forces, mechanical vibrations such as impacts, oscillations of buildings, unevenlyrunning transmissions and others) which cannot be determined in a well-defined manner and therefore cannot be taken into account in a control system.

An analysis of controlled positions shows that it is inconvenient to use changeover arrangements, since: in the immediate vicinity of the position the amplification by changing over to fine drive is reduced, so that the stabilising effect of the controller deteriorates and the disturbance variable dependence of the system increases; the positioning time of the system is increased, although of course a reduction in amplification results in a reduction in the inclination of the system to overswing.

It is an object of the invention to enable the positioning time to be substantially shortened with maximum positioning precision, thereby increasing labour productivity, with substantially overswing-free adjustment of the position.

It is another object of the invention to develop a method in which the control precision of the system is adequate to reduce the disturbance variable dependence while at the same time keeping the tendency to overswing low.

To this end the present invention consists in a method for the rapid, high-precision, controlled adjustment of physical values, in which the physical value is changed via an adjusting system with a wide control range and the actual values required for adjustment are obtained via a measuring system, more particularly for the rapid, high-precision, controlled positioning of mechanical objects, characterised in that the control deviation is non-linearly amplified in a position controller in dependence on the amplitude of said deviation, while at the same time the phase position of the control deviation is non-linearly corrected in the position controller.

Advantageously with small control deviations, feedback signals are additionally fed to the position controller which are obtained directly from the object or the measuring system. With small control deviations there is preferably a larger amplification than with large deviations; a frequency-dependent phase lead of 90 and more may be produced, while maintaining the amplitude.

Final control elements with internal feedback are used as the adjusting system having a wide control range, so that there is no need for a coarse-fine changeover.

It is also presupposed that the dynamic properties of the object to be adjusted are known or measurable and invariable within predetermined time limits, and that a measuring system having the necessary resolution and precision (in dependence on the actual problem even relative precision) and the necessary long-term constancy is present, by means of which measurements can be affected dynamically.

In order that the invention may be more readily understood, reference is made to the accompanying drawings which illustrate diagrammatically and by way of example an embodiment thereof, and in which: Figure 1 shows the basic construction of a high-pcision positioning system; Figures 2a and 2b show the frequency path of the object to be controlled; Figure 3 shows the construction of the position contrpller; and Figures 4a and 4b show the frequency path of the open control circuit with non-linear position controller.

Fig. 1 is a block circuit diagram showing the structure of a rapid high-precision positioning system which relates to an example of the high-precision controlled positioning of mechanical objects. A mechanical object 5 is moved by means of a driving system comprising an amplifier 1, a driving motor 2, and a tachometer 3 disposed in a feedback branch and having a connected drive reguiator 4. The particular position in which the object 5 is situated is determined by a measuring system 6 and a control deviation is formed from the actual position value x(t) and the required position value xO.

In an acceleration measuring system 7 derivations of the movement value of the mechanical object 5 in time are determined which are required to optimise control. The derivation of the movement value in time is fed in addition to the control deviation e to a position controller 8.

To move the object 5 a ball-bearing-mounted measuring carriage is provided which rolis over a basic bed insulated against oscillation. The movement range is 250 mm, the required positioning precision being + 0.1 lim and the required positioning time for the transition from any position to a fresh position at a distance of 10 mm being 1 sec.

The measuring carriage is driven by a ball and nut spindle drive whose nut is connected via a universal joint to the measuring carriage. The drive (motor-tachometer set) is applied to the spindle via a singie-stage, clearance-free transmission. The mechanical structure, designed having regard to dynamic demands, shows a marked resonance place at 30 Hz with very low damping, which is produced from the mass of the carriage in combination with the spring properties of the universal joint. Further resonance places lie above 100 Hz.

The motor circuit with tacho-feedback is so designed that for input voltages at the amplifier of 1.5 mV...7.5 V the speed depends linearly on the input voltage. Maximum speed about 5000 rpm, minimum speed about 1 rpm. With a step-down transmission of 1:25 and a spindle lead of 5 mm per revolution, carriage speeds of 3.3 jum/sec. . . 1 7 mm/sec can therefore be lineariy controlled and paths of less than 50 nm resolved.

