CN113759713B - Harmonic reducer error compensation control method by mixing memristor model with neural network - Google Patents
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Abstract
The invention discloses a harmonic reducer error compensation control method with a memristor model and a neural network mixed, which is used for improving the memristor model into a memristor hysteresis model and describing the basic change rule of hysteresis output of the harmonic reducer; and compensating the difference between the harmonic reducer hysteresis model and the memristive hysteresis model by means of an RBF neural network with nonlinear fitting capability. The RBF neural network is overlapped with memristor hysteresis model output to form a harmonic reducer hybrid hysteresis model, torsion angle output under different torques is predicted through harmonic reducer hysteresis characteristic modeling, and transmission error compensation is carried out from a harmonic reducer driving end. Completely different from a method for solving the transmission error of the harmonic speed reducer from the manufacturing perspective, the complex structure of the harmonic speed reducer and a complex operation mechanism of forward and reverse rotation transmission of periodic engagement, disengagement and re-engagement between the flexible gear and the rigid gear are avoided, and the conversion precision of the harmonic speed reducer is improved from the aspects of information modeling and compensation.
Description
Technical Field
The invention relates to the technical field of precise control of robots, in particular to a harmonic reducer error compensation control method by mixing a memristor model with a neural network.
Background
The harmonic reducer with the advantages of large transmission ratio, compact structure, high transmission precision and the like is one of the core components of the industrial robot transmission system. However, in the transmission process of the harmonic reducer, the harmonic reducer shows hysteresis characteristics due to various friction, return difference, transmission error and other reasons caused by elliptical deformation of the flexible gear, and belongs to the inherent attribute of the harmonic reducer, so that the transmission precision of the harmonic reducer is severely restricted. Aiming at nonlinear characteristics of the domestic harmonic reducer, besides solving the problems from the aspects of structure and processing, the method compensates the hysteresis characteristics of the harmonic reducer through modeling, and is another effective way for improving the transmission precision of a harmonic transmission system.
Aiming at the hysteresis characteristic of the speed reducer, the existing method is used for discussing a plurality of interference factors and constructing a relevant hysteresis model. However, the formation of the hysteresis of the harmonic speed reducer is affected by various factors, such as assembly errors in static state, transmission return errors in motion, friction, interference and the like in various forms, only one or more interference factors of the speed reducer are discussed in the existing method, the influence of other nonlinear factors on the hysteresis characteristics of the speed reducer is ignored, and the built hysteresis model of the speed reducer is not high in precision.
Disclosure of Invention
The invention provides a harmonic reducer error compensation control method by mixing a memristor model with a neural network, aiming at the problem that the conversion precision of the harmonic reducer is reduced due to the hysteresis characteristics of load torque and torsion angle of the harmonic reducer along with load change.
