阅读说明：本技术 一种用于硬脆材料超声加工的鲁棒自适应振幅控制方法 (Robust adaptive amplitude control method for ultrasonic processing of hard and brittle materials ) 是由 周丽娟 于 2020-06-18 设计创作，主要内容包括：本发明涉及一种用于硬脆材料超声加工的鲁棒自适应振幅控制方法。本发明首先,设计前馈补偿的方式,解决换能器温度、匹配电感温度的阻抗变化导致振幅变动问题。然后,由于超声振幅与谐振频率存在强耦合关联,为了保证系统的振幅控制精度,消除系统参数的不确定性的影响,提高系统的抗干扰性,设计了一种鲁棒自适应控制器在线调整自适应控制率,确保系统参数不确定时的振幅控制精度。本发明可解决在复杂加工环境下,由于加工过程中由于负载、工艺及环境的变化以及换能器温度、匹配电感温度等原因导致振幅波动的问题,设计的强耦合鲁棒自适应振幅控制实现振幅的高精度稳定输出,保证硬脆材料在实际加工过程中的加工精度、加工工艺要求以及加工成品率。(The invention relates to a robust self-adaptive amplitude control method for ultrasonic processing of a hard and brittle material. The invention firstly designs a feedforward compensation mode to solve the problem of amplitude variation caused by impedance changes of transducer temperature and matching inductance temperature. Then, as strong coupling correlation exists between the ultrasonic amplitude and the resonant frequency, in order to ensure the amplitude control precision of the system, eliminate the influence of uncertainty of system parameters and improve the anti-interference performance of the system, a robust adaptive controller is designed to adjust the adaptive control rate on line and ensure the amplitude control precision when the system parameters are uncertain. The invention can solve the problem of amplitude fluctuation caused by load, process and environment changes, transducer temperature, matching inductance temperature and other reasons in the processing process under a complex processing environment, and the designed strong coupling robust adaptive amplitude control realizes high-precision stable output of the amplitude and ensures the processing precision, processing process requirements and processing yield of the hard and brittle materials in the actual processing process.)

1. A robust adaptive amplitude control method for ultrasonic processing of hard and brittle materials comprises the following steps:

the method comprises the following steps: establishing an amplitude control system model

The amplitude control system model was built as follows:

x₂＝f(x₁,u)+d(x₁,t)＝f(x₁,t)+g(x₁,t)u+d(x₁,t)

y＝T(x₂,t)

wherein: x is the number of₁＝[x₁₁,x₁₂,...,x_1n]^TIs a matrix of measurable state variables in the vibration system, wherein the variables include power supply drive voltage, phase shift angle, compensation capacitance, x₂＝[x₂₁,x₂₂,...,x_2k]The state variable matrix is measurable state variable matrix of the sound sensor and the piezoelectric acceleration sensor; u is a voltage parameter of system control input; y is the system amplitude output, f (x)₁,t),g(x₁T) is a non-linear continuous function; d (x)₁T) is the external disturbance of the system, T (x)₂T) is an amplitude calculation function obtained according to data of the sound sensor and the piezoelectric acceleration sensor;

the final control objective is to have the system amplitude output y (t) track the reference amplitude r (t);

step two: amplitude soft measurement

A piezoelectric acceleration sensor and a sound sensor are arranged at the position of the knife handle, and acceleration of the vibration of the knife handle and a sound signal caused by ultrasonic grinding processing are measured respectively, so that the amplitude of the ultrasonic knife handle is obtained in real time;

step three: designing feedforward compensators

Establishing a relation model of the resonant frequency, the transducer temperature and the control voltage variation influencing the amplitude in an offline manner by adopting a RBF neural network, and training a large amount of offline data by adopting the neural network to obtain a nonlinear relation function of the control voltage variation influencing the amplitude, the resonant frequency and the transducer temperature in an approaching manner;

u_p(t)＝h(x₃,t)

wherein x₃＝[x₃₁,x₃₂,...,x_3m]Is a measurable vector including a measurable vector of transducer temperature, a measurable vector of resonant frequency, u_p(t) is the control voltage variable obtained by the feedforward compensator, h (x)₃T) is a nonlinear function obtained by RBF neural network approximation;

step four: establishing a robust adaptive controller model

The following nonlinear system is further obtained from the amplitude control system model in the step one:

x₂ ⁽ⁿ⁾＝[f_n(x₁)+Δf(x₁,t)]+[g_n(x₁)+Δg(x₁,t)]u+d(x₁,t)

