CN105786037A

CN105786037A - Input shaper for suppressing residual vibration of mechanical system

Info

Publication number: CN105786037A
Application number: CN201610120646.2A
Authority: CN
Inventors: 吴立; 覃海涛; 田天胜; 李卫平
Original assignee: Shenzhen Leisai Software Technology Co ltd; Leadshine Technology Co Ltd
Current assignee: Shenzhen Leisai Software Technology Co ltd; Leadshine Technology Co Ltd
Priority date: 2016-03-03
Filing date: 2016-03-03
Publication date: 2016-07-20
Anticipated expiration: 2036-03-03
Also published as: CN105786037B

Abstract

The invention discloses an input shaper for inhibiting residual vibration of a mechanical system, which is characterized in that the transfer function of the shaper is as follows:wherein k is₁、k₂、k₃、k₄Is a gain coefficient and n is a time lag coefficient. The input shaper reduces system impact: the step signal can be differentiated in the first order, is similar to a first-order filter, eliminates medium-high frequency vibration and impact of moment, is suitable for a mechanical system with poor rigidity, and can reduce mechanical abrasion.

Description

Suppress the input shaper of mechanical system residual vibration

[technical field]

The present invention relates to mechanical system control field, be specifically related to suppress the input shaper of mechanical system residual vibration.

[background technology]

In positioning control system, due to the reason such as plant equipment end rigidity is relatively low, can there is low-frequency vibration in plant equipment end, be commonly referred to residual vibration when state switches, thus affecting positioning precision.The general suppression to low-frequency vibration mainly has three kinds of approach: (1) Optimal Structure Designing, (2) feedback control, (3) input shaper.Optimal Structure Designing it is generally required to by increase mass of system increase system damping, improve system stiffness, but this will affect speed responsive or increase system energy consumption；Feedback control needs to increase sensor and testing circuit, makes system cost increase, and sensor is inconvenient to install sometimes, and poor signal is measured.Input shaper technology realizes quickly location with simple opened loop control, and can effectively suppress residual vibration, therefore is used widely in high speed and super precision alignment system.Conventional input shaper mainly has the notch filter etc. that ZV (zero vibration) reshaper, ZVD (zero vibration and zero derivative) reshaper, each servo producer servo-driver are integrated.

If Fig. 1, ZV input shaper is to after original step signal a shaping, obtaining output waveform b1, if Fig. 2, ZVD input shaper is to after original step signal a shaping, obtain output waveform b2, notch filter, to after original step signal a shaping, obtains output waveform b3.

Although existing input shaper can effectively suppress residual vibration, but during to the shaping of step signal, its shaping output signal still has sudden change, and system has impact, influential system running stability.The integrated notch filter of each servo producer servo-driver impacts little, but has conditions of streaking, and response speed is slow.The shaping output signal schematic diagram of conventional input shaper as shown in Figure 1.

[summary of the invention]

When the present invention solves existing input shaper to step signal shaping, shaping output still has transition, system have impact and harmonic shaping export the problem with conditions of streaking, novel input shaper is proposed, make mechanical system while suppressing residual vibration, reduce the step response impact to system.

Suppressing the input shaper of mechanical system residual vibration, the transmission function of input shaper is:

H (z) = \frac{1}{n \cdot (1 - z^{- 1})} \cdot (k_{1} + k_{2} \cdot z^{- n} + k_{3} \cdot z^{- 2 n} + k_{4} \cdot z^{- 3 n}),

Wherein, k₁、k₂、k₃、k₄For gain coefficient, n is time delay.

In one embodiment,

\{\begin{matrix} k_{1} = 1 \\ k_{2} = - 2 \\ k_{3} = 2 \\ k_{4} = - 1 \\ n = \frac{f_{s}}{6 f} \end{matrix}

f_sFor the input shaper sample frequency to command input signals, f is the frequency of residual vibration needing to suppress, and n is positive integer.

Described mechanical system is the rigidity mechanical system less than rigidity threshold value.

