CN114609975B - FTS control method based on composite active disturbance rejection control - Google Patents
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Abstract
The invention discloses an FTS control method based on composite active disturbance rejection control, and belongs to the field of precision machining. In the method, when an FTS system model is built, a dual-time-lag system with completely unknown lag nonlinear functions, state time lags and time-varying time lags and internal non-modeling dynamic nonlinearities are introduced, a controller designed for the built FTS system model regards the lag time lags and the dynamic nonlinearities in the system as total disturbance to the FTS system, the linear observer estimates the total disturbance in real time, and an adaptive neural network approximates the unknown nonlinear error function to realize a lag time lag compensation function. Therefore, the flutter phenomenon in the precise cutting process is well described, and the problems that the amplitude distortion phenomenon, the relation between stable amplitude and cutting parameters, the influence of the jump phenomenon on the stability of the cutting process, the influence of external interference on the cutting accuracy and the like caused by cutting flutter cannot be explained and predicted by the existing FTS model are solved.
Description
Technical Field
The invention relates to an FTS control method based on composite active disturbance rejection control, and belongs to the field of precision machining.
Background
At present, micromechanical parts are widely used in various fields such as information processing, space technology and optical fiber communication. The machining process of the micro-mechanical part is usually finished by installing a cutter micro-feed Servo system with quick response capability on a lathe, the cutter micro-feed Servo system is also called a Fast Tool Servo (FTS) system, and in the turning process, the FTS drives a cutter to finish high-frequency and high-precision tracking motion, so that the micro-mechanical part is a key part for machining micro-nano parts.
The existing FTS comprises a piezoelectric ceramic type FTS, a magnetostrictive type FTS, a Lorentz force FTS and a Maxwell force FTS; the piezoelectric ceramic type FTS has the advantages of high response speed, high acceleration, frequency response range of thousands of hertz and the like, so that the piezoelectric ceramic type FTS is widely applied to non-axisymmetric turning and achieves good effects, but due to the fact that cutting chatter is often generated due to self-excited vibration in the precise turning process, machining quality is affected, cutting efficiency is limited, noise pollution is generated, mechanical abrasion of a system is increased, and service lives of a machine tool and a cutter are greatly shortened. Due to the complexity of the cutting chatter mechanism and the influence of numerous interference factors in the cutting process, the cutting chatter mechanism is difficult to effectively predict and eliminate. Therefore, the relation between the cutting force and the cutting thickness in the cutting process of the FTS system is researched and analyzed, a related mathematical model is established, and the design of the controller to restrain the cutting chatter has important theoretical significance and engineering practical value.
In the field of modeling and control of a fast tool servo system in recent years, a nonlinear time-lapse FTS model gradually replaces a linear time-lapse FTS model to become a mainstream, and further inversion of the nonlinear time-lapse FTS model is controlled to obtain an inverse model of the nonlinear time-lapse FTS model, but the nonlinear time-lapse FTS model often needs to obtain an accurate mathematical model of a controlled object. The existing nonlinear time-lapse FTS model cannot explain and predict the amplitude distortion phenomenon, the relation between stable amplitude and cutting parameters, the influence of jump phenomenon on the stability of the cutting process, the influence of external interference on the cutting accuracy and the like caused by cutting chatter, so that a more accurate mathematical model cannot be further provided, and the cutting accuracy cannot be further improved.
The active disturbance rejection control is a new model-free disturbance rejection control, however, the traditional active disturbance rejection control parameter setting is complex, and a group of parameters are only applicable to a single system. The linear active disturbance rejection control solves the difficult problem of complex setting of the traditional active disturbance rejection control parameters, however, in the actual turning process, the bandwidth of the controller is limited by a plurality of factors such as production cost, noise sensitivity and the like. Therefore, when the observer bandwidth cannot reach the actual required value, the cutting accuracy cannot be ensured.
