Servo Plant Compensation Techniques potx

11 Servo Plant Compensation Techniques Servo compensation usually implies that some type of filter network such as lead/lag circuits or proportional, integral, or differential (PID) algorithms will be used to stabilize the servo drive. However, there are other types of compensation that can be used external to the servo drive to compensate for other things in the servo plant (machine) that can, for example, be structural resonances or nonlinearities such as lost motion or stiction. These machine compensation techniques are shown in Figure 1 and are valid for either hydraulic or electric servo drives. 11.1 DEAD-ZONE NONLINEARITY Stiction, sometimes referred to as stick-slip, occurring inside a positioning servo, can result in a servo drive that will null hunt. The definition of a null hunt is an unstable position loop that has a very low periodic frequency such as 1 Hz or less with a small (a few thousandths) peak-to-peak amplitude (limit cycle). The most successful way to avoid stiction problems is to use antifriction machine way (rollers or hydrostatics) or use a way linear material that has minimal stiction properties. If stiction-free machine slide ways cannot be provided, the use of a small dead-zone nonlinearity placed inside the position loop, preferably at the input to the velocity servo, has Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved had some success in overcoming a null hunt problem. However the dead zone must be very small (e.g., 0.001 in.); otherwise, the servo drive will have an instability from too much lost motion. A simple analog dead-zone nonlinear circuit is shown in Figure 2. The same function can be provided with a digital algorithm in computer control of machines. 11.2 CHANGE-IN-GAIN NONLINEARITY In some industrial servo drives it is a requirement to position to a very low feed rate to obtain a smooth surface finish. This requirement usually occurs Fig. 1 Servo plant compensation techniques. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved in a turning machine application. At feed rates below 0.01 ipm, the requirement for a smooth surface may not be easily attainable because the servo drive may have a cogging problem at these low federates. Increasing the forward loop gain to the velocity drive can overcome the lowfeed cogging problem but will result in an unstable servo drive. As a compromise, a change in gain nonlinear circuit can be used to improve the low-feed-rate smoothness and still have a stable servo drive. The object is to have a high forward-loop gain in the velocity servo (which is inside a position loop). For normal operation, the high servo loop gain is reduced by the change-in-gain circuit at a low velocity to its normal gain, thus maintaining a stable servo drive. This type of nonlinear circuit has been used successfully for smooth Fig. 2 Dead-zone nonlinearity. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved feed rates down to 0.001 ipm. The analog version of a change-in-gain nonlinearity is shown in Figure 3. With digital controls a digital algorithm can be used. 11.3 STRUCTURAL RESONANCES Structural resonances or machine dynamics, as it often referred to, is certainly not a new subject. However, on the morning of November 7, 1940, the nation awoke to the destruction of the Tacoma Narrows Bridge. A 42 mile-per-hour gale caused the bridge to oscillate thus exciting the structural resonances of the bridge to a final destruction frequency of about 14 Hz and a peak-to-peak amplitude of 28 ft. The destruction of the bridge was a wake-up call to the importance of dynamic analysis in structural Fig. 3 Change-in-gain nonlinearity. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved design in addition to static analysis and design. Some sixty years later the technology of dynamic analysis is now well known. To further investigate machine resonances, a typical linear industrial servo drive can be represented as in Figure 4. The mechanical components of this servo drive are referred to as the servo system plant. The servo plant may have a multiplicity of resonant frequencies resulting from a number of degrees of freedom. In actual practice there will be some resonant frequencies that are high in frequency and far enough above the servo drive bandwidth so that they can be ignored. In general there will be a predominant low resonant frequency that could possibly be close enough to the servo drive bandwidth to cause a stability problem. Therefore a single degree of freedom model as shown in Figure 5 can represent the predominant low-resonant frequency, where: B L ¼viscous friction coefficient (lb-in min/rad) T ¼driving torque, developed by the servo motor (lb-in.) K ¼mechanical stiffness of the spring mass model (lb-in./rad) J M ¼inertia of the motor (lb-in sec 2 ) J L ¼inertia of the load (lb-in sec 2 ) S ¼laplace operator From Newton’s second law of motion, the classical equations for this servo plant (industrial machine system) can be written. In most industrial machines it can be assumed that the damping B L is zero. Therefore the Fig. 4 Block diagram of a machine feed drive. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved motor equation is: T M ¼ J M s 2 y M þ Kðy M À y L Þ (11.3-1) Also the load equation is: 0 ¼ J Ls y L þ Kðy L À y M Þ (11.3-2) Solving for the motor position y M and the load position y L : ðJ M s 2 þ KÞy M ¼ T M þ y L (11.3-3) y M ¼ T M þ Ky L J M s 2 þ K (11.3-4) and ðJ L s 2 þ KÞy M ¼ Ky M (11.3-5) y L ¼ Ky M J L s 2 þ K (11.3-6) Fig. 5 Machine slide free-body diagram. