CN111913506A - Terminal vibration suppression method based on equivalent input interference and input shaper - Google Patents
Terminal vibration suppression method based on equivalent input interference and input shaper Download PDFInfo
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Abstract
The invention provides a terminal vibration suppression method based on equivalent input interference and an input shaper, which comprises the following steps: modeling an elastic connecting device of a servo system to obtain a system model of the elastic connecting device; designing an input shaper according to the system model to inhibit the influence of disturbance; and according to the system model, equivalent input interference is introduced, and the influence of disturbance is further eliminated. The invention has the beneficial effects that: the method is used for constructing a system based on equivalent input interference and an input shaper, firstly, the input shaper is used for restraining vibration when the input of the system is changed, the vibration of the system is small when the system is not disturbed, and when the input of the system is unchanged, parameters are changed or external disturbance exists, the equivalent input interference is introduced for disturbance restraint, and further the dynamic performance of the system is improved.
Description
Technical Field
The invention relates to the field of motor control, in particular to a terminal vibration suppression method based on equivalent input interference and an input shaper.
Background
With the development of power electronic technology, microelectronic technology and motor manufacturing technology for many years, the performance of a servo system is greatly improved. The servo control technology has been deeply applied to various social fields from resident life, industrial production to military weapons and the like, and is a branch which is the most closely connected with industrial departments and has the most extensive service in the automation subject. In the application of these servo systems to industrial robots, some high reduction ratio mechanisms are commonly used in industrial robots to achieve high load ratio performance, such as some harmonic gears, and another is a load actuator made of light or flexible material, which has the advantages of light weight, low cost, compact structure, high safety, etc., and is gradually applied to the fields of manufacturing, robot arms, etc. The elastic gear reduction device in the driving system can cause a lag error of position transmission, and when the servo system is suddenly positioned at a high rotating speed, the load tail end of the servo system can generate a strong buffeting phenomenon, namely tail end vibration.
The existence of the tail end vibration can seriously reduce the positioning precision and the movement precision of the servo system, influence the accurate positioning and the quick and stable carrying of the system, even generate obvious noise, and particularly have obvious influence on the tail end vibration in the high-speed movement process. Meanwhile, the long-term existence of the residual vibration can also cause the deformation of the connecting rod and the loosening of the moving part, and cause the reduction of the movement performance of the mechanism and the fatigue failure of the mechanical structure. Therefore, the suppression of the positioning jitter of the servo system is a key common technology in the field of motor driving, and has very important significance for improving the stability of the servo system and the dynamic response quality of the system.
Similar published patents exist:
industrial robot vibration suppression method (CN 111015738A) Shanghai Zhi Yin Automation technology Co Ltd
The steps of the patent are:
the method comprises the following steps: dividing the motion range of each axis of the industrial robot into a plurality of parts, measuring the torsional rigidity corresponding to each joint angle by using a torsional rigidity measuring device according to the subdivided joint angle nodes, and obtaining each axis joint angle from the track information planned by the upper controller;
step two: interpolating the torsional rigidity of each axis determined by subdivision according to the joint angle of each axis to obtain corresponding torsional rigidity, calculating the equivalent inertia of each axis joint angle and the equivalent inertia of each axis, and calculating the center frequency of the notch filter according to the torsional rigidity and the equivalent inertia;
step three: and filtering the resonance frequency signal of each axis track signal by a notch filter obtained by calculating each axis, and sending the filtered signal to a servo driver for execution.
Force control end actuating mechanism and force control method (CN 110861097A) Ningbo material technology and engineering research institute of Chinese academy of sciences for reducing vibration of mechanical arm
The steps of the patent are:
the method comprises the following steps: obtaining, by means of a sensor, a contact force signal of the end-effector with the environment received by the force sensor and a frequency response function H (ω) of a response signal of the first sensor, including Z from impedance information of the industrial robotM、ZB、ZK、ZM、ZB、ZKRespectively representing inertia, damping and rigidity of the industrial robot in an acceleration impedance mode, and establishing a dynamic model of an integral system formed by the industrial robot and an end effector;
step two: expressing the dynamic model according to the step one as a dynamic equation of the industrial robot, a dynamic equation of the end effector and an integral dynamic equation of the industrial robot and the end effector, and converting corresponding parameters in the dynamic equation into impedance so as to conveniently analyze the force control method;
step three: the impedance of the serial coupling part of the industrial robot and the end effector is obtained through impedance conversion, signals collected by the acceleration sensor and the acceleration sensor are input into the impedance compensator and processed by the impedance compensator, and then compensation force is output, so that vibration is suppressed.