Disclosure of Invention
In order to further improve cutting precision, the invention provides an FTS control method based on composite active disturbance rejection control, which is applied to a piezoelectric ceramic type FTS, wherein the piezoelectric ceramic type FTS comprises a main shaft, a working room, a cutter and a piezoelectric actuator, and the cutter is connected with the piezoelectric actuator through a spring; the method comprises the following steps:
Step 1: establishing an FTS system model based on the combination of state time lag beta 1 under spindle rotation, piezoelectric actuator hysteresis nonlinearity and internal unmodeled dynamic nonlinearity and time-varying time lag beta 2 generated by transverse feeding of a cutter; the internal unmodeled dynamic nonlinearity refers to the sum of dynamic nonlinearities which are not clear except time-varying time lag, state time lag and hysteresis nonlinearity in the piezoelectric ceramic type FTS;
Step 2: aiming at the FTS system model established in the step 1, the combination of state time lag beta 1 under spindle rotation, piezoelectric actuator hysteresis nonlinearity and internal unmodeled dynamic nonlinearity in the system and time-varying time lag beta 2 generated by transverse feeding of a cutter are regarded as total disturbance, and a linear self-anti-interference controller is adopted to preliminarily estimate the total disturbance;
Step 3: aiming at the estimation error generated by preliminary estimation of the total disturbance by adopting a linear self-anti-interference controller in the step 2, approximating the estimation error of the total disturbance by adopting a BP neural network controller, thereby determining the accurate estimation of the total disturbance;
Step 4: and (3) compensating the system according to the accurate estimation of the total disturbance finally obtained in the steps (2) and (3), and realizing the accurate tracking of the piezoelectric ceramic type FTS.
Optionally, in the step 1, a Backlash model is used for describing hysteresis nonlinearity of the piezoelectric actuator.
Optionally, the step 1 includes:
the dynamics of a piezoceramic FTS system are described as:
Where x represents a fluctuation portion of the cutting thickness of the workpiece, m, c and k are equivalent mass, damping coefficient and spring rate of the metal cutting machine, k a is spring rate of the piezoelectric actuator, u is a control input signal applied to the piezoelectric actuator, and F 1 represents a variation amount of cutting force expressed as:
F1＝kmv(t) (2)
Where k m is a constant and v (t) is the rate of change of the cutting thickness over time, expressed as:
v(t)＝x-αx(t-β) (3)
Where β is the time interval between successive cuts and α is the overlap factor;
The nonlinear function of the cutting force variation in relation to the cutting thickness variation is expressed as:
F1＝H(v)＝H(x-αx(t-β)) (4)
Wherein H (v) is composed of a linear function f (v (t)) and a bounded nonlinear function h·v (t), and represents a time-lag characteristic and a hysteresis characteristic, respectively, that is:
H(v)＝h·v(t)+f(v(t)) (5)
wherein h represents hysteresis nonlinearity of the piezoelectric actuator;
Thus, substitution of formula (3) into formula (1) can be obtained:
Wherein, the state time lag β 1 is a time delay generated by spindle rotation, when spindle rotation speed Ω changes, Ω and β 1 satisfy the following relationship:
The time-varying time delay beta 2 is a random number uniformly distributed between 0 and 1, and the sampling time is 0.1s;
taking into account the unmodeled dynamic nonlinearity inside the system, let The FTS system described by equation (6) is:
wherein Γ represents the unmodeled dynamic nonlinearity inside the FTS system;
The transformed FTS system is represented as:
In the formula (9), y represents a tracking signal output from the FTS system.
Optionally, the step 2 includes:
For the FTS system described by equation (9), consider all uncertainties of the system as the total disturbance x 3, namely, let:
The method for performing preliminary estimation on the total disturbance x 3 by adopting a linear self-anti-interference controller comprises the following steps:
defining equation (9) as an extended state space expression:
Wherein the method comprises the steps of
Taking x 3 as a state variable, estimating x 3 in real time by using an LADRC linear expansion state observer;
The LADRC linear extended state observer is:
Wherein η= [ η 1 η2 η3]T,θ＝[θ1 θ2 θ3]T;
performing Laplace transformation on the formula (13) to obtain a characteristic equation:
λ0(s)＝s3+θ1s2+θ2s+θ3＝(s+ω0)3
θ is the observer gain vector obtained by simplifying the characteristic equation, and can be obtained Where ω 0 is the bandwidth of the observer; estimate/>
The FTS system described by formula (9) is simplified to
Wherein η 3 represents a preliminary estimated value obtained by preliminarily estimating the total disturbance x 3 by using a linear self-anti-interference controller.