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved Further solving for y M and y L by combining Eq. (11.3-4) and (11.3-6): y M ¼ T M þ KðKy M =J L s 2 þ KÞ J M s 2 þ K (11.3-7) y M ¼ T M ðJ L s 2 þ KÞþK 2 y M ðJ M s 2 þ KÞðJ L s 2 þ KÞ (11.3-8) y M ¼ T M ðJ L s 2 þ KÞ ðJ M s 2 þ KÞðJ L s 2 þ KÞ þ K 2 y M ðJ M s 2 þ KÞðJ L s 2 þ KÞ (11.3-9) y M À K 2 y M ðJ M s 2 þ KÞðJ L s 2 þ KÞ ¼ T M ðJ L s 2 þ KÞ ðJ M s 2 þ KÞðJ L s 2 þ KÞ (11.3-10) ððJ M s 2 þ KÞðJ L s 2 þ KÞÀK 2 Þy M ¼ T M ðJ L s 2 þ KÞ (11.3-11) y M ¼ T M ðJ L s 2 þ KÞ ðJ M s 2 þ KÞðJ L s 2 þ KÞÀK 2 (11.3-12) y M ¼ T M ðJ L s 2 þ KÞ J M J L s 4 þ KðJ M þ J L Þs 2 (11.3-13) y M ¼ T M ðJ L s 2 þ KÞ s 2 ðJ M J L s 2 þðJ M þ J L ÞK (11.3-14) y M ¼ T M ðJ L s 2 þ KÞ s 2 ðJ M þ J L ÞððJ M J L =J M þ J L Þs 2 þ KÞ (11.3-15) Let: J ¼ J M þ J L J P ¼ J M J L =ðJ M þ J L Þ y M ¼ T M ðJ L s 2 þ KÞ s 2 Jðs 2 J P þ 1Þ (11.3-16) Also: y L ¼ Ky M J L s 2 þ K (11.3-17) Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved y L ¼ K ðJ L s 2 þ KÞ 6 T M ðJ L s 2 þ KÞ s 2 Jðs 2 J P þ KÞ (11.3-18) y L ¼ T M K s 2 Jðs 2 J p þ KÞ (11.3-19) y L T M ¼ 1 ðJ=KÞs 2 ðs 2 ðJ p =KÞþ1Þ (11.3-20) y L T M ¼ 1 ðJ=KÞs 2 ððs 2 =o 2 r Þþ1Þ (11.3-21) o r ¼ load resonant frequency ¼ ffiffiffiffiffi K J p s ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KðJ M þ J L Þ J M J L s (11.3-22) From a practical point of view industrial machines and their servo drives (hydraulic and electric) are to this day still subject to resonant frequency stability problems. Most industrial servo drives use an inner velocity servo inside a position servo loop. Hydraulic servo drives have the added variable of hydraulic fluid resonance, which can be a limiting factor of stability. The hydraulic resonance o r can be observed as a typical second order response in the Bode frequency response of Figure 6. For hydraulic drives having a low damping factor d h , the resonant peak may be higher than 0 dB gain, which will result in a resonant oscillation. There are a number of methods to compensate for this resonant oscillation. First, a small cross-port damping hole of about 0.002 in. can be used across the motor ports. Secondly, the velocity loop differential compensation can be varied, which quite often eliminates the oscillation. Lastly, the velocity loop gain could be lowered, which can also lower the velocity servo bandwidth. As an index of performance (I.P.) the hydraulic resonance should by proper sizing be above 200 Hz, and the separation between the velocity servo loop bandwidth o c and the hydraulic resonance o h should be three to one or greater. Brushless DC electric drives do not usually have velocity loop resonance problems unless a more compliant coupling is used internally in the motor to couple a position transducer to the motor shaft. Both hydraulic and brushless DC electric drives can have resonance (stability) problems if the machine is included in the position servo loop. This is an ongoing problem with industrial machines, in spite of all the available technology to minimize stability problems. A typical position servo Bode frequency response is shown in Figure 7. As a figure of merit the separation between the velocity loop bandwidth o c and the position-loop velocity constant K v (gain) should be two to one or greater. The machine Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved resonance o r should be at least three times greater than the velocity servo bandwidth o c . However in actual practice the machine resonance inside the position loop is often quite low (such as 15 Hz). The resonant peak in this case should be above 0 dB gain, resulting in a resonant oscillation. There are a number of control techniques that can be applied to compensate for machine structural resonances that are both low in frequency and inside the position servo loop. The first control technique is to lower the position-loop gain K v (velocity constant). Depending on how low the machine resonance is, the position-loop gain may have to be lowered to about 0.5 ipm/mil (8.33/ sec). This solution has been used in numerous industrial positioning servo drives. However, such a solution degrades servo performance. For very large machines this may not be acceptable. The I.P. that the servo loop gain (velocity constant) should be lower than the velocity servo bandwidth by a factor of two, will be compromised in these circumstances. A very useful control technique to compensate for a machine resonance is the use of notch filters. These notch filters are most effective Fig. 6 Hydraulic velocity servo. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved when placed in cascade with the input to the velocity servo drive. These notch filters should have a tunable range from approximately 5 Hz to a couple of decades higher in frequency. The notch filters are effective to compensate for fixed structural resonances. If the resonance varies due to such things as load changes, the notch filter will not be effective. Since most of these unwanted resonant frequencies are analog sinusoidal voltages, a notch filter can effectively remove these frequencies. In digital control the algorithm for the notch filter can be used. A simple analog notch filter is shown in Figure 8 as it appeared in Electronics Magazine, December 7, 1978. This filter is equivalent to a twin T-notch filter but it is an active filter versus passive networks, so there are no signal losses. The frequency of the notch is set by the selection of resistor R. For a 1-microfarad (mF) capacitor (C), the values for R versus the notch frequency are shown in Figure 9. The depth of the notch is adjusted by varying the potentiometer P 1 . Frequency responses of the notch filter for values of R ranging from 40 K ohms to 200 ohms are shown in Figure 10. A 40-Hz notch filter frequency response is shown in Figure 11 with a number of potentiometer settings to Fig. 7 Position loop frequency response. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved [...]... is the servo drive and inner-loop transfer function typically of the following form: GðsÞ ¼ Kv sFðsÞ (11.5-1) F ðsÞ is a polynomial that represents the dynamics of the servo drive and servo plant What is really desired of the servo of Figure 17 is that yi ¼ y0 under all conditions That is, for any yi ; e ¼ 0 Clearly, this is not possible for a type 1 servo described by Figure 17 Fig 16 Type 1 servo. .. type 1 servo control, it is a requirement that each machine axis have matched position-loop gains to maintain accuracy in positioning Quite often this means that all machine axis servo drives must have their position-loop gains K v adjusted to the poorest performing axis Consider the basic approach to the design of a poisoning servo drive illustrated in Figure 16 This is the classical type 1 servo, ... resonance from the position servo loop, resulting in a stable servo drive but with significant position errors These position errors are compensated for by measuring the slide position through a low-pass filter; taking the position difference between the servo motor position and the machine slide position; and making a correction to the position loop, which is primarily closed at the servo motor Compensator... Rights Reserved As a position error is developed between the feed servo- drive motor position ym and machine slide position ys , an error is developed at the instrument servo drive (Figure 13) The error is also a function of yc ye ¼ ym À yc À ys ¼ ðym À ys Þ À yc (11.4-2) It is significant to note that the bandwidth of the instrument correction servo must be a low frequency such as 1.5 Hz This is required... frequency selective feedback control function A correction yc is developed at the output of the instrument servo drive, which is a function of: yc ¼ G1 ½ðym À ys Þ À yc Š (11.4-3) The correction yc is added to the main-feed servo drive by means of resolver (5) The correction yc causes the feed servo drive to move by the amount of the correction Therefore both ym (at the motor) and ys (at the machine... in Figure 14 For illustration the relation of the feed servo- drive position ym to the machine slide position ys will remain constant during the correction Figure 14 shows that the machine slide position ys moves by the amount of the correction The feed servo- drive motor position moves by the same amount From another point of view the instrument servo- drive error must be reduced to zero after the correction... equivalent to 0.01 in.) had to be included in the error of the instrument servo Since the relation of ðym À ys Þ remains constant, a correction must be made in the instrument servo loop to reduce the error to zero: yc ¼ 0 ¼ ðym À ys Þ À yc (11.4-8) The compensator correction resolver (4) serves the purpose to reduce the instrument servo error to zero As the correction process becomes a continual process,... the rear of the servo motor A position transducer such as a resolver will be geared to the motor shaft with a ratio determined by the resolution of the machine slide feedback transducer 11.5 FEEDFORWARD CONTROL The problem of developing an industrial servo drive with high-performance capabilities for accurate positioning is a subject of much importance On multiaxis industrial machine servos using classical... few case histories are of interest In a hydraulic servo valve feed drive, pump pulsations of 500 Hz traveled through the machine piping to the servo valve, the hydraulic motor, and finally the feedback tachometer of the velocity loop The high sensitivity of the tachometer (100 V/1000 rpm) sensed the 500-Hz vibration and generated this voltage into the servo drive electronics, where it was amplified through... circuit with the correction resolver (5) The compensator circuit includes the positioning servo- motor position measuring resolver called a compensator feedback resolver (2), a machine slide linear position measuring transducer (3), and an instrument type correction servo drive The difference between the feed servo- drive motor position and the machine slide position is measured with the compensator . 11 Servo Plant Compensation Techniques Servo compensation usually implies that some type of filter network such as lead/lag. typical linear industrial servo drive can be represented as in Figure 4. The mechanical components of this servo drive are referred to as the servo system plant. The servo plant may have a multiplicity. some industrial servo drives it is a requirement to position to a very low feed rate to obtain a smooth surface finish. This requirement usually occurs Fig. 1 Servo plant compensation techniques. Copyright