＝f_n(x₁)+g_n(x₁)u+z(x₁,t)+d(x₁,t)

＝f_n(x₁)+g_n(x₁)u+z_n(x₁)+z_d(x₁,t)+d(x₁,t)

wherein f is_n(x₁) And g_n(x₁) Are respectively f (x)₁T) and g (x)₁T) nominal fraction of; Δ f (x)₁T) and Δ g (x)₁T) are each f (x)₁T) and g (x)₁T) uncertain variation part;

let z (x)₁,t)＝Δf(x₁,t)+Δg(x₁,t)u＝z_n(x₁)+z_d(x₁T) is the unknown uncertainty part of the system, z_n(x₁) Is z (x)₁) Nominal part of, z_d(x₁T) is z (x)₁) Is not determined to vary part, | z_d(x₁,t)|≤_zd，_zdIs a given constant;

the problem of the amplitude control system is that the control voltage variable u is obtained to lead the output amplitude y (t) of the system to track the reference amplitude r (t);

step five: constructing a slip form surface:

the tracking error of the system is defined as:

the surface of the slip form is

Wherein c ═ c₁,c₂,…,c_n-1,1]^TFor the selected respective characteristic polynomial;

step six: determining an adaptive learning rate

Approximating a non-linear function f using a RBF neural network_n(x),g_n(x),z_n(x) I.e. by

WhereinAre respectively f_n(x₁),g_n(x₁),z_n(x₁) An approximation function of;are respectively asThe weight vector of (2); phi (x)₁)，ψ(x₁)，ξ(x₁) Are respectively asA basis function of (a);

step seven: determining control rates of RBF neural network

And adopting self-adaptive PID control, wherein the control voltage variable obtained by adopting self-adaptive sliding film PID control is as follows:

wherein k is_sCoefficient of control for the synovial membrane and k_s≥_zd；r⁽ⁿ⁾An n-state being a reference amplitude;

if the selected control voltage variable is u ═ u_f+u_s+u_n+u_PIDThen u is_f,u_s,u_n,u_PIDRespectively as follows:

whereinθ^T _PID＝[K_P,K_I,K_D]^T，K_P,K_I,K_DRespectively a proportional regulating coefficient, an integral regulating coefficient and a differential regulating coefficient,is a positive constant;

to ensure the gradual convergence of the tracking error of the system, the adaptive learning rate is:

wherein gamma is₁,γ₂,γ₃,γ₄Respectively adaptive learning rateThe adaptive parameters of (2);

step eight: amplitude stable control by adjusting PWM

The control voltage variable obtained by robust self-adaptation and the control voltage variable obtained by a feedforward controller are superposed to obtain the final control voltage variable u (t) + u_pAnd (t) regulating the voltage duty ratio through PWM to further realize the amplitude stability control of the vibration system.

Technical Field

The invention relates to the field of ultrasonic processing of hard and brittle materials, in particular to a strong coupling robust adaptive amplitude control method applied to the ultrasonic processing process of hard and brittle materials.

Background

With the advent of the 5G era, mobile phone manufacturers are beginning to cut into the 5G market with operators, and in 2019, the 5G mobile phones will be released by the large mobile phone factories of huashi, apple, samsung and the like, because the 5G communication frequency band covers the low frequency band of 3.3GHz-4.2GHz, 4.4GHz-5.0GHz and the millimeter wave high frequency band of 26GHz/28GHz/39 GHz. The 5G signal is very sensitive to metal shielding, and especially for the new generation of 5G mobile phones, the metal shell is not suitable for the high-frequency millimeter wave band, and higher requirements are provided for the signal transmission capability of the mobile phone shell.

The novel material such as ceramic, sapphire, glass and composite material for the mobile phone shell has good texture, excellent wear resistance and heat dissipation performance, and can well meet the requirements of 5G communication and wireless charging technology on the material of the mobile phone body. However, sapphire, ceramic, glass, composite materials and the like have the characteristics of high hardness, high strength, good wear resistance, high brittleness, frangibility and the like, so that the problems of difficult processing, poor processing quality, low processing efficiency, serious cutter abrasion and the like are caused. The ultrasonic processing utilizes the collision effect of high-frequency vibration to realize micro-removal of materials, and the acting force is small, so the processing quality is good, the surface damage is small, and the ultrasonic processing is one of the most effective means for processing hard and brittle materials at present.