Optionally, the step 3 includes:
Defining a tracking error:
e＝x-xd
wherein x d represents a desired signal;
Defining a filtered tracking error:
γ＝[ΛT 1]e (15)
Deriving formula (15):
Wherein,
The pseudo-control feedback linearization technique is adopted, and the input signal u is defined as:
wherein phi is the pseudo control input of the BP neural network;
Training the BP neural network by using historical input and output data of the FTS system as a data set to determine a pseudo control input phi of the BP neural network, thereby determining a weight self-adaptive law of the BP neural network;
and (3) utilizing the BP neural network with the weight self-adaptive law determined to realize estimation error approximation on the total disturbance, thereby determining accurate estimation on the total disturbance.
Optionally, the unmodeled dynamic nonlinear Γ expression inside the FTS system is
Optionally, the number of hidden layer nodes in the BP neural network is 30;
The weight self-adaption law is as follows:
Where p=p T > 0 and q=q T > 0 are arbitrary constant matrices;
x bp is the input vector of the neural network, σ (·) is the sigmod excitation function of the hidden layer neurons.
The application also provides a piezoelectric ceramic type FTS, which comprises a main shaft, a working room, a cutter and a piezoelectric actuator, wherein the cutter is connected with the piezoelectric actuator through a spring; the piezoelectric ceramic type FTS is controlled by adopting the FTS control method based on the composite active disturbance rejection control.
The invention has the beneficial effects that:
(1) When the FTS system model is built, a dual-time-lag system with completely unknown lag nonlinear functions, state time lags and time-varying time lags and internal non-modeling dynamic nonlinearities are introduced, a controller designed for the built FTS system model regards the lag time lags and the dynamic nonlinearities in the system as total disturbance to the FTS system, the total disturbance is estimated in real time by a linear observer, and an adaptive neural network is utilized to approach the unknown nonlinear error function, so that the lag time lag compensation function is realized. Therefore, the flutter phenomenon in the precise cutting process is well described, and the problems that the amplitude distortion phenomenon, the relation between stable amplitude and cutting parameters, the influence of the jump phenomenon on the stability of the cutting process, the influence of external interference on the cutting accuracy and the like caused by cutting flutter cannot be explained and predicted by the existing FTS model are solved.
(2) The application adopts a composite control strategy formed by combining two control schemes, can estimate and compensate the unknown interference of the system without an accurate model, can realize high-precision control, has stronger anti-interference capability, selects bandwidth as the measure of the performance of the composite controller, reduces the controller parameters needing to be set, has better robustness and has higher engineering application value.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic view of a metal cutting process.
Fig. 2 is a schematic diagram of a backslash hysteresis model referred to in one embodiment of the invention.
FIG. 3 is a schematic representation of the total disturbance of the fast prop servo provided by the present invention.
Fig. 4 is a block diagram of the composite active disturbance rejection control provided by the present invention.
Figure 5 is a graph of linear active-disturbance-rejection tracking at different bandwidths provided by one embodiment of the present invention.
Figure 6 is a graph of linear active disturbance rejection tracking curve error at different bandwidths provided by one embodiment of the present invention.
Fig. 7 is a graph of tracking under different bandwidths using a linear active disturbance rejection control method and a composite control method according to an embodiment of the present application.
Fig. 8 is a graph of tracking curve errors under different bandwidths using a linear active disturbance rejection control method and a composite control method according to an embodiment of the present application.
Fig. 9 is a graph comparing time-varying time-lag output signals of a conventional control method provided by an embodiment of the present application, which is based on a neural network, which is based on linear active disturbance rejection, and which is based on a composite control provided by the present application.
Fig. 10 is a graph comparing hysteresis loop curves of a prior control method provided by an embodiment of the present application, which is based on a neural network, which is based on linear active disturbance rejection, and which is based on a composite control provided by the present application.
FIG. 11 is a graph comparing tracking curves of the prior control method provided by the application, which is based on a neural network only, linear active disturbance rejection only and compound control provided by the application.