In order to solve the problems, the invention is realized by the following technical scheme:
the harmonic reducer error compensation control method for the memristor model and the neural network comprises the following steps:
step 1, collecting output shaft torque u (k) and output torsion angle theta of harmonic speed reducer at M latest historical moments of current moment k' to be compensated d (k)；
Step 2, constructing a mixed hysteresis model with a memristor hysteresis model and a neural network connected in parallel, and utilizing the output shaft torque u (k) and the output torsion angle theta of the harmonic reducer at M historical moments with the nearest current moment k' to be compensated acquired in the step 1 d (k) Training the mixed hysteresis model to obtain a mixed hysteresis model at the current time k' to be compensated; during the training process of the hybrid hysteresis model:
step 2.1, the output shaft torque u (k) of the harmonic speed reducer at M historical moments is sent into a memristive hysteresis model, and the output of the memristive hysteresis model at M historical moments is obtainedTorsion angle theta 0 (k)；
Step 2.2, output torque u (k) of the harmonic reducer at M historical moments and output torsion angle theta of memristor hysteresis model are calculated 0 (k) And the output torsion angle theta (k-1) of the RBF dynamic neural network is taken as the input of the RBF dynamic neural network, and the output torsion angles theta of the harmonic reducers at M historical moments are taken as the input of the RBF dynamic neural network d (k) Output torsion angle theta with memristive hysteresis model 0 (k) Deviation value theta of e (k) As the error of the RBF dynamic neural network, obtaining the output torsion angles theta (k) of the RBF dynamic neural network at M historical moments;
step 2.3, outputting torsion angles theta of memristor hysteresis models at M historical moments 0 (k) Adding the output torsion angle theta (k) of the RBF dynamic neural network to obtain unit torsion angle compensation quantity of M historical moments
Step 3, the output shaft torque u (k ') and the output torsion angle theta of the harmonic reducer at the current time k' to be compensated d (k ') feeding the obtained mixed hysteresis model of the current time k ' to be compensated in the step 2 to obtain the unit torsion angle compensation quantity of the current time k ' to be compensated
Step 4, compensating the unit torsion angle of the current time k' to be compensated obtained in the step 3Multiplying the input end torsion angle compensation quantity of the harmonic speed reducer at the current time k' to be compensated by the reduction ratio N of the harmonic speed reducer>The input torsion angle compensation of the harmonic reducer at the current time k' to be compensated is added>Adding the set torsion angle of the harmonic reducer at the input end of the current time k' to be compensated to realize the compensation control of the transmission error of the harmonic reducer;
where k=1, 2, …, M, k' =m+1, m+2, …, M is the number of set history times.
In the step 2.1, the output torsion angle θ of the memristive hysteresis model at the kth historical time 0 (k) The method comprises the following steps:
where u (k) is the output shaft torque of the harmonic reducer at the kth historical time, M (z) is the resistance value of the memristor, and k=1, 2, …, M is the number of set historical times.
In the above step 2.2, the deviation value θ at the kth history time e (k) The method comprises the following steps:
θ e (k)＝θ d (k)-θ 0 (k)
in θ d (k) Output torsion angle of harmonic reducer at kth historical moment, θ 0 (k) The k=1, 2, …, M is the number of set historical moments, which is the output torsion angle of the memristive hysteresis model at the kth historical moment.
In the above step 2.3, the unit torsion angle compensation amount at the kth history timeThe method comprises the following steps:
in θ 0 (k) And θ (k) is the output torsion angle of the RBF dynamic neural network at the kth historical moment, and k=1, 2, …, M and M are the number of the set historical moments.
Compared with the prior art, the invention has the following characteristics:
1. in consideration of the fact that the memristor hysteresis model harmonic reducer is directly used for modeling, model errors exist and parameters are difficult to identify on line, the RBF (radial Basis Function) neural network is adopted to effectively conduct output error compensation of the memristor hysteresis model, the memristor hysteresis model and the RBF neural network are connected in parallel to form a hybrid hysteresis model of the harmonic reducer, the hybrid hysteresis model is used for describing complex hysteresis characteristics of the reducer, and accuracy of the hysteresis model is effectively improved.
2. After the memristor model is improved by means of the memory characteristic of the memristor model, a memristor hysteresis model is built and used for describing the nonlinear hysteresis characteristic of the harmonic reducer.
3. The complex structure of the harmonic speed reducer and the complex operation mechanism of the forward and reverse rotation transmission of periodic engagement, disengagement and re-engagement between the flexible gear and the rigid gear are avoided, which are completely different from the manufacturing angle. Through a hysteresis model of the harmonic speed reducer, the torsion angle of the harmonic speed reducer is predicted under different loads, the transmission error compensation control is carried out from the driving input end of the harmonic speed reducer, and the conversion precision of the harmonic speed reducer is improved from the angles of information modeling and feedforward compensation.
Drawings
Fig. 1 is a hybrid hysteresis model structure.
FIG. 2 is a hysteresis characteristic of a memristor model.
FIG. 3 is a memristive hysteresis model characteristic.