The limit frequency of the drive lies about 80 Hz. The mechanical object 5 with drive can be described by the following transference function, ignoring non-linear effects caused by friction and residual clearance: x(p) x: change in distance travelled in mm WO(p) = - U: input voltage in V U(p) K W,(p)= . WOR(P) (1) pT(1 + pea)(1 + 2DoTop + To2p2) T integration time constant 270 msec TA time constant drive with load 4.6 msec time constant of resonance member 5.3 msec Do damping of resonance member 0.1 K dimensional factor 1 mm/V WOR(P) contains further resonance places and time constants in the range above 100 Hz; for basic considerations the approximation WOR(P) = 1 is permissible.

The oscillation-insulated basic bed shows resonance behaviour in the x-direction at 0.5 Hz.

This resonance place is excited by the movement of the carriage and in the uncontrolied state produces disturbance amplitudes of 20 jum with 0.5 Hz at the carriage. To enable such disturbance amplitudes to be brought under control, the control circuit amplification of 0.5 Hz must be greater than 200. The measuring system 6 used is a laser path (distance) measuring system with a resolution of 40 nm. The time constants of the measuring system 6 and its operative time lie far outside the frequency range of interest.

Figs. 2a and 2b show the frequency path for the complete object 5 to be controlled, having regard to Equation (1). The amplitude path in Fig. 2a and the phase path in Fig. 2b show that the system does not meet the required parameters with a P-controller and dynamic correction.

Fig. 3 shows the construction of the position controller 8. In addition to the path signal x(t) the acceleration d2 X (t) dt2 at the measuring carriage is directly measured and processed in parallel. The actual value of the position x(t), which is present as the dynamic counter state of the measuring system 6, is subtracted from the required value xO, and the error signal Edig(t) present in digital form is processed by amount and sign.Via a logical coupling of a D/A transducer 9 in the example the change in amplification is so effected that for slight differences between required and actual value #an 5mV V /#/#/#o/:-- = --, that is to say 125 - #dig 1 bit mm and for large differences between the required and actual values àn 5mV V = ) , = -, that is to say 3,9 we have 1 1 bit mm The changeover point E, lies at about 10 ym. The signal àn is fed via an analog amplifier 10 with adjustable amplification VR1~2 (amplitude channel) to a changeover switch 11 in which it receives the sign, which is determined in a zero discriminator 12 from the sum, formed in transfer member 13, of the error signal ean of correct sign formed in changeover switch 14 and its derivation d,an(t) TNK . - produced by differentiation (phase channel). (1) dt A connected linear filter 15 with low-pass properties TKO = 190 msec, TK1 = 16 msec...50 msec (adjustable) results in an additional reduction of the amplitude path in the range of 0.8. . 10 Hz. The acceleration feedback via the amplifier 16 acts as a damping of the resonance place.

Figs. 4a and 4b show the frequency path of the open control circuit with non-linear position controller, curves 1 with small differences between the actual and required values, and curves 2 with larger deviations.

By altering the changeover point and the amplification VRt it is possible to optimise the building-up behaviour as a whole, while by altering the time constant TKO the building-up behaviour can be optimised immediately around the required position.

Claims (5)

1. A method for the rapid, high-precision, controlled adjustment of physical values, in which the physical value is changed via an adjusting system with a wide control range and the actual values required for adjustment are obtained via a measuring system, more particularly for the rapid, high-precision, controlled positioning of mechanical objects, characterised in that the control deviation is non-linearly amplified in a position controller in dependence on the amplitude of said deviation, while at the same time the phase position of the control deviation is non-linearly corrected in the position controller.

2. A method according to claim 1, wherein with small control deviations, feedback signals are additionally fed to the position controller which signals are obtained directly from the object or the measuring system.

3. A method according to claim 1, wherein with small control deviations there is a larger amplification than with large deviations.

4. A method according to claim 1, wherein with small control deviations a frequencydependent phase lead of 90 and more is produced, while maintaining the amplitude.

5. A method for the rapid, high-precision controlled adjustment of physical values, substantially as herein described with reference to and as shown in the accompanying drawings.