Fig. 12 is a tracking error comparison chart of the prior control method provided by the application, which is based on a neural network only, linear active disturbance rejection only and composite control provided by the application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
The terms involved in the present application are explained as follows:
The dead zone width, in a control system, if some actuating mechanisms act frequently, small vibration can be caused, and serious mechanical abrasion is caused. Many systems, in turn, allow for errors in the controlled quantity over a range of control requirements. While the amount of error that allows for the controlled amount is referred to as the dead zone width.
Time-varying time-lag: the cutter is transversely fed to generate time lag.
State time lag: the time delay caused by spindle rotation.
Hysteresis nonlinearity: the inherent characteristics of intelligent materials such as piezoelectric ceramics and the like, and the input and output are represented as hysteresis loops.
Unmodeled dynamic nonlinearity: other dynamic nonlinearity sums in the piezoceramic FTS than time-varying time-lag, state-time-lag, and hysteresis nonlinearity are not specified.
FIG. 1 is a schematic diagram of a metal cutting process of a piezoelectric ceramic type FTS, wherein the piezoelectric ceramic type FTS comprises a main shaft, a working room, a cutter, a piezoelectric actuator and other parts, and the cutter is connected with the piezoelectric actuator through a spring; in the turning process, the main shaft drives the workpiece to axially rotate through the damping spring, and the cutter is driven by the piezoelectric actuator to make reciprocating feeding motion along the radial direction or the axial direction of the workpiece at a frequency related to the rotating speed of the main shaft, so that the end face of the workpiece is processed.
Embodiment one:
The embodiment provides an FTS control method based on composite active disturbance rejection control,
Step 1: establishing an FTS system model based on the combination of state time lag beta 1 under spindle rotation, piezoelectric actuator hysteresis nonlinearity and internal unmodeled dynamic nonlinearity and time-varying time lag beta 2 generated by transverse feeding of a cutter; the internal unmodeled dynamic nonlinearity refers to the sum of dynamic nonlinearities which are not clear except time-varying time lag, state time lag and hysteresis nonlinearity in the piezoelectric ceramic type FTS;
Step 2: aiming at the FTS system model established in the step 1, the combination of state time lag beta 1 under spindle rotation, piezoelectric actuator hysteresis nonlinearity and internal unmodeled dynamic nonlinearity in the system and time-varying time lag beta 2 generated by transverse feeding of a cutter are regarded as total disturbance, and a linear self-anti-interference controller is adopted to preliminarily estimate the total disturbance;
Step 3: aiming at the estimation error generated by preliminary estimation of the total disturbance by adopting a linear self-anti-interference controller in the step 2, approximating the estimation error of the total disturbance by adopting a BP neural network controller, thereby determining the accurate estimation of the total disturbance;
Step 4: and (3) compensating the system according to the accurate estimation of the total disturbance finally obtained in the steps (2) and (3), and realizing the accurate tracking of the piezoelectric ceramic type FTS.
Embodiment two:
the embodiment provides an FTS control method based on composite active disturbance rejection control, the method comprising:
step1: considering the state time lag beta 1 under spindle rotation, the hysteresis nonlinearity of the piezoelectric actuator and the internal unmodeled dynamic nonlinearity combination, and simultaneously introducing time-varying time lag beta 2 under regeneration effect to establish an FTS system model;
Unlike the existing FTS system model which only considers the state time lag beta 1 and the time-varying time lag beta 2, the application also considers the hysteresis nonlinearity of the piezoelectric actuator and the internal unmodeled dynamic nonlinearity when modeling the FTS system; in addition, in modeling, the hysteresis nonlinearity h is simulated by a certain number of backslash models.