FIG. 4 is a graph comparing memristive hysteresis model output with harmonic reducer output.
Fig. 5 is an RBF dynamic neural network structure.
Fig. 6 is a hybrid hysteresis model.
FIG. 7 is a compensation control system for harmonic reducer transmission errors in an industrial robot joint.
Detailed Description
The present invention will be further described in detail with reference to specific examples in order to make the objects, technical solutions and advantages of the present invention more apparent.
The output torsion angle is the difference between the theoretical output and the actual output of the harmonic reducer according to the angle of the system, and changes along with the load change. The invention constructs a hybrid hysteresis model capable of describing the hysteresis relationship between the output shaft torque and the output torsion angle of the speed reducer. The hybrid hysteresis model is of a parallel structure: on one hand, the hysteresis characteristic of the memristor model is improved, so that the hysteresis curve of the memristor model is consistent with the hysteresis characteristic curve rule of the harmonic reducer; and on the other hand, compensating the difference between the memristor hysteresis model characteristic curve and the harmonic reducer hysteresis characteristic curve by utilizing the nonlinear fitting capacity of the neural network. The memristive hysteresis model is overlapped with the neural network, and the structure of the built mixed hysteresis model is shown in fig. 1.
1) Memristor hysteresis model
And constructing a memristor hysteresis model based on the dynamic characteristics of the memristor model, so that the output of the memristor model can show the basic change rule of hysteresis output of the harmonic speed reducer.
The memristor model hysteresis curve in fig. 2 differs from the harmonic reducer hysteresis characteristic curve in that: the two hysteresis characteristic curves have different directions, and the memristor hysteresis characteristic curve has an intersection point at the abscissa of 0, so that the memristor model needs to be improved to ensure that the output of the memristor model is consistent with the change rule of the hysteresis curve of the harmonic reducer. Changing the bowknot-shaped direction of the memristor output curve; the curve is then approximately regarded as a function of the torsion angle θ when the input torque u < 0 0 The = -u symmetry is adopted, the intersection point of the output curve when the abscissa is 0 is solved by adopting the formula (1), the improved memristive hysteresis model is shown in the formula (1), and the corresponding curve is shown in fig. 3.
Where M (z) is the resistance of the memristor:
M(z)＝R ON z+R OFF (1-z) (2)
wherein D is the total thickness of the memristor, ω is the width of the doped region, R ON And R is R OFF Is the extreme resistance, mu v ≈10 -14 m 2 s -1 V -1 Is the average ion drift rate and the average ion drift rate,f is a scale factor between the moving speed and the torsion angle of the boundary n (z) is a window function, taking F n (z) =1, z being an internal state variable. R is taken ON ＝100Ω，R OFF ＝1.6kΩ，D＝10nm，z＝0.6。
Collecting output shaft torque u and actual output torsion angle theta of harmonic speed reducer d The method comprises the steps of carrying out a first treatment on the surface of the Taking the collected experimental data torque u (k) as the input of the memristive hysteresis model, and obtaining the output theta of the memristive hysteresis model by the formula (1) 0 (k) Adjusting memristor hysteresis model parameters, and under the same input, adjusting harmonic speed reducers u (k) and theta d (k) Characteristic curve and memristive hysteresis models u (k) and θ 0 (k) The characteristic curve pair is shown in fig. 4, for example.
The memristor hysteresis model characteristic curve is similar to the harmonic reducer hysteresis characteristic curve, but errors exist, and the memristor hysteresis model parameters are difficult to identify on line. The invention adopts the RBF dynamic neural network with parameter self-learning capability to compensate the difference between the memristor hysteresis model characteristic curve and the harmonic reducer hysteresis characteristic curve.
2) RBF dynamic neural network
The neural network structure is shown in fig. 5, in the RBF neural network, the output shaft torque u (k) of the harmonic reducer is set, and the memristor hysteresis model outputs theta 0 (k) And the value θ (k-1) of the RBF neural network at the previous time is input as the neural network.
