Method and control system for compensating for friction

A method for compensating for static friction in an actuating device includes the steps of generating an actual signal y.sub.2 (t) corresponding to a quantity which is controllable by the actuating device, generating a set value signal y.sub.1 (t) generating a control signal s.sub.1 (t) based on the set value signal y.sub.1 (t) and the actual value signal y.sub.2 (t), and supplying the control signal to the actuating device for controlling the same. The method also includes the steps of generating an intermittent signal s.sub.2 (t) compensating for friction, sensing the sign of the derivative with respect to time of the control signal s.sub.1 (t), giving the signal s.sub.2 (t) compensating for friction the same sign as the derivative, and adding the signal s.sub.2 (t) compensating for friction to the control signal s.sub.1 (t) before supplying the same to the actuating device.

FIELD OF THE INVENTION
 The present invention relates to controlling in the presence of static
 friction, especially to reducing the effects of static friction in the
 controlling of valves.
 BACKGROUND ART
 Static friction, so-called stiction, occurs everywhere in the environment.
 As a rule, the friction when passing from rest to motion (static friction)
 is greater than the friction during the continuance of the motion (sliding
 friction). To move an object from its resting position, a force greater
 than the sliding friction must thus be applied to the object.
 The existence of static friction is a general problem in all types of
 controlling that means that an actuating means is to be stopped and later
 to be moved again. The term actuating means signifies in this context the
 subject of the control, i.e. the component/components actuated during the
 control.
 In valves there is static friction, for instance, between the valve spindle
 and the packing box, especially if this is tightened firmly. Moreover,
 static friction may occur in other positions in a valve, for instance,
 between ball and seat in a ball valve.
 Static friction manifests itself by so-called stick-slip motion, i.e. the
 valve sticks owing to the friction in a certain position, which requires a
 certain amount of force to overcome the resistance from the stiction. Once
 the static friction resistance has been overcome and the actuating means
 moves towards its desired position, the applied force is too great
 relative to the sliding friction, which means that the actuating means
 will be accelerated and therefore pass the desired position before the
 control system has time to brake the actuating means. This problem is
 particularly pronounced when small valve movements are desired, or when
 the time constant of the control system is great and, consequently, the
 controlling occurs slowly relative to the motion of the actuating means.
 When controlling, for example, a flow passing through a valve, static
 friction in the valve thus gives rise to oscillations in the controlled
 flow round the set value thereof. If the static friction increases during
 operation, for instance, owing to wear or clogging, the size of the
 oscillations will increase.
 It is desirable to reduce the effect of the static friction in valves, of
 which a large number may be included in process equipment, since the
 above-described oscillations in processes give rise to an increased power
 consumption and waste of raw material. As a rule, it is however not
 economically defensible to interrupt the process and take care of the
 problems of friction each time an unacceptably great stick-slip motion is
 discovered in one of the valves. For this reason, it is desirable to be
 able to compensate for static friction during operation.
 A difficulty in compensating for static friction is that this may vary with
 valve position, time and between different cases of operation. For
 instance, the valve is in most cases worn unevenly, and therefore the
 friction is not the same in different positions of the valve. Moreover,
 variations in temperature cause corresponding variations in static
 friction, since at high temperatures the material expands and causes
 increased friction. In a process, the temperature can, of course, vary
 both in time and between different cases of operation. Also the valve
 becoming dirty may give rise to variations in friction.
 A previously well-known technique of compensating for static friction is
 called dithering. This technique is disclosed in, inter alia, U.S. Pat.
 No. 3,562,620 in connection with the controlling of electric motors, and
 in CH-600,219 in connection with the controlling of a hydraulic valve.
 Dithering implies that a high-frequency signal is superposed on, i.e.
 added to, the control signal. The amplitude of the signal should be
 sufficiently high to overcome the static friction, and the frequency of
 the signal should be so high that the disturbance generated by such
 superposing is above the relevant frequency range of the system. The mean
 value of the superposed signal is zero, which results in the
 high-frequency valve constantly oscillating on the spot. This
 high-frequency oscillation prevents the valve from sticking in the
 above-described fashion, thereby avoiding the problem of stick-slip
 motion.