Control method (CN 105375850B) of motor vibration suppression for Nanjing Estan automatic control technology Limited company
The steps of the patent are:
the method comprises the following steps: the motor is sampled in the whole rotation process, the sampling result is firstly stored in a buffer area, and then the stored sampling result is subjected to fast Fourier transform and is converted to a frequency domain, so that the analysis is convenient;
step two: using motor speed vibration frequency average value omega0On the basis, the surrounding frequencies are analyzed simultaneously, the sizes of different conditions are calculated according to the amplitudes of the different conditions, and filter parameters meeting the actual engineering requirements are designed according to the central frequency so as to achieve the purpose of suppressing the vibration tail end;
step three: and analyzing the amplitude-frequency characteristic after the filter is designed, and judging whether the vibration suppression condition meets the actual requirement. If the requirements are met, finishing the configuration of the filter; if the requirement is not met, analyzing the reason, which is most probably because the vibration center frequency is not completely attenuated due to improper filter parameter values, and returning to the second step to re-sample and configure the filter.
There are many methods for the end-shake phenomenon, and the three patents mentioned above are based on notch filter and compensation control, and actively analyze the frequency and suppress the shake of the frequency. The above-described method still has many disadvantages. Firstly, an input shaper method generally needs FFT to accurately acquire vibration frequency, but the FFT needs a certain amount of data cache to acquire frequency information, so that adjustment is performed according to the information, a large lag is ensured, and particularly when the vibration frequency is changed; secondly, compensation control is carried out according to modeling, wherein a sensor of the end effector acquires system parameters and then compensation is added; a further common method is an input shaper method, which is designed based on system parameters and has a good effect of suppressing the system with little variation of the system parameters, but when internal parameters are changed, the effect of suppressing subsequent vibrations is deteriorated or even lost.
In summary, these methods all have certain disadvantages, and they mostly do not consider external disturbance and change of system parameters, but there is disturbance in the actual situation, when the system tends to a steady state, the load is unloaded and suddenly changes, at this time, the end forms a new end vibration again due to elastic potential energy, and when the load change is large, the vibration amplitude is also large, resulting in poor dynamic effect of the system.
The commonly used suppression method is mainly used for robust control or active disturbance suppression, and the equivalent input disturbance is widely applied with the advantages of capability of suppressing unmatched disturbance and simple structure, and convenience for complementation with other methods.
Disclosure of Invention
In order to solve the problem that disturbance change is not considered in the prior art, the invention provides a terminal vibration suppression method based on equivalent input interference and an input shaper, which is used for suppressing the terminal vibration of a system in two stages: firstly, the input shaper is utilized to restrain the vibration of the input in the changing process, the system vibration is small when the system is not disturbed, when the input is not changed, the system parameters are changed or external disturbance exists, equivalent input interference is introduced to restrain the disturbance, and the dynamic performance of the system is further improved.
The terminal vibration suppression method based on equivalent input interference and an input shaper is characterized by comprising the following steps of: the method comprises the following steps:
s101: modeling an elastic connecting device of a servo system to obtain a system model of the elastic connecting device;
s102: designing an input shaper according to the system model to inhibit the influence of disturbance;
s103: according to the system model, equivalent input interference is introduced, the influence of disturbance is further eliminated, and the dynamic performance of the servo system is improved.
Further, in step S101, the system model includes: transfer function G of motor speed1(s) transfer function G of load speed2(s) and transfer function G of electromagnetic torqueω(s); specifically, as shown in formula (1):
in the above formula, C1The damping coefficient of the rotating shaft of the driving motor; c2Is the load spindle damping coefficient; cωThe damping coefficient of the transmission shaft; j. the design is a square1Is the rotational inertia of the rotating shaft of the driving motor; j. the design is a square2Is the moment of inertia of the load motor; omega1The rotating speed of a rotating shaft of the driving motor; omega2Is the load motor speed; theta1The rotation angle of the rotating shaft of the driving motor is set; theta2Turning a load motor; t iseIs the active motor electromagnetic torque; t islIs the load motor electromagnetic torque; t isωIs the torque of the transmission shafting; k is the torsional elasticity coefficient of the transmission shaft.