Difference theta e (k) Is the torsion angle output theta of the harmonic speed reducer at k moment d (k) Output theta with memristive hysteresis model 0 (k) The difference between them is expressed as:
θ e (k)＝θ d (k)-θ 0 (k) (5)
θ e (k) Is used for RBF parameter learning, in RBF network, w= [ w ] 1 ,w i ,…,w n ] T To output the weight vector, phi= [ phi ] 1 ,φ i ,…,φ n ] T Is radial basis vector phi i As a gaussian function, the input x= [ u (k), θ of the neural network 0 (k),θ(k-1)] T I=1, 2, … n gives the neural network model:
wherein C is i ＝[c i1 ，c ij ...c nm ] T And b i Center point vector sum width of the ith neuron, j=1, 2, … m b respectively i ＞0。
Let the error loss function be:
according to the gradient descent method, the neural network weight is updated as follows:
w i (k)＝w i (k-1)+Δw i (k)+α(w i (k-1)-w i (k-2)) (9)
b i (k)＝b i (k-1)+Δb i (k)+α(b i (k-1)-b i (k-2)) (11)
c ij (k)＝c ij (k-1)+Δc ij (k)+α(c ij (k-1)-c ij (k-2)) (13)
wherein eta is E [0,1 ]]Is the learning rate; alpha E [0,1 ]]Is a momentum factor, i=1,.. 6,j =1,..3. k is the current time to be compensated, k-1 is the current time before, and k-2 is the time before k-1. w (w) i (k)，w i (k-1)，w i (k-2) respectively representing the weight coefficient w of the ith hidden node corresponding to the current time to be compensated, the time before k and the time before k-1 i Values. Δw i (k) Weighting coefficient w of current time to be compensated of ith hidden node k i Increment value, other parameters b i ，c ij Meaning and w i Similarly.
The RBF neural network is connected with the memristor hysteresis model in parallel, parameters of the neural network are regulated, and a harmonic reducer mixed hysteresis model is constructed and used for describing abrupt change and non-smooth hysteresis characteristics of the harmonic reducer.
3) Harmonic reducer hybrid hysteresis model with memristive hysteresis model and neural network connected in parallel
Adjusting memristor hysteresis model parameters to enable the parameters to show basic change rules of a characteristic curve of the speed reducer; for the difference between memristor hysteresis model output and harmonic reducer hysteresis characteristics, learning and compensating the difference through a parallel RBF neural network; the mixed hysteresis model constructed by superposition of the memristive hysteresis model and the neural network is shown in fig. 6, wherein a dotted line in the figure represents the mixed hysteresis model constructed by the parallel structure.
The input torque u (k) of the hysteresis model of the harmonic speed reducer corresponds to the output torsion angle of the model as follows:
based on the analysis, the harmonic reducer error compensation control method for the memristor model and neural network mixture, which is realized by the invention, comprises the following steps:
step 1, collecting harmonic deceleration of M latest historical moments of current moment k' to be compensatedOutput shaft torque u (k) and output torsion angle θ of the device d (k)。
Where k=1, 2, …, M, k' =m+1, m+2, …, M is the number of set history times, in this embodiment, m=100.
Step 2, constructing a mixed hysteresis model with a memristor hysteresis model and a neural network connected in parallel, and utilizing the output shaft torque u (k) and the output torsion angle theta of the harmonic reducer at M historical moments with the nearest current moment k' to be compensated acquired in the step 1 d (k) Training the mixed hysteresis model to obtain a mixed hysteresis model at the current time k' to be compensated; during the training process of the hybrid hysteresis model:
step 2.1, the output shaft torque u (k) of the harmonic speed reducer at M historical moments is sent into a memristive hysteresis model, and the output torsion angle theta of the memristive hysteresis model at M historical moments is obtained 0 (k)；
Wherein the output torsion angle theta of the memristive hysteresis model at the kth historical time 0 (k) The method comprises the following steps:
where u (k) is the output shaft torque of the harmonic reducer at the kth historical moment, and M (z) is the resistance value of the memristor.