 The main drawback of dithering is precisely that the valve is forced to
 oscillate continuously, which, of course, results in an increased wear of
 all moving parts of the valve. Besides, this technique is not usable to
 overcome and compensate for static friction in valves where the control
 signal will be low-pass filtered (integrated) in the actuator, such as in
 pneumatically controlled valves. This problem will be further discussed
 below with reference to the drawings.
 A further compensating technique, so-called impulsive control, is described
 in "A Survey of Models, Analysis Tools and Compensation Methods for
 Control of Machines with Friction", Armstrong-Helouvry et al, Automatica,
 Vol. 30, No. 7, pp 1083-1138. Impulsive control means that the actual
 control signal is generated as a sequence of pulses, and therefore both
 controlling and overcoming of friction are accomplished by means of the
 same signal. Each pulse results in a certain movement of the actuating
 means. Variations with respect to time in the static friction consequently
 cause corresponding variations with respect to time in the movement of the
 actuating means. To obtain a control signal which as much as possible is
 independent of any variations in static friction, the pulses must have a
 high amplitude and a short duration.
 Impulsive control suffers from, inter alia, the drawback that the static
 friction resistance must be known, at least in the sense that the
 generated pulses must have a sufficient amplitude to overcome every
 conceivable friction resistance. Moreover, the pulses have a short
 duration, which means that a high-frequency signal is to be transferred to
 the actuating means. Therefore, this technique is not applicable in valves
 having a low-pass filtration of the control signal, for instance,
 pneumatically controlled valves.
 OBJECTS OF THE INVENTION
 An object of the present invention is to overcome, wholly or partly, the
 problems connected with prior art technique, i.e. to provide a method and
 a control system reducing the effect of static friction when controlling
 an actuating means and causing a minimum wear of the moving parts of the
 actuating means. The method and the control system according to the
 present invention should also be substantially independent of variations
 in the static friction.
 A further object of the invention is to suggest a method and a control
 system which can be used for compensating for static friction in actuating
 means having low-pass filtering components.
 The invention is specifically, but not exclusively, adapted to be used for
 the controlling of valves.
 SUMMARY OF THE INVENTION
 According to the invention, these and other objects which will appear from
 the following description have been achieved by a method and a control
 system according to appended claims 1 and 7, respectively. Preferred
 embodiments of the invention are defined in the appended subclaims.
 In summary, the idea of the invention is that pulses, which are small in
 relation to the static friction, are superposed on the control signal. The
 sign of each pulse conforms with the sign of the derivative with respect
 to time of the control signal when generating the pulse. Thus, the idea of
 the technique is that the pulses coact with the control signal and "knock"
 at the actuating means in the same direction as the control signal tends
 to move it. Thanks to this knocking, the friction will be overcome at an
 earlier stage in the course of the control signal, i.e. the stick phase is
 shortened. Owing to the small energy content of the pulses in relation to
 the static friction, the overshoot of the actuating means round the
 desired position will be relatively small once the static friction has
 been overcome, i.e. the slip phase is shortened.
 Without compensation for static friction, the quantity controlled by the
 actuating means will, as mentioned above, perform considerable
 oscillations round the desired value owing to stick-slip motion. While
 using the invention, this quantity will have significantly more rapid and
 smaller oscillations round the set value.

DESCRIPTION OF EMBODIMENTS OF THE INVENTION
 FIG. 1 is a schematic view of one type of pneumatic control valve. The
 three main parts of the control valve are a valve positioner 1, an
 actuator 2 and a valve 3, the actuator 2 and the valve 3 together forming
 an actuating means, i.e. the means subjected to the above-mentioned static
 friction.
 The valve positioner 1 is arranged in a casing 4, which is provided with an
 air supply opening 5, a lower connecting port 6 and an upper connecting
 port 7. The air supply opening 5 is connected to a compressed air source
 (not shown) applying a constant air pressure to the valve positioner 1.
 The connecting ports 6, 7 are interconnected by means of a first duct 8,
 which in turn is connected to the air supply opening 5 by means of a
 second duct 9. In the first duct 8, a pilot valve 10 is arranged in the
 form of a movable slide, which is connected to an operable diaphragm 11.