Further, in step S102, according to the system model, an input shaper is designed, influence of disturbance is suppressed, and an ideal model is constructed; the method specifically comprises the following steps:
according to a system model, the system is a typical second-order oscillation link, and because the input shaper is composed of a series of pulse signals with different amplitudes and time lags, the pulse expression formula I (t) of the input shaper is obtained as shown in formula (2):
in the above formula, n is the number of pulses in the input shaper; a. theiThe amplitude of the ith pulse signal; t is tiIs the time lag of the ith pulse signal; t is time.
Further, the pulse expression of the input shaper is as follows:
in the above formula, the first and second carbon atoms are,
omega is the natural vibration frequency of the system,
is the system damping ratio.
Further, in step S103, according to the system model, equivalent input interference is introduced; the method comprises the following steps:
s201: the state space expression of the servo system is as formula (3):
in the above formula, A, B, C is a constant system parameter, obtained by simultaneous G1(s)、G2(s)、Gω(s) obtaining; x (t) is the system state, u (t) is the control input, y (t) is the system output, d (t) is the actual disturbance;
is the first differential of x (t);
s202: the equivalent input interference comprises a state observer and a disturbance estimator, wherein the interference is observed by the state observer, and the equivalent input interference is obtained through a low-pass filter F(s) in the disturbance estimator; wherein, the expression of the state observer is as formula (4):
in the above equation, L is the gain of the state observer,
and
is the observed values of x (t) and y (t);
is that
First order differentiation of;
s204: obtaining the equivalent value of disturbance at the input end by designing the gain L of the state observer and the parameters of a low-pass filter F(s) in the disturbance estimator
Further, in step S204, the gain L of the state observer is calculated by the linear quadratic regulator LQR algorithm, and the parameter of the low pass filter f (S) in the disturbance estimator is adjusted according to the system baud chart to realize disturbance suppression.
The technical scheme provided by the invention has the beneficial effects that: the method is used for constructing a system based on equivalent input interference and an input shaper, firstly, the input shaper is used for restraining vibration when the input of the system is changed, the vibration of the system is small when the system is not disturbed, and when the input of the system is unchanged, parameters are changed or external disturbance exists, the equivalent input interference is introduced for disturbance restraint, and further the dynamic performance of the system is improved.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method for tip vibration suppression based on equivalent input disturbances and an input shaper in an embodiment of the present invention;
FIG. 2 is a schematic representation of an exemplary dual inertia mechanical transmission model in an embodiment of the present invention;
FIG. 3 is a schematic diagram of an input shaper in an embodiment of the invention;
fig. 4 is a schematic structural diagram of equivalent input interference in the embodiment of the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
Embodiments of the present invention provide a method of tip vibration suppression based on equivalent input disturbances and input shapers.
Referring to fig. 1, fig. 1 is a flowchart of a method for suppressing end vibration based on equivalent input disturbance and an input shaper according to an embodiment of the present invention, which specifically includes the following steps:
s101: modeling an elastic connecting device of a servo system to obtain a system model of the elastic connecting device;
s102: designing an input shaper according to the system model, inhibiting the influence of disturbance and constructing an ideal model;
s103: according to the system model, equivalent input interference is introduced, the influence of disturbance is further eliminated, and the dynamic performance of the servo system is improved.
Referring to FIG. 2, FIG. 2 is a model schematic diagram of an exemplary dual inertia mechanical transmission in accordance with an embodiment of the present disclosure; the relation is as formula (1):
in the above formula, the first and second carbon atoms are,
the rotating speed of the rotating shaft of the driving motor,
is the angular acceleration of the rotating shaft of the active motor;
load motor angular velocity;
is the angular acceleration of the load motor.
In step S101, the system model includes: transfer function G of motor speed1(s) transfer function G of load speed2(s) and transfer function G of electromagnetic torqueω(s); neglecting the damping coefficient, the transfer functions of the motor speed, the load speed and the electromagnetic torque are obtained as shown in formula (2):
wherein, the parameters and contents of the system are shown in the following table:
the parameters in the table above can be obtained through the motor delivery specification, and can also be obtained through a parameter identification method.
