Method for controlling mechanical vibrations

Abstract

The application provides a mechanical vibration control method, and belongs to the technical field of advanced manufacturing and automation. The application provides a 15-segment non-smooth segmented smoother, which can be used in vibration control of a mechanical system. The application solves the problems of long adjustment time of smooth curves, poor adaptability to system dynamic behavior change, and poor robustness. The application solves the problem that input shaping technology may have large boundary impact. The application solves the problem that feedback control is difficult to detect vibration state and is limited in application. The application solves the problem that the adjustment time of part of the Command smoothing technology is fixed and long. The main point of the 15-segment non-smooth segmented smoother is to combine a notch filter and a low-pass filter. The vibration of the main vibration mode can be suppressed by the notch filter characteristic, and the vibration of the high mode can be controlled by the low-pass filter characteristic. The implementation process of the method is embodied in the specific embodiments.

Description

TECHNICAL FIELD

[0001] The present application relates to a control method aiming at reducing the vibration of a mechanical system. The method involves filtering the driving command using a 15-segment non-smooth piecewise smoother, and driving the mechanical system with the processed command to control the vibration, belonging to the technical field of advanced manufacturing and automation. BACKGROUND

[0002] With the increasing demand for lightweight structures, more and more mechanical systems are adopting lightweight structures. Beams, shafts, links, plates, ropes and membranes are typical lightweight structures, and their technical characteristics are low frequency and small damping, so they are prone to sustained vibration. This will affect the motion performance of the mechanical system and also threaten the safe operation. The vibration control methods mainly include smooth curve, input shaping and closed-loop feedback control.

[0003] Smooth curves are widely used in numerical control systems due to their low-pass filtering characteristics, which can eliminate vibration. The advantages of smooth curves include not requiring prior knowledge of system dynamic performance, and having good application prospects in high-order complex systems with unknown dynamic processes. However, they have a long adjustment time and poor adaptability to changes in system dynamic behavior, resulting in poor robustness.

[0004] The input shaping technology mentioned in US patents 4916635 and 5638267 does not use the principle of smooth functions to drive machines. However, it constructs a shaped command by convolving the input command with a series of pulses, and then drives the machine motion. The shaper based on discrete convolution is called input shaper, and commonly used input shapers include ZVshaper, ZVD shaper, EI shaper and SI shaper. These technologies have been successfully applied in three-coordinate measuring machines, industrial cranes, robot vibration control, etc. However, due to the discontinuity of the shaped command constructed by input shaping, large shocks may occur near the boundary.

[0005] Linear control, nonlinear control and intelligent control are common in feedback control methods, which are usually used to suppress vibration by detecting the vibration state and forming a closed-loop feedback. Feedback control has been applied in various fields such as industrial cranes and flexible robots. However, in some cases, it is difficult to detect the vibration state, making feedback control in practical applications limited.

[0006] Command smoothing techniques convolve the original drive command with a continuous function to produce a smoothed command to drive the machine motion. Several Command smoothing techniques are provided in invention patents 201210507110.8, 201810198149.3 and 202110271019.X to control the vibration of a mechanical system. However, these methods have a fixed regulation time of twice the oscillation period of the damping, which is long for many applications and the time cannot be adjusted. SUMMARY

[0007] The technical problem to be solved by the 15-segment non-smooth piecewise smoother provided by the present application is to solve the problems of long adjustment time of the smoothed curve, poor adaptability to changes in system dynamic behavior, and poor robustness; to solve the problem that the input shaping technique may generate large impact near the boundary; to solve the problem that feedback control is limited in application due to the difficulty of detecting the vibration state in some cases; and to solve the problem of fixed and long regulation time of several Command smoothing techniques provided in invention patents 201210507110.8, 201810198149.3 and 202110271019.X.

[0008] The purpose of the present application is achieved by the following technical solutions.

[0009] Step one, estimate the frequency and damping ratio of the mechanical system for the design of the 15-segment non-smooth piecewise smoother.

[0010] Step two, filter the drive instruction by the 15-segment non-smooth piecewise smoother.

[0011] Step three, the mechanical system is driven by the filtered instruction to control the vibration.