The modeling process is as follows:
first, the dynamics of the FTS system are described as
Where x represents the fluctuation of the cutting thickness of the workpiece, m, c and k are the equivalent mass, damping coefficient and spring rate of the metal cutting machine, respectively, k a is the spring rate of the piezoelectric actuator, u is the control input applied to the piezoelectric actuator, F 1 represents the relation of the cutting force of the tool to the cutting thickness, expressed as
F1＝kmv(t) (2)
Where k m is a constant and v (t) is the rate of change of the cutting thickness over time, expressed as:
v(t)＝x-αx(t-β) (3)
Where β is the time interval between successive cuts and α is the overlap factor. The cutting force depends on the current cutting thickness, while the current turning is performed on the surface that was cut the previous time, and the cutting force fluctuates with the chip thickness to generate regenerative chatter. The nonlinear function of the machine tool's cutting force variation versus cutting thickness variation can be expressed as:
F1＝H(v)＝H(x-αx(t-β)) (4)
Wherein H (v) is composed of a linear function and a bounded nonlinear function, and represents hysteresis characteristics and time-lag characteristics, respectively, namely:
H(v)＝h·v(t)+f(v(t)) (5)
Thus, substitution of formula (3) into formula (1) can be obtained:
Wherein, the state time lag β 1 is a time delay generated by spindle rotation, when spindle rotation speed Ω changes, Ω and β 1 satisfy the following relationship:
The time-varying time delay beta 2 is a random number uniformly distributed between 0 and 1, and the sampling time is 0.1s. h represents unknown hysteresis nonlinearity. The application adopts a certain number of backslash models to simulate hysteresis nonlinearity h, and the mathematical model is expressed as If/>And τ=mu-md +, or/>And τ=mu-md -, then/>And the other is 0.
The backlish nonlinear model is a first-order velocity-driven dynamic system, where u andIs the input, τ is the state of the system, and d is the dead zone width of the model. When the direction of movement of u changes, the direction of movement of τ does not change immediately, but lags behind for a period of time, thereby creating a hysteresis. The backflash hysteresis model is shown in figure 2.
Let x 1 be =x,The method can obtain:
where Γ represents the unmodeled dynamic nonlinearity inside the FTS system, the transformed metal cutting system may be represented as
The FTS system model constructed by the invention shown in the formula (9) mainly considers the state time lag under the rotation of the main shaft, the hysteresis nonlinearity of the piezoelectric actuator and the internal unmodeled dynamic nonlinearity combination, and simultaneously introduces the time-varying time lag under the regeneration effect. The model describes the non-linear relationship between the cutting force variation and the chip thickness variation, and the combination of hysteresis and double-hysteresis puts higher demands on the design of the controller.
Step2: aiming at the FTS system model established in the step 1, combining state time lag beta 1 under spindle rotation, hysteresis nonlinearity of a piezoelectric actuator and internal unmodeled dynamic nonlinearity in the system, and time-varying time lag beta 2 generated by transverse feeding of a cutter as total disturbance, designing a linear self-interference rejection controller LADRC in the composite self-interference rejection device, and carrying out preliminary estimation on the total disturbance by adopting the linear self-interference rejection controller;
The LADRC takes the controlled object as a cascade integral model, takes all other object information and external disturbance as generalized disturbance, estimates the generalized disturbance by using a linear expansion state observer, and brings the generalized disturbance into a linear state feedback control law so as to quickly suppress the disturbance, and a total disturbance diagram of the quick tool servo system is shown in figure 3.
For the FTS system described by equation (9), consider all uncertainties of the system as the total disturbance x 3, namely, let:
The heart of the LADRC is to estimate and compensate the uncertainty of the system as the total disturbance, if x 3 can be estimated in real time, then the disturbance information can be actively extracted and cancelled.
Equation (9) may be defined as an extended state space expression:
Wherein the method comprises the steps of
Taking x 3 as a state variable, estimating x 3 in real time by using an LADRC linear expansion state observer;
The LADRC linear extended state observer is:
Wherein η= [ η 1 η2 η3]T,θ＝[θ1 θ2 θ3]T;
performing Laplace transformation on the formula (13) to obtain a characteristic equation:
λ0(s)＝s3+θ1s2+θ2s+θ3＝(s+ω0)3
θ is the observer gain vector obtained by simplifying the characteristic equation, and can be obtained Where ω 0 is the bandwidth of the observer. Estimate/>From this, it can be seen that the accuracy of the estimation of the total disturbance x 3 depends on the bandwidth of the observer; the higher the bandwidth, the higher the accuracy of the estimated value for the disturbance;
the metal cutting system described by formula (9) can be simplified to
In the prior art, the observer bandwidth is typically assumed to be large enough, thus reducing equation (14) to:
however, in practical application, the bandwidth of the observer is limited, so that the BP neural network controller is adopted to approach the estimation error of the total disturbance, namely x 3-η3, so as to supplement the estimation error, and realize high-precision tracking control.