 The actuator 2 comprises a cylinder 12 and a piston 13 movably arranged in
 the cylinder and dividing the cylinder into an upper chamber 14 and a
 lower chamber 15. The piston 13 is connected to a valve spindle 16
 extending through one end wall of the cylinder 12. The spindle 16 is
 sealed against the cylinder 12 by means of a seal 17, a so-called packing
 box. The cylinder 12 further has two connecting ports 18, 19 which are
 each connected, by means of air ducts, to one of the connecting ports 6, 7
 of the valve positioner 1. A beam 20 is arranged on the valve spindle 16.
 The beam 20 is inserted into the valve positioner 1 and is connected, by
 means of a helical spring 21, to the operable diaphragm 11.
 The valve 3 comprises a valve cone 22, which is pivoted to the valve
 spindle 16. The valve cone 22 is arranged on a shaft 24 for rotation in
 front of a valve seat 23.
 The control valve is operated by a control signal s(t) moving the diaphragm
 11 in the direction of arrow A, whereby a corresponding movement of the
 slide 10 is accomplished. According to the size of the control signal,
 part of the upper connecting port 7 thus is uncovered, whereupon air flows
 into the upper chamber 14 of the actuator 2. At the same time, part of the
 lower connecting port 6 is uncovered and air flows out of the lower
 chamber 15 of the actuator 2. The thus established difference in pressure
 between the chambers 14, 15 generates a force acting on the piston 13 and
 moving this and the valve spindle 16 in the direction of arrow B. The
 movement of the valve spindle 16 is transferred to the valve cone 22,
 which is rotated relative to the valve seat 23. The movement is also
 transferred to the beam 20, and consequently the spring 21 is stretched.
 The force which owing to this stretching is generated in the spring 21
 returns the diaphragm 11 and the slide 10 to the state of equilibrium
 shown in FIG. 1. The valve cone 22 thus has been moved to a new position
 and will remain in this position as long as the control signal s(t) is not
 changed.
 Of course, the valve can be operated in the opposite direction by an
 opposite movement of the diaphragm 11.
 The operation of the control valve is rendered difficult by static
 friction, which may occur, for instance, in the seal 17 between the valve
 spindle 16 and the cylinder 12, or between the cone 22 and the seat 23 if
 these are mechanically connected with each other. As the control valve is
 worn, the static friction will increase and, besides, vary with valve
 position, time and between different cases of operation. The control valve
 will thus jam and tend to stick in different positions, and therefore the
 problems described by way of introduction will arise when controlling the
 flow passing through the control valve.
 These problems cannot be circumvented either by applying to the valve
 spindle 16 a high-frequency oscillation about a state of equilibrium, i.e.
 by dithering, or by using impulsive control, since the
 compression-air-distributing pilot valve 10 cannot, owing to the inherent
 inertia of the system, transfer to the piston 13 such vibrations at a
 sufficiently high frequency and amplitude.
 FIG. 2 is a block diagram of a system according to the present invention
 for controlling a process, for instance, the flow passing through a
 control valve. A set value signal y.sub.1 (t) is generated and fed to a
 controller. An actual value signal y.sub.2 (t), which is characteristic of
 the process, is generated, sensed and fed to the controller. On the basis
 of the set value signal y.sub.1 (t) and the actual value signal y.sub.2
 (t), a control signal s.sub.1 (t) is generated. A compensator senses the
 control signal s.sub.1 (t) from the controller and emits an intermittent
 compensation signal s.sub.2 (t) which is added to said control signal,
 whereupon the formed control signal s(t) is fed on to the process.
 In the normal case, the controller is a PID controller, which is controlled
 by the parameters amplification, integration time and derivation time.
 However, it should be pointed out that every type of controller is usable
 within the scope of the invention.
 FIG. 3 illustrates an example of an inventive control signal fed to the
 process. In the shown example, short pulses of equal amplitude and
 duration are thus added to the output signal of the controller. The sign
 of the pulses conforms with the sign of the derivative with respect to
 time of the control signal at the time of the addition, i.e. the pulses
 act on the valve spindle in the same direction as the control signal.