[0012] The beneficial effects of the present application are as follows:

[0013] The present application can effectively control the vibration of a mechanical system. By using the technical solutions provided by the present application, both the vibration of the mechanical system can be reduced and the best working efficiency and operation safety can be achieved. The 15-segment non-smooth piecewise smoother provided by the present application has variable regulation time and good adaptability to changes in system dynamic behavior, good robustness, small impact near the boundary, and small application limitation. Finally, a specific example is given to illustrate how the present method controls the vibration of a mechanical system. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 A mechanical system vibration control process diagram is shown.

[0015] Figure 2 frequency sensitive plot;

[0016] Figure 3 spring swing time domain plot;

[0017] Figure 4 spring swing time domain plot;

[0018] Figure 5 spring swing time domain plot;

[0019] Figure 6 spring swing time domain plot;

[0020] Figure 7 spring swing time domain plot;

[0021] Figure 8 spring swing time domain plot; DETAILED DESCRIPTION

[0022] The control method will be described in detail below in conjunction with the accompanying drawings and embodiments. The aspects of the present application will be described, but the ordinary skilled person only needs to use all or part of the structure and process to put the present application into practice. In order to clearly illustrate, specific numbers, sequences and configurations have been mentioned, but the present application is also feasible without these specific details. For the features well known to people, this paper will not be specifically introduced, so as to avoid confusion.

[0023] Figure 1 The vibration control process diagram of the mechanical system. The system has a 15-segment non-smooth segmented smoother for filtering processing of the driving instruction and driving the mechanical system movement to control vibration. The following is the design process of the 15-segment non-smooth segmented smoother. The second-order mechanical system response of function c:

[0024]

[0025] Where: ω is the natural frequency of the second-order mechanical system, ζ is the damping ratio of the second-order mechanical system, e is the natural constant, t and τ are time, and c is the function name. The corresponding amplitude is:

[0026]

[0027] Where:

[0028]

[0029] (3) and (4) are constrained to zero to achieve zero residual vibration. Function c also has a unit gain

[0030] Constraints:

[0031]

[0032] At the design frequency ω m Two nearby frequencies pω m ,qω m The location has zero residual vibration constraints:

[0033]

[0034]

[0035] in:

[0036] p≤1, q≥1 (10)

[0037] ω m For design frequency; ζ m The damping ratio is defined by sin; cos is the sine; p and q are the design frequencies ω and ω, respectively. m Two nearby frequencies pω m ,qω m The coefficient.

[0038] Between two nearby frequencies, vω m There exists an amplitude peak point with a zero slope constraint and a constraint that is not greater than the maximum allowable amplitude:

[0039]

[0040] in:

[0041] p≤v≤q(13)

[0042] v represents two nearby frequencies pω m ,qω m The frequency between vω m coefficient; V tol This represents the maximum permissible percentage of residual vibration.

[0043] It should also have a constraint at high frequencies that does not exceed the maximum allowable amplitude, when ω is greater than (1+p)ω m ,have:

[0044]

[0045] Satisfying constraint (5-9), find the time-optimal solution, and the resulting function is:

[0046]

[0047] in:

[0048]

[0049] A = σ - σ h (22)

[0050] Ψ = θ h - θ (23)

[0051] π is the constant of the circle; h is the time adjustment factor, which makes the adjustment time variable.

[0052] Taking Laplace transform of (15) gives

[0053]

[0054] (15) and (24) are the same.

[0055] where:

[0056]

[0057] For formula (24), the expression of the rise time t r is:

[0058] There are three coefficients h, p, q in formula (24), which can be solved by solving constraints (11), (12), (14).

[0059] The expression of the percentage of residual amplitude PRV is:

[0060]

[0061] The function c given by formula (24) is the 15-segment non-smooth piecewise smoother proposed in this patent.

[0062] Figure 2 The figure of the frequency sensitivity curve changes with the maximum allowable value of the residual vibration percentage (V tol ). When V tol = 10%, the range of frequency insensitivity is larger than that when V tol = 5%. The values of p, q, h corresponding to different V tol are shown in Table 1.