The amplitude control in the ultrasonic processing process of the hard and brittle material is the most critical factor for determining the processing effect of the hard and brittle material, but in the actual processing process, due to the changes of load, process and environment, the impedance characteristic and resonant frequency of a vibration system can be changed, so that the ultrasonic amplitude is influenced. Meanwhile, the impedance changes due to the temperature of the transducer, the temperature of the matching inductor and the like, and amplitude fluctuation is also caused. In addition, in the processing process of the hard and brittle materials, the control precision of the ultrasonic amplitude is often up to 0.1um level. However, in the conventional ultrasonic amplitude control method, it is often difficult to cope with a complicated environment and a change of a plurality of influence factors in an actual machining process, and it is difficult to achieve stable amplitude control for an amplitude control requirement with high precision.

Disclosure of Invention

In order to solve the problem that the impedance characteristic and the resonant frequency of a vibration system are changed due to the change of load, process and environment in the actual processing process, the invention provides a robust adaptive amplitude control method for ultrasonic processing of hard and brittle materials.

The invention firstly designs a feedforward compensation mode to solve the problem of amplitude variation caused by impedance changes of the temperature of the transducer and the temperature of the matching inductor; because the ultrasonic amplitude and the resonant frequency have strong coupling association, in order to ensure the amplitude control precision of the system, eliminate the influence of uncertainty of system parameters and improve the anti-interference performance of the system, a robust adaptive controller is designed to adjust the adaptive control rate on line and ensure the amplitude control precision when the system parameters are uncertain; and finally, the robust adaptive control and feedforward control are combined to perform strong coupling robust adaptive amplitude control.

The technical scheme adopted by the invention for solving the technical problem is as follows:

the invention comprises the following steps:

the method comprises the following steps: establishing an amplitude control system model

The amplitude control system model was built as follows:

x₂＝f(x₁,u)+d(x₁,t)＝f(x₁,t)+g(x₁,t)u+d(x₁,t)

y＝T(x₂,t)

wherein: x is the number of₁＝[x₁₁,x₁₂,...,x_1n]^TIs a measurable state variable matrix in the vibration system, including power supply driving voltage, phase shift angle, compensation capacitor, x₂＝[x₂₁,x₂₂,...,x_2k]The state variable matrix is measurable state variable matrix of the sound sensor and the piezoelectric acceleration sensor; u is a voltage parameter of system control input; y is the system amplitude output, f (x)₁,t),g(x₁T) is a non-linear continuous function; d (x)₁T) is the external disturbance of the system, T (x)₂And t) is a calculation function for obtaining the amplitude according to the data of the sound sensor and the piezoelectric acceleration sensor. The final control objective is to have the system amplitude output y (t) track the reference amplitude r (t).

Step two: amplitude soft measurement

A piezoelectric acceleration sensor and a sound sensor are installed on the cutter handle, and acceleration of vibration of the cutter handle and a sound signal caused by ultrasonic grinding are measured respectively, so that amplitude of the ultrasonic cutter handle is obtained in real time.

Step three: designing feedforward compensators

A relation model of the resonant frequency, the transducer temperature and the control voltage variation influencing the amplitude is established in an off-line mode through a RBF neural network, and a nonlinear relation function of the control voltage variation influencing the amplitude, the resonant frequency and the transducer temperature is obtained in an approaching mode through training a large amount of off-line data through the neural network.

u_p(t)＝h(x₃,t)

Wherein x₃＝[x₃₁,x₃₂,...,x_3m]For measurable vectors, including transducer temperature, resonant frequency, u_p(t) is the control voltage variable obtained by the feedforward compensator, h (x)₃And t) is a nonlinear function obtained by RBF neural network approximation.

Step four: establishing a robust adaptive controller model

The following nonlinear system is further obtained from the amplitude control system model in the step one:

x₂ ⁽ⁿ⁾＝[f_n(x₁)+Δf(x₁,t)]+[g_n(x₁)+Δg(x₁,t)]u+d(x₁,t)

＝f_n(x₁)+g_n(x₁)u+z(x₁,t)+d(x₁,t)

＝f_n(x₁)+g_n(x₁)u+z_n(x₁)+z_d(x₁,t)+d(x₁,t)

wherein f is_n(x₁) And g_n(x₁) Are respectively f (x)₁T) and g (x)₁T) nominal fraction of; Δ f (x)₁T) and Δ g (x)₁T) are each f (x)₁T) and g (x)₁T) uncertain variation part;

let z (x)₁,t)＝Δf(x₁,t)+Δg(x₁,t)u＝z_n(x₁)+z_d(x₁T) is the unknown uncertainty part of the system, z_n(x₁) Is z (x)₁) Nominal part of, z_d(x₁T) is z (x)₁) Uncertain fluctuation part of, z_d(x₁,t)≤_zd，_zdGiven a constant. The problem of the amplitude control system is to obtain the control voltage variableu is such that the output amplitude y (t) of the system tracks the reference amplitude r (t).