Step3, aiming at an estimation error generated by preliminary estimation of the total disturbance by adopting a linear self-anti-interference controller in the Step 2, approximating the estimation error of the total disturbance by adopting a BP neural network controller, thereby determining accurate estimation of the total disturbance;
Defining a tracking error:
e＝x-xd
wherein x d represents a desired signal;
Defining a filtered tracking error:
γ＝[ΛT 1]e (15)
By selecting the appropriate coefficient vector Λ= [ f 1,f1]T, so that when γ→0, e→0.
The derivation of formula (15) can be obtained:
Wherein,
The input signal is defined by adopting a pseudo-control feedback linearization technology:
Where phi is referred to as the pseudo-control, Is an approximation of the neural network of g (x, u), satisfying the following conditions:
Modified at the right side of formula (17) The method can obtain:
the approximation error is expressed as:
The design pseudo control input is:
where δ is the adaptive robust term. Substitution of formulas (20) and (22) into formula (16) can be obtained
The self-adaptive BP neural network can approach to the complex nonlinear relation to the maximum extent and automatically correct the neural network parameters. The processing structure is parallel, so that the operation speed is high, and the fault tolerance is high.
Training the BP neural network by using historical input and output data of the FTS system as a data set to determine a pseudo control input phi of the BP neural network, thereby determining a weight self-adaptive law of the BP neural network;
approximation of the estimation error is achieved by using a BP neural network with a weight adaptive law determined:
Wherein g= [ t ij]T and k= [ w jb]T are two adjustable weights of the BP neural network,
For the input vector of the neural network, σ (·) is the sigmod firing function of the hidden layer neurons, the approximation error iota (x bp) is bounded, |iota (x bp)|≤ιN,ιN > 0 is an unknown constant:
Wherein the method comprises the steps of And/>Estimated values of G and K, respectively. Considering the FTS system described by equation (9), if the pseudo control input is selected as equation (22), the neural network weight adaptation law is:
where p=p T > 0 and q=q T > 0 are arbitrary constant matrices. A composite active disturbance rejection control block diagram based on the neural network is shown in fig. 4.
Step4 FTS system chatter suppression control
The mathematical model of the hysteresis dual-lag fast tool servo is shown in formula (9), where c=1.5, m=5 kg, k=1250N/m, a=1,Is assumed to be unmodeled dynamic nonlinearity.
A backslash-like hysteresis model is formed by using 50 backslash models, and the dead zone width distribution is 1/50-50/50. The state time lag omega is set to be [1 305 610 560 760 560 800 1120] when the rotating speed changes every two seconds, the time lag is set to be a random number between 0 and 1, and the sampling time is 0.1s. The input vector of the neural network isThe number of hidden layer nodes is 30, the initial weight is set to zero, the weight of the neural network is dynamically adjusted through an adaptive law, and P=8I G,Q＝5Ik,IG,Ik is an identity matrix. The input signal used is x d (t) =0.1pi (sin 2t-0.1cos t).
In order to prove the control effect of the composite control method provided by the application, the application carries out comparative analysis on the tracking characteristics of the linear active disturbance rejection control and the composite control provided by the application in the prior art through a simulation experiment:
In the simulation experiment, observer bandwidths ω 0 were set to 40, 70, and 100, respectively. The traditional linear active disturbance rejection adopts PD control, so two adjustable parameters k p and k d are also required to be set, and three PD parameters which are adjusted according to the bandwidth are set for three linear active disturbance rejection controllers with different bandwidths, namely k p40＝64,kd40＝16,kp70＝196,kd70＝28,kp100＝400,kd100 =40.