[0063] Table 1 Values of p, q, h corresponding to different V tol

[0064]

[0065] The following example is to control the vibration of a spring pendulum by using the 15-segment non-smooth piecewise smoother provided by this invention. The spring pendulum is a typical two-degree-of-freedom nonlinear vibration system, and its practical applications are, for example, gantry cranes. The specific description of this embodiment is as follows: when V tol ​When the control ratio is 10%, the vibration of the spring pendulum is controlled to prove that the 15-segment non-smooth segmented smoother in the present application can effectively control the vibration of the mechanical system. Figure 3 The time-domain experimental graph of the swing under the controlled and uncontrolled conditions. In the uncontrolled condition, the experimental result of the swing transient amplitude is 13.96°, and the experimental result of the residual amplitude is 26.69°. Under the action of the smoother, the experimental result of the swing transient amplitude is 3.63°, and the experimental result of the residual amplitude is 2.76°. Figure 4 The time-domain experimental graph of the spring under the controlled and uncontrolled conditions. In the uncontrolled condition, the experimental result of the spring transient amplitude is 6.34mm, and the experimental result of the residual amplitude is 12.48mm. Under the action of the smoother, the experimental result of the spring transient amplitude is 1.41mm, and the experimental result of the residual amplitude is 1.03mm. Figure 5 The driving distance change experiment and simulation results of the swing transient amplitude under the controlled and uncontrolled conditions are given. The experimental and simulation results of the average suppression rate of the swing transient amplitude are 67.47% and 80.48%, respectively. Figure 6 The driving distance change experiment and simulation results of the swing residual amplitude under the controlled and uncontrolled conditions are given. The experimental and simulation results of the average suppression rate of the swing residual amplitude are 81.67% and 91.25%, respectively. Figure 7 The driving distance change experiment and simulation results of the spring transient amplitude under the controlled and uncontrolled conditions are given. The experimental and simulation results of the average suppression rate of the spring transient amplitude are 64.54% and 99.05%, respectively. Figure 8 The driving distance change experiment and simulation results of the spring residual amplitude under the controlled and uncontrolled conditions are given. The experimental and simulation results of the average suppression rate of the spring residual amplitude are 83.43% and 99.31%, respectively. The above results show that under the action of the 15-segment non-smooth segmented smoother in the present application, the vibration of the spring pendulum is greatly suppressed, which can meet the safety requirements and has good robustness to the driving distance change.

[0066] Finally, it should be pointed out that the above examples are only used to illustrate the technical method of the present application, but not to limit the technical method. Therefore, the application scope of the present application can be extended to other changes, applications and embodiments. And we believe that all these changes, applications and embodiments are included in the spirit and teaching scope of the present application.

Claims

1. A method for controlling mechanical vibration, characterized in that: Includes the following steps, Step 1: Estimate the frequency and damping ratio of the mechanical system for the design of a non-smooth segmented smoother with 15 segments; Step 2: Filter the driving command using a non-smooth piecewise smoother with 15 segments. The time function of the non-smooth piecewise smoother with 15 segments is as follows: in: L=s-s h (8) Ψ=θ h -θ (9) π is the constant of pi; e is the natural constant; ω m For design frequency; ζ m The damping ratio is denoted by h; the time adjustment coefficient is denoted by p and q, respectively, representing the design frequency ω. m Two nearby frequencies pω m ,qω m The coefficients; τ is time; c is the function name of a non-smooth piecewise smoother with 15 segments; Step 3: The mechanical system is driven by the filtered commands to control vibration.

2. The method for controlling mechanical vibration as described in claim 1, characterized in that: The transfer function of a non-smooth piecewise smoother with 15 segments is: in: s is a complex variable.

3. The method for controlling mechanical vibration as described in claim 2, characterized in that: The solution method for the three coefficients h, p, and q of a non-smooth piecewise smoother with 15 segments is as follows. At two nearby frequencies pω m and qω m Between, vω m At a certain point, there exists an amplitude peak point with a zero slope constraint and a constraint that the amplitude is not greater than the maximum allowable amplitude: Where: V tol The maximum permissible percentage of residual vibration; sin is sine; cos is cosine; ω is the natural frequency of the second-order mechanical system; ζ is the damping ratio of the second-order mechanical system; v is the two nearby frequencies pω m ,qω m The frequency between vω m The coefficient; in: p≤v≤q (14) It should also have a constraint at high frequencies that does not exceed the maximum allowable amplitude, when ω is greater than (1+p)ω m ,have: Among them, h, p, q can be obtained by solving constraints (12), (13), and (15) to obtain numerical solutions.

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