Step five: constructing a slip form surface:

the tracking error of the system is defined as:

the surface of the slip form is

Wherein c ═ c₁,c₂,…,c_n-1,1]^TIs the corresponding characteristic polynomial selected.

Step six: determining an adaptive learning rate

Approximating a non-linear function f using a RBF neural network_n(x),g_n(x),z_n(x) I.e. by

WhereinAre respectively f_n(x₁),g_n(x₁),z_n(x₁) An approximation function of;are respectively asThe weight vector of (2); phi (x)₁)，ψ(x₁)，ξ(x₁) Are respectively asThe basis function of (2).

Step seven: determining control rates of RBF neural network

And adopting self-adaptive PID control, wherein the control voltage variable obtained by adopting self-adaptive sliding film PID control is as follows:

wherein k is_sCoefficient of control for the synovial membrane and k_s≥_zd；r⁽ⁿ⁾An n-state being a reference amplitude; if the selected control voltage variable is u ═ u_f+u_s+u_n+u_PIDThen u is_f,u_s,u_n,u_PIDRespectively as follows:

whereinθ^T _PID＝[K_P,K_I,K_D]^T，K_P,K_I,K_DRespectively a proportional regulating coefficient, an integral regulating coefficient and a differential regulating coefficient,is a positive constant.

To ensure the gradual convergence of the tracking error of the system, the adaptive learning rate is:

wherein gamma is₁,γ₂,γ₃,γ₄Respectively adaptive learning rateThe adaptive parameters of (1).

Step eight: amplitude stable control by adjusting PWM

The control voltage variable obtained by robust self-adaptation and the control voltage variable obtained by a feedforward controller are superposed to obtain the final control voltage variable u (t) + u_pAnd (t) regulating the voltage duty ratio through PWM to further realize the amplitude stability control of the vibration system.

The invention has the beneficial effects that:

the output duty ratio, the output frequency and the input voltage amplitude of the ultrasonic generator are influence factors influencing the amplitude of the ultrasonic vibration system, and the control on the ultrasonic amplitude is realized by adjusting the output duty ratio of the ultrasonic generator because the duty ratio adjustment is easy to realize and has certain linear adjustment capability.

In the process of processing the novel material, uncertainty often exists in the amplitude control of the vibration system, such as uncertainty of parameters, uncertainty of structure and uncertainty of external interference. And performing strong coupling robust adaptive amplitude control by adopting a method of combining robust adaptive control and feedforward control. The feedforward control is used for compensating amplitude change caused by resonance frequency and transducer temperature change, and the robust self-adaptive control is used for solving amplitude stability control under the conditions of uncertain parameters, uncertain interference and the like.

The method finally solves the problem of amplitude fluctuation caused by load, process and environment changes, transducer temperature, matching inductance temperature and the like in the machining process under a complex machining environment, the designed strong coupling robust adaptive amplitude control realizes high-precision stable output of the amplitude, and the machining precision, the machining process requirement and the machining yield of the hard and brittle material in the actual machining process are ensured.

Drawings

FIG. 1 an ultrasonic amplitude soft measurement model;

FIG. 2 is a schematic view of an RBF neural network;

fig. 3 is a block diagram of a strongly coupled robust adaptive controller system.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The invention comprises the following steps:

the method comprises the following steps: establishing an amplitude control system model:

the amplitude control system for ultrasonic processing of the hard and brittle material is a multi-input single-output system, the nonlinearity of a feedback linearization control model counteracting system is established, and the following system model is established:

wherein: x is the number of₁＝[x₁₁,x₁₂,...,x_1n]^TFor the measurable state variable matrix x of the internal power supply driving voltage, phase shift angle, compensation capacitor, etc. of the vibration system₂＝[x₂₁,x₂₂,...,x_2k]The state variable matrix is a measurable state variable matrix of voltage, frequency and the like which can be measured by a sound sensor and a piezoelectric acceleration sensor; u is a voltage parameter of system control input; y is the system amplitude output, f (x)₁,t),g(x₁T) is a non-linear continuous function; d (x)₁T) is the external disturbance of the system, T (x)₂And t) is a calculation function for obtaining the amplitude according to the data of the sound sensor and the piezoelectric acceleration sensor. The final control objective is to have the output amplitude y (t) of the system track the reference amplitude r (t).