 The compensation technique can be described as follows: the superposed
 pulses coact with the control signal and intermittently knock at the valve
 spindle in the same direction as this is affected by the control signal.
 The knocks result in the static friction being overcome earlier than is
 normal during the course of the control signal, i.e. the jamming valve
 begins to move earlier. When the valve has been released from its locked
 position, the control signal changes direction and is superposed on pulses
 having the opposite sign.
 The output signal s.sub.2 (t) from the compensator may, as shown in FIG. 3,
 be a pulse sequence, which is characterised by the distance h.sub.k
 between the pulses, the amplitude a of the pulses and the width .tau. of
 the pulses. The energy content of a pulse is determined by the product of
 its amplitude and width and should, according to that stated above, not be
 so great that the force exerted by the pulse and acting on the valve cone
 exceeds the minimum stiction.
 The amplitude a should be kept relatively low. As appears from FIG. 1,
 great deflections of the pilot valve 10 result in the connecting ports 6,
 7 being completely uncovered. The air in the lower chamber 15 will then be
 blown out in an uncontrolled manner from the lower chamber of the actuator
 2, while air flows into the upper chamber 14 of the actuator 2. Normally,
 the piston is subjected to a certain balancing counterpressure exerted by
 the air in the lower chamber 15. An uncontrolled emptying as described
 above results in the complete disappearance of this counterpressure, and
 therefore the piston, once moved in the desired direction, is subjected to
 an unnecessarily great force relative to the friction to be overcome.
 Consequently, there is a risk that the slip phase is prolonged, which may
 counteract the purpose of the invention.
 Tests have shown that the amplitude should suitably be in the range 1-10%
 of the total controlling range of the control signal.
 Since it is desirable to keep the energy content of the pulses down, also
 the pulse width .tau. should be relatively small. For practical reasons,
 the pulse width cannot be smaller than the sampling interval of the
 controller. When a controller having a sampling time of 0.2 s is used to
 control a 150 mm valve, 0.2-0.4 s was found to be a suitable pulse width.
 When controlling larger valves, the pulses may probably have a longer
 duration.
 The distance h.sub.k between subsequent pulses must be greater than the
 sampling time of the controller and also greater than the pulse width
 .tau.. Said distance should, however, be so short in relation to the
 integration time of the controller that the base level of the pulses does
 not change too much between subsequent pulses. By having too great a
 distance between the pulses, the control signal between the pulses will
 have time to approach the slip position, and therefore the pressure drop
 over the piston, once the pulse is applied to the control valve, will be
 too great in relation to the static friction, which may result in
 considerable oscillations of the "controlled" flow.
 In one test, a flow of water was controlled by means of a very worn 150 mm
 ball valve. As controller, use was made of a PI controller having the
 amplification 1, the integration time 5 s and the sampling interval 0.2 s.
 The flow signal was fed through a first order low-pass filter having the
 time constant 5 s, before it was fed back to the controller. The test was
 carried out by using and without using a compensator. The compensator was
 set for the amplitude 3%, the pulse width 0.4 s and the pulse distance 1
 s.
 FIG. 4a shows the result of the test in conventional controlling by means
 of a pure PI controller, i.e. without any compensator. FIG. 4b shows the
 result of the corresponding test, using a control system according to the
 present invention. The set value as set in the test is indicated by the
 horizontal line in the actual value diagrams. It is obvious that the
 control system according to the invention gives rise to considerably
 shorter stick and slip phases than does a conventional control system. It
 should be emphasised that the total controlling range of the control
 signal in FIGS. 4a and 4b is between 0 and 1.
 The use of the compensator according to the invention thus reduces the
 amplitude of the oscillations and increases the frequency of the
 oscillations, meaning that the error in controlling decreases
 significantly.
 Since the energy content of the pulses is smaller than the static friction,
 the controlling will function in a satisfactory manner even if the
 friction increases or varies during operation.
 It will also be appreciated that the control valve is subjected to wear
 which is less that in conventional methods of compensation.
 Although the above description concerns valves only, the problems in
 connection with static friction are, of course, applicable to other
 technical fields, for instance, positioning by means of electric motors,
 where the stiction must be overcome in order to carry out a movement of
 some sort of actuating means.