The present invention has the beneficial effects that:

This input shaper decreases system shock: to step signal can single order differentiable, similar firstorder filter, eliminate the medium-high frequency vibration of moment and impact, it is adaptable to rigidity inferior mechanical system, and mechanical wear can be reduced.

The shaping output signal of step signal is broken line shape by novel input shaper, it does not have Spline smoothing, also without conditions of streaking.

The gain coefficient of this input shaper is fixed, and its Slack time is only relevant with system sampling frequency and residual vibration frequency, it is not necessary to considers system damping coefficient, greatly reduces the design difficulty of input shaper.

This input shaper is possible not only to suppress the residual vibration of required elimination, the residual vibration amplitude of high frequency also can also must decay simultaneously, but also can suppress the input of high frequency noise.

[accompanying drawing explanation]

Fig. 1 is the shaping output signal schematic diagram of the ZV input shaper of prior art

Fig. 2 is the shaping output signal schematic diagram of the ZVD input shaper of prior art

Fig. 3 is the shaping output signal schematic diagram of the notch filter of prior art

Fig. 4 is the input shaper transmission function block diagram of the suppression mechanical system residual vibration of an embodiment of the present invention

Fig. 5 is Fig. 4 shaping output signal schematic diagram suppressing the input shaper of mechanical system residual vibration

Fig. 6 is the transmission function block diagram of the input shaper of the suppression mechanical system residual vibration of an embodiment of the present invention

Fig. 7 is the amplitude-versus-frequency curve figure of Fig. 6 input shaper and ZV shaping

Fig. 8 is the amplitude-versus-frequency curve figure of Fig. 6 input shaper and ZV shaping

Fig. 9 is various time domain beamformer

[detailed description of the invention]

Hereinafter the preferred embodiment of invention is described in further detail.

Embodiment 1

As shown in Figures 4 and 5, the input shaper of the suppression mechanical system residual vibration of an embodiment, the transmission function of reshaper is:

H (z) = \frac{1}{n \cdot (1 - z^{- 1})} \cdot (k_{1} + k_{2} \cdot z^{- n} + k_{3} \cdot z^{- 2 n} + k_{4} \cdot z^{- 3 n}),

Formula 1-1

Wherein, k₁、k₂、k₃、k₄For gain coefficient, n is time delay.

Control instruction for mechanical end comprises original step signal a, such as, control instruction needs to control mechanical end and arrives certain position from initial position, the reshaping signal b4 of output after the shaping of reshaper, from figure 3, it can be seen that the shaping output signal of step signal is broken line shape by this novel input shaper, it does not have Spline smoothing, thus reducing the impact of system, and the frequency of mechanical system residual vibration effectively can be suppressed.

In one embodiment,

\{\begin{matrix} k_{1} = 1 \\ k_{2} = - 2 \\ k_{3} = 2 \\ k_{4} = - 1 \\ n = \frac{f_{s}}{6 f} \end{matrix}

Formula 1-2

In formula 1-2, gain coefficient k₁、k₂、k₃、k₄Immobilize, f_sFor system sampling frequency, f is the frequency of residual vibration needing to suppress, and time delay n belongs to positive integer, if there is decimal, then and round, and n minima takes 1.

Novel input shaper is compared with ZV reshaper, ZVD reshaper, many integrators, and gain coefficient fixes, and its Slack time is only relevant with system sampling frequency and residual vibration frequency, without considering system damping coefficient, greatly reduce the design difficulty of input shaper.

Embodiment 2

Novel input shaper and ZV reshaper are contrasted by the present embodiment by MATLAB emulation.

Considering the mechanical system that there is residual vibration, its transmission function is such as shown in formula 1-3.

G (s) = \frac{2763 s^{2} + 15590000}{s^{4} + 125.7 s^{3} + 7896 s^{2} + 496100 s + 15590000}

Formula 1-3

S1, design novel input shaper

As sample frequency f_s=12000Hz, it is necessary to during the frequency f=10Hz of the residual vibration of suppression, formula 1-3 obtain formula 1-4:

\{\begin{matrix} k_{1} = 1 \\ k_{2} = - 2 \\ k_{3} = 2 \\ k_{4} = - 1 \\ n = \frac{f_{s}}{6 f} = \frac{1200}{6 \times 10} = 200 \end{matrix}

Formula 1-4

The novel input shaper transmission function designed by formula 1-4 is such as shown in formula 1-5.