The following description is made in connection with the simulation diagrams:
Fig. 5 shows a linear active-disturbance-rejection tracking graph under different bandwidths, and fig. 6 shows a linear active-disturbance-rejection tracking graph error graph under different bandwidths. As is apparent from fig. 5 and 6, the tracking accuracy of the linear active disturbance rejection controller in the prior art is greatly affected by the bandwidth, and the tracking accuracy when the bandwidth ω 0 =100 is far greater than the tracking accuracy when the bandwidth ω 0 =40, that is, the greater the bandwidth, the higher the tracking accuracy.
Fig. 7 is a graph of tracking curves of the linear active disturbance rejection control and the composite control proposed by the application under different bandwidths, and fig. 8 is a graph of tracking curve errors of the linear active disturbance rejection control and the composite control under different bandwidths. As can be seen from fig. 8, the composite active-disturbance-rejection control scheme provided by the application is less affected by the bandwidth, and the tracking precision when the bandwidth ω 0 =100 is almost the same as the tracking precision when the bandwidth ω 0 =70, because when the bandwidth of the observer is limited, the neural network in the composite active-disturbance-rejection control scheme provided by the application can timely compensate the estimation error, and high-precision tracking control is realized, so that the influence of the bandwidth is avoided.
Fig. 9 is a time-varying time-lag output signal diagram of the prior art respectively using the linear active disturbance rejection, the neural network and the composite control according to the present application, and fig. 10 is a hysteresis loop curve formed by the linear active disturbance rejection, the neural network and the composite control respectively, wherein the input data are generated by the data of the system itself. From the figure, the novel FTS model constructed by the application effectively describes the asymmetric hysteresis nonlinear characteristic.
Figure 11 is a graph of the prior art tracking using a linear active disturbance rejection, neural network and the proposed composite control scheme of the present application, FIG. 12 is a graph comparing tracking errors for a linear active disturbance rejection, neural network and compound control scheme. It can be seen from fig. 12 that although the linear active disturbance rejection control, the neural network control and the compound control scheme can realize effective tracking control for the hysteresis time-lag fast tool servo system, the initial error of the compound control provided by the application is minimum, and compared with the linear active disturbance rejection control and the neural network control, the compound control has the minimum tracking error and the highest tracking precision, so that the quality and the efficiency of the processed tool can be improved.
Some steps in the embodiments of the present invention may be implemented by using software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (7)
1. The method is applied to a piezoelectric ceramic type FTS, wherein the piezoelectric ceramic type FTS comprises a main shaft, a working room, a cutter and a piezoelectric actuator, and the cutter is connected with the piezoelectric actuator through a spring; characterized in that the method comprises:
Step 1: establishing an FTS system model based on the combination of state time lag beta 1 under spindle rotation, piezoelectric actuator hysteresis nonlinearity and internal unmodeled dynamic nonlinearity and time-varying time lag beta 2 generated by transverse feeding of a cutter; the internal unmodeled dynamic nonlinearity refers to the sum of dynamic nonlinearities which are not clear except time-varying time lag, state time lag and hysteresis nonlinearity in the piezoelectric ceramic type FTS;
Step 2: aiming at the FTS system model established in the step 1, the combination of state time lag beta 1 under spindle rotation, piezoelectric actuator hysteresis nonlinearity and internal unmodeled dynamic nonlinearity in the system and time-varying time lag beta 2 generated by transverse feeding of a cutter are regarded as total disturbance, and a linear self-anti-interference controller is adopted to preliminarily estimate the total disturbance;
Step 3: aiming at the estimation error generated by preliminary estimation of the total disturbance by adopting a linear self-anti-interference controller in the step 2, approximating the estimation error of the total disturbance by adopting a BP neural network controller, thereby determining the accurate estimation of the total disturbance;
Step 4: compensating the system according to the accurate estimation of the total disturbance finally obtained in the steps 2 and 3, and realizing the accurate tracking of the piezoelectric ceramic type FTS;