Step 2.2, output torque u (k) of the harmonic reducer at M historical moments and output torsion angle theta of memristor hysteresis model are calculated 0 (k) And the output torsion angle theta (k-1) of the RBF dynamic neural network is taken as the input of the RBF dynamic neural network, and the output torsion angles theta of the harmonic reducers at M historical moments are taken as the input of the RBF dynamic neural network d (k) Output torsion angle theta with memristive hysteresis model 0 (k) Deviation value theta of e (k) As the error of the RBF dynamic neural network, obtaining the output torsion angles theta (k) of the RBF dynamic neural network at M historical moments;
wherein the deviation value θ at the kth historical time e (k) The method comprises the following steps:
θ e (k)＝θ d (k)-θ 0 (k)
in the method, in the process of the invention,θ d (k) Output torsion angle of harmonic reducer at kth historical moment, θ 0 (k) The output torsion angle of the memristive hysteresis model at the kth historical moment.
Step 2.3, outputting torsion angles theta of memristor hysteresis models at M historical moments 0 (k) Adding the output torsion angle theta (k) of the RBF dynamic neural network to obtain unit torsion angle compensation quantity of M historical moments
Wherein the unit torsion angle compensation amount at the kth history timeThe method comprises the following steps:
in θ 0 (k) And θ (k) is the output torsion angle of the RBF dynamic neural network at the kth historical moment, which is the output torsion angle of the memristive hysteresis model at the kth historical moment.
Step 3, the output shaft torque u (k ') and the output torsion angle theta of the harmonic reducer at the current time k' to be compensated d (k ') feeding the obtained mixed hysteresis model of the current time k ' to be compensated in the step 2 to obtain the unit torsion angle compensation quantity of the current time k ' to be compensated
Step 4, compensating the unit torsion angle of the current time k' to be compensated obtained in the step 3Multiplying the input end torsion angle compensation quantity of the harmonic speed reducer at the current time k' to be compensated by the reduction ratio N of the harmonic speed reducer>The input torsion angle compensation of the harmonic reducer at the current time k' to be compensated is added>And adding the set torsion angle of the harmonic reducer at the input end of the current time k' to be compensated to realize the compensation control of the transmission error of the harmonic reducer.
According to the invention, various interference factors causing the hysteresis of the harmonic speed reducer are comprehensively considered from the system angle, the moment and torsion angle at the output end of the speed reducer are taken as research objects, a hybrid hysteresis model is constructed, the complex hysteresis characteristic of the speed reducer due to the influence of a plurality of factors is described, and the compensation control of the transmission error caused by the hysteresis characteristic of the harmonic speed reducer is realized by using the model.
The harmonic reducer error control system for realizing the memristor model and neural network mixture of the method is composed of a coding angle detector, a torque detector and an embedded control system as shown in fig. 7. The embedded control system comprises an analog-to-digital converter, a data register, a program register and a microcontroller. The encoding angle detector is used for acquiring the angles of the harmonic reducer at all times, calculating the actual torsion angle according to the input rotation angle set by the harmonic reducer, and the torque detector is used for acquiring the actual torque of the harmonic reducer at all times in the flexible joint. The outputs of the encoder angle detector and the torque detector are fed into the microcontroller via analog-to-digital converters. The data register and the program register are connected to the microcontroller.