Step two: amplitude soft measurement model design

Due to the complex environment of a processing field, some existing ultrasonic amplitude measuring methods such as laser measurement, microscope measurement and the like are difficult to apply to the processing field, and most methods cannot achieve real-time measurement. And because various noise signals exist in the ultrasonic processing process, the ultrasonic amplitude soft measurement is carried out by adopting a multi-source sensor data fusion method. As shown in the attached figure 1, a piezoelectric acceleration sensor and a sound sensor are arranged at the position of the cutter handle, acceleration of the vibration of the cutter handle and a sound signal caused by ultrasonic grinding are respectively measured and combined with an electric signal at the end of a transducer, and the amplitude of the ultrasonic cutter handle is measured in real time. And feeds the amplitude signal back to the amplitude control system in real time.

Step three: design of a feedforward compensator:

a relation model of the resonant frequency, the transducer temperature and the control voltage variation influencing the amplitude is established in an off-line mode through a RBF neural network, and a nonlinear relation function of the control voltage variation influencing the amplitude, the resonant frequency and the transducer temperature is obtained in an approaching mode through training a large amount of off-line data through the neural network. The schematic diagram of the RBF neural network is shown in figure 2.

u_p(t)＝h(x₃,t) (2)

Wherein x₃＝[x₃₁,x₃₂,...,x_3m]For externally measurable vectors, u, of transducer temperature, resonant frequency, etc_p(t) is the control voltage variable obtained by the feedforward compensator, h (x)₃And t) is a nonlinear function obtained by RBF neural network approximation.

Step four: establishing a robust adaptive controller model

The amplitude control system model determined by equation (1) may further yield a nonlinear system as follows:

wherein f is_n(x₁) And g_n(x₁) Are respectively f (x)₁T) and g (x)₁T) nominal fraction of; Δ f (x)₁T) and Δ g (x)₁T) are each f (x)₁T) and g (x)₁T) uncertainty variance.

Let z (x)₁,t)＝Δf(x₁,t)+Δg(x₁,t)u＝z_n(x₁)+z_d(x₁T) is the unknown uncertainty part of the system, z_n(x₁) Is z (x)₁) Nominal part of, z_d(x₁T) is z (x)₁) Is not determined to vary part, | z_d(x₁,t)|≤_zd，_zdGiven a constant. In this case, the problem of the amplitude control system is to find the control input voltage parameter u such that the output amplitude y (t) of the system tracks the reference amplitude r (t).

Step five: constructing a slip form surface:

the tracking error of the system is defined as:

the surface of the slip form is

Wherein c ═ c₁,c₂,…,c_n-1,1]^TIs the corresponding characteristic polynomial selected.

Step six: determining an adaptive learning rate:

approximating a non-linear function f using a RBF neural network_n(x),g_n(x),z_n(x) I.e. by

WhereinAre respectively f_n(x₁),g_n(x₁),z_n(x₁) An approximation function of;are respectively asThe weight vector of (2); phi (x)₁)，ψ(x₁)，ξ(x₁) Are respectively asThe basis function of (2).

Step seven: determining the control rates of the RBF neural network:

in order to improve a system, self-adaptive PID control is adopted, and control voltage variables obtained by adopting self-adaptive sliding film PID control are as follows:

if the selected control voltage variable is u ═ u_f+u_s+u_n+u_PIDThen u is_f,u_s,u_n,u_PIDRespectively as follows:

whereinθ^T _PID＝[K_P,K_I,K_D]^T，K_P,K_I,K_DRespectively a proportional regulating coefficient, an integral regulating coefficient and a differential regulating coefficient,is a positive constant.

To ensure the gradual convergence of the tracking error of the system, the adaptive learning rate is:

wherein gamma is₁,γ₂,γ₃,γ₄Respectively adaptive learning rateThe adaptive parameters of (1).

Step eight: and adjusting PWM to realize amplitude stable control:

the control voltage variable obtained by robust self-adaptation and the control voltage variable obtained by a feedforward controller are superposed to obtain the final control voltage variable u (t) + u_pAnd (t) regulating the voltage duty ratio through PWM to further realize the amplitude stability control of the vibration system, wherein the system block diagram of the strong coupling robust adaptive controller is shown in figure 3.