the step 1 comprises the following steps:
the dynamics of a piezoceramic FTS system are described as:
Where x represents a fluctuation portion of the cutting thickness of the workpiece, m, c and k are equivalent mass, damping coefficient and spring rate of the metal cutting machine, k a is spring rate of the piezoelectric actuator, u is a control input signal applied to the piezoelectric actuator, and F 1 represents a variation amount of cutting force expressed as:
F1＝kmv(t) (2)
Where k m is a constant and v (t) is the rate of change of the cutting thickness over time, expressed as:
v(t)＝x-αx(t-β) (3)
Where β is the time interval between successive cuts and α is the overlap factor;
The nonlinear function of the cutting force variation in relation to the cutting thickness variation is expressed as:
F1＝H(v)＝H(x-αx(t-β)) (4)
Wherein H (v) is composed of a linear function f (v (t)) and a bounded nonlinear function h·v (t), and represents a time-lag characteristic and a hysteresis characteristic, respectively, that is:
H(v)＝h·v(t)+f(v(t)) (5)
wherein h represents hysteresis nonlinearity of the piezoelectric actuator;
Thus, substitution of formula (3) into formula (1) can be obtained:
Wherein, the state time lag β 1 is a time delay generated by spindle rotation, when spindle rotation speed Ω changes, Ω and β 1 satisfy the following relationship:
The time-varying time delay beta 2 is a random number uniformly distributed between 0 and 1, and the sampling time is 0.1s;
Taking into account the non-modeled dynamic nonlinearity inside the system, let x 1 = x, The FTS system described by equation (6) is:
wherein Γ represents the unmodeled dynamic nonlinearity inside the FTS system;
The transformed FTS system is represented as:
In the formula (9), y represents a tracking signal output from the FTS system.
2. The method according to claim 1, wherein in the step 1, for the piezoelectric actuator hysteresis nonlinearity, a backflash model is used for description.
3. The method according to claim 1, wherein the step 2 comprises:
For the FTS system described by equation (9), consider all uncertainties of the system as the total disturbance x 3, namely, let:
The method for performing preliminary estimation on the total disturbance x 3 by adopting a linear self-anti-interference controller comprises the following steps:
defining equation (9) as an extended state space expression:
Wherein the method comprises the steps of
Taking x 3 as a state variable, estimating x 3 in real time by using an LADRC linear expansion state observer;
The LADRC linear extended state observer is:
Wherein η= [ η 1 η2 η3]T,θ＝[θ1 θ2 θ3]T;
performing Laplace transformation on the formula (13) to obtain a characteristic equation:
λ0(s)＝s3+θ1s2+θ2s+θ3＝(s+ω0)3
θ is the observer gain vector obtained by simplifying the characteristic equation, and can be obtained Where ω 0 is the bandwidth of the observer; estimate/>
The FTS system described by formula (9) is simplified to
Wherein η 3 represents a preliminary estimated value obtained by preliminarily estimating the total disturbance x 3 by using a linear self-anti-interference controller.
4. A method according to claim 3, wherein said step 3 comprises:
Defining a tracking error:
e＝x-xd
wherein x d represents a desired signal;
Defining a filtered tracking error:
γ＝[ΛT 1]e (15)
Deriving formula (15):
Wherein,
The pseudo-control feedback linearization technique is adopted, and the input signal u is defined as:
wherein phi is the pseudo control input of the BP neural network;
Training the BP neural network by using historical input and output data of the FTS system as a data set to determine a pseudo control input phi of the BP neural network, thereby determining a weight self-adaptive law of the BP neural network;
and (3) utilizing the BP neural network with the weight self-adaptive law determined to realize estimation error approximation on the total disturbance, thereby determining accurate estimation on the total disturbance.
5. The method of claim 4, wherein the non-modeled dynamic nonlinear Γ expression inside the FTS system is
6. The method of claim 5, wherein the number of hidden layer nodes in the BP neural network is 30;
The weight self-adaption law is as follows:
Where p=p T > 0 and q=q T > 0 are arbitrary constant matrices;
x bp is the input vector of the neural network, σ (·) is the sigmod excitation function of the hidden layer neurons.
7. A piezoelectric ceramic type FTS comprises a main shaft, a working room, a cutter and a piezoelectric actuator, wherein the cutter is connected with the piezoelectric actuator through a spring; the method is characterized in that the piezoelectric ceramic type FTS is controlled by adopting the FTS control method based on the composite active disturbance rejection control according to any one of claims 1-6.
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