Referring to fig. 3, fig. 3 is a schematic diagram of an input shaper; in FIG. 3, A1Is the vibration, A, initially generated2Effect of input from the shaper, A1+A2Is the effect after the superposition of the vibration and the input shaper.
Neglecting the damping coefficient CωTransfer function G of electromagnetic torqueω(s) a typical second order oscillating element. The input shaper is now designed to cancel this vibration. The essence of the input shaper is to shape the input command into a series of input sequences of different amplitudes and time lags, so that the responses generated by multiple inputs are superposed to zero, thereby suppressing residual oscillation. The effect is shown in FIG. 3, assuming T1The amplitude of the moment action is A1The system generates pulses as in a of fig. 31The oscillation period of the oscillation curve of (1) is T. In that
The amplitude of the moment action is A2Of (2) is performed. According to the superposition principle of a linear system, two oscillations are mutually counteracted, and finally, the generated residual oscillation is 0. The input shaper analyzes from the time domain, integrates the input signal into a signal which rises section by section, and generates an upward input when vibrating downwards, so that the counteracting effect can be achieved.
In step S102, designing an input shaper according to the system model, suppressing the influence of disturbance, and constructing an ideal model; the method specifically comprises the following steps:
according to a system model, the system is a typical second-order oscillation link, and because the input shaper is composed of a series of pulse signals with different amplitudes and time lags, the pulse expression formula I (t) of the input shaper is obtained as shown in formula (3):
in the above formula, n is the number of pulses in the input shaper; a. theiThe amplitude of the ith pulse signal; t is tiIs the time lag of the ith pulse signal; t is time.
The specific design idea is as follows:
s201: firstly, the system model is simplified into a common second-order system, and the transfer function of the system model is shown as formula (4):
in the above formula, ω is the natural frequency of the system,
the system damping ratio; the step response of the system is shown in equation (5):
in the above formula, the first and second carbon atoms are,
t0is the moment of the step input action;
the sum of the responses of the n pulse sequences is then:
applying trigonometric equations, equation (7) can be derived:
defining:
after n steps are appliedThe ratio of the amplitude of the oscillating portion to the amplitude of the oscillating portion of the unit step response is defined as the system residual oscillation:
suppression of residual oscillation of the system to 0, i.e. required
And
all equal to 0, and the steady state response of the command after passing through the shaper is consistent with the steady state response of the original command, there are:
the following can be obtained in a simultaneous manner: t is t1＝0,
Taking n as 2, then carrying the n into a formula of a pulse expression formula I (t) of the input Shaper to calculate to obtain an expression of ZV _ Shaper (zero oscillation Shaper), and finally carrying out algebraic operation by carrying corresponding system parameters to finish the design of the input Shaper.
The equivalent input interference is widely applied with the advantages that the unmatched disturbance can be suppressed and the structure is simple, so that the method is complementary with other methods. The structure of the equivalent input interference is shown in fig. 4.
In step S103, according to the system model, equivalent input interference is introduced; the method comprises the following steps:
s201: the state space expression of the servo system is as formula (8):
where x (t) is the system state, u (t) is the control input, y (t) is the system output, d (t) is the actual disturbance,
is the first differential of x (t); A. b, BdC is a constant system parameter, by simultaneous G1(s)、G2(s)、Gω(s) obtaining; specifically, G is1(s)、G2(s)、Gω(s) is converted into a corresponding state space equation, and then the corresponding state space equation is corresponding to a standard system formula (4), so that A, B, B can be obtainedd、C；
S202: since the perturbation d (t) is unknown, consider: b × d (t) ═ BdX d (t), transforming the state space expression into formula (9):
s203: the equivalent input interference comprises a state observer and a disturbance estimator, wherein the interference is observed by the state observer, and the equivalent input interference is obtained through a low-pass filter F(s) in the disturbance estimator; wherein, the expression of the state observer is as the formula (10):
in the above equation, L is the gain of the state observer,
and
is the observed values of x (t) and y (t);
is that
First order differentiation of;
s204: obtaining the equivalent value of disturbance at the input end by designing the gain L of the state observer and the parameters of a low-pass filter F(s) in the disturbance estimator
As shown in FIG. 4, wherein B+＝(BTB)-1BT，uf(t) is the output of the PID controller.
In step S204, the gain L of the state observer is calculated through a linear quadratic regulator LQR algorithm, and the parameter of a low-pass filter F (S) in the disturbance estimator is adjusted according to the system baud chart to realize disturbance suppression.