H (z) = \frac{1}{200 (1 - z^{- 1})} \cdot (1 - 2 z^{- 200} + 2 z^{- 400} - z^{- 600})

Formula 1-5

Novel input shaper embodiment transmission function block diagram as shown in Figure 6 is obtained by formula 1-5.

S2, design ZV reshaper

As sample frequency f_s=12000Hz, it is necessary to during the frequency f=10Hz of the residual vibration of suppression, design obtains the transmission function such as ZV reshaper shown in formula 1-6.

H (z) = \frac{1}{2} (1 + z^{- 600})

Formula 1-6

It is the amplitude-versus-frequency curve figure of novel input shaper and ZV shaping as shown in Figure 7 and Figure 8.

From figure 7 it can be seen that needing to suppress the residual vibration place of frequency f=10Hz, novel input shaper and ZV reshaper can both suppress to be 0 by the amplitude of residual vibration.

From figure 8, it is seen that the residual vibration of high frequency is also had an attenuation by novel input shaper, and the undamped effect of residual vibration that ZV reshaper is to major part high frequency.

In Fig. 9, the time domain waveform L1 of novel input shaper output, the output of ZV reshaper time domain waveform L5, use ZV reshaper system unit step response time domain waveform L4, use the system unit step response time domain waveform L3 of Novel shaping device, without the time domain waveform L2 of system unit step response of input shaper.The unit step input without input shaper in Fig. 9 is mingled with high frequency noise.

As can be seen from Figure 9:

(1) the output broken line shape of novel input shaper, it does not have Spline smoothing, also without conditions of streaking, can filter high frequency noise simultaneously, and ZV reshaper is output as stairstepping, still has Spline smoothing, but cannot filter high frequency noise.

(2) there is reforming phenomena in the system unit step response without input shaper, and the system unit step response employing input shaper eliminates reforming phenomena.

(3) use novel input shaper and use the system unit step response curve of ZV reshaper almost to overlap, illustrating that novel input shaper and ZV reshaper are suitable to the inhibition of system reforming phenomena.

Above content is in conjunction with concrete preferred implementation further description made for the present invention, it is impossible to assert that specific embodiment of the invention is confined to these explanations.For general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, it is also possible to make some simple deduction or replace, the scope of patent protection that the present invention is determined all should be considered as belonging to by submitted claims.

Claims

1. suppressing the input shaper of mechanical system residual vibration, it is characterized in that, the transmission function of input shaper is:

H (z) = \frac{1}{n \cdot (1 - z^{- 1})} \cdot (k_{1} + k_{2} \cdot z^{- n} + k_{3} \cdot z^{- 2 n} + k_{4} \cdot z^{- 3 n}),

Wherein, k₁、k₂、k₃、k₄For gain coefficient, n is time delay.

2. the input shaper suppressing mechanical system residual vibration as claimed in claim 1, is characterized in that, k₁=1.

3. the input shaper suppressing mechanical system residual vibration as claimed in claim 1, is characterized in that, k₂=-2.

4. the input shaper suppressing mechanical system residual vibration as claimed in claim 1, is characterized in that, k₃=2.

5. the input shaper suppressing mechanical system residual vibration as claimed in claim 1, is characterized in that, k₄=-1.

6. the input shaper suppressing mechanical system residual vibration as claimed in claim 1, is characterized in that,f_sFor the input shaper sample frequency to command input signals, f is the frequency of residual vibration needing to suppress.

7. the input shaper suppressing mechanical system residual vibration as claimed in claim 1, is characterized in that, n is positive integer.

8. the input shaper suppressing mechanical system residual vibration as claimed in claim 1, is characterized in that, described mechanical system is the rigidity mechanical system less than rigidity threshold value.