The invention has the beneficial effects that: the method is used for constructing a system based on equivalent input interference and an input shaper, firstly, the input shaper is used for restraining vibration when the input of the system is changed, the vibration of the system is small when the system is not disturbed, and when the input of the system is unchanged, parameters are changed or external disturbance exists, the equivalent input interference is introduced for disturbance restraint, and further the dynamic performance of the system is improved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (6)
1. A method for suppressing terminal vibration based on equivalent input interference and an input shaper is characterized in that: the method comprises the following steps:
s101: modeling an elastic connecting device of a servo system to obtain a system model of the elastic connecting device;
s102: designing an input shaper according to the system model to inhibit the influence of disturbance;
s103: according to the system model, equivalent input interference is introduced, the influence of disturbance is further eliminated, and the dynamic performance of the servo system is improved.
2. The method of claim 1 for tip vibration suppression based on equivalent input disturbance and input shaper, wherein: in step S101, the system model includes: transfer function G of motor speed1(s) transfer function G of load speed2(s) and transfer function G of electromagnetic torqueω(s); specifically, as shown in formula (1):
in the above formula, C1The damping coefficient of the rotating shaft of the driving motor; c2Is the load spindle damping coefficient; cωThe damping coefficient of the transmission shaft; j. the design is a square1Is the rotational inertia of the rotating shaft of the driving motor; j. the design is a square2Is the moment of inertia of the load motor; omega1The rotating speed of a rotating shaft of the driving motor; omega2Is the load motor speed; theta1The rotation angle of the rotating shaft of the driving motor is set; theta2Turning a load motor; t iseIs the active motor electromagnetic torque; t islIs the load motor electromagnetic torque; t isωIs the torque of the transmission shafting; k is the torsional elasticity coefficient of the transmission shaft.
3. The method of claim 1 for tip vibration suppression based on equivalent input disturbance and input shaper, wherein: in step S102, designing an input shaper according to the system model, suppressing the influence of disturbance, and constructing an ideal model; the method specifically comprises the following steps:
according to a system model, the system is a typical second-order oscillation link, and because the input shaper is composed of a series of pulse signals with different amplitudes and time lags, the pulse expression formula I (t) of the input shaper is obtained as shown in formula (2):
in the above formula, n is the number of pulses in the input shaper; a. theiThe amplitude of the ith pulse signal; t is tiIs the time lag of the ith pulse signal; t is time.
4. A method of suppressing tip vibration based on an equivalent input disturbance and input shaper as set forth in claim 3, characterized in that: the pulse expression of the input shaper is shown as I (t):
in the above formula, the first and second carbon atoms are,
omega is the natural vibration frequency of the system,
is the system damping ratio.
5. The method of claim 1 for tip vibration suppression based on equivalent input disturbance and input shaper, wherein: in step S103, according to the system model, equivalent input interference is introduced; the method comprises the following steps:
s201: the state space expression of the servo system is as formula (3):
in the above formula, A, B, C is a constant system parameter, obtained by simultaneous G1(s)、G2(s)、Gω(s) obtaining; x (t) is the system state, u (t) is the control input, y (t) is the system output, d (t) is the actual disturbance;
is the first differential of x (t);
s202: the equivalent input interference comprises a state observer and a disturbance estimator, wherein the interference is observed by the state observer, and the equivalent input interference is obtained through a low-pass filter F(s) in the disturbance estimator; wherein, the expression of the state observer is as formula (4):
in the above equation, L is the gain of the state observer,
and
is the observed values of x (t) and y (t);
is that
First order differentiation of;
s204: obtaining the equivalent value of disturbance at the input end by designing the gain L of the state observer and the parameters of a low-pass filter F(s) in the disturbance estimator
6. The method of claim 5 for tip vibration suppression based on equivalent input disturbance and input shaper, wherein: in step S204, the gain L of the state observer is calculated through a linear quadratic regulator LQR algorithm, and the parameter of a low-pass filter F (S) in the disturbance estimator is adjusted according to the system baud chart to realize disturbance suppression.
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| CN114215357A (en) * | 2021-11-11 | 2022-03-22 | 浙江大学 | Pump truck arm support tail end vibration suppression method based on combination of input shaping and time-lag compensation |
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