The memristor model is improved into a memristor hysteresis model, and the memristor model is used for describing a basic change rule of hysteresis output of the harmonic speed reducer; and compensating the difference between the harmonic reducer hysteresis model and the memristive hysteresis model by means of an RBF neural network with nonlinear fitting capability. The RBF neural network is overlapped with memristor hysteresis model output to form a harmonic reducer hybrid hysteresis model, torsion angle output under different torques is predicted through harmonic reducer hysteresis characteristic modeling, and transmission error compensation is carried out from a harmonic reducer driving end. Completely different from a method for solving the transmission error of the harmonic speed reducer from the manufacturing perspective, the complex structure of the harmonic speed reducer and a complex operation mechanism of forward and reverse rotation transmission of periodic engagement, disengagement and re-engagement between the flexible gear and the rigid gear are avoided, and the conversion precision of the harmonic speed reducer is improved from the aspects of information modeling and compensation.
It should be noted that, although the examples described above are illustrative, this is not a limitation of the present invention, and thus the present invention is not limited to the above-described specific embodiments. Other embodiments, which are apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein, are considered to be within the scope of the invention as claimed.
Claims (4)
1. The harmonic reducer error compensation control method mixed by the memristor model and the neural network is characterized by comprising the following steps:
step 1, collecting output shaft torque u (k) and output torsion angle theta of harmonic speed reducer at M latest historical moments of current moment k' to be compensated d (k)；
Step 2, constructing a mixed hysteresis model with a memristor hysteresis model and a neural network connected in parallel, and utilizing the output shaft torque u (k) and the output torsion angle theta of the harmonic reducer at M historical moments with the nearest current moment k' to be compensated acquired in the step 1 d (k) Training the mixed hysteresis model to obtain a mixed hysteresis model at the current time k' to be compensated; during the training process of the hybrid hysteresis model:
step 2.1, the output shaft torque u (k) of the harmonic speed reducer at M historical moments is sent into a memristive hysteresis model, and the output torsion angle theta of the memristive hysteresis model at M historical moments is obtained 0 (k)；
Step 2.2, output torque u (k) of the harmonic reducer at M historical moments and output torsion angle theta of memristor hysteresis model are calculated 0 (k) And the output torsion angle theta (k-1) of the RBF dynamic neural network is taken as the input of the RBF dynamic neural network, and the output torsion angles theta of the harmonic reducers at M historical moments are taken as the input of the RBF dynamic neural network d (k) And memristive hysteresis modeOutput torsion angle θ 0 (k) Deviation value theta of e (k) As the error of the RBF dynamic neural network, obtaining the output torsion angles theta (k) of the RBF dynamic neural network at M historical moments;
step 2.3, outputting torsion angles theta of memristor hysteresis models at M historical moments 0 (k) Adding the output torsion angle theta (k) of the RBF dynamic neural network to obtain unit torsion angle compensation quantity of M historical moments
Step 3, the output shaft torque u (k ') and the output torsion angle theta of the harmonic reducer at the current time k' to be compensated d (k ') feeding the obtained mixed hysteresis model of the current time k ' to be compensated in the step 2 to obtain the unit torsion angle compensation quantity of the current time k ' to be compensated
Step 4, compensating the unit torsion angle of the current time k' to be compensated obtained in the step 3Multiplying the input end torsion angle compensation quantity of the harmonic speed reducer at the current time k' to be compensated by the reduction ratio N of the harmonic speed reducer>The input torsion angle compensation of the harmonic reducer at the current time k' to be compensated is added>Adding the set torsion angle of the harmonic reducer at the input end of the current time k' to be compensated to realize the compensation control of the transmission error of the harmonic reducer;
where k=1, 2, …, M, k' =m+1, m+2, …, M is the number of set history times.
2. The method for controlling error compensation of a harmonic reducer by mixing a memristive model with a neural network according to claim 1, wherein in step 2.1, the output torsion angle θ of the memristive hysteresis model at the kth historical moment 0 (k) The method comprises the following steps:
where u (k) is the output shaft torque of the harmonic reducer at the kth historical time, M (z) is the resistance value of the memristor, and k=1, 2, …, M is the number of set historical times.
3. The method for controlling error compensation of a harmonic reducer by combining a memristive model with a neural network according to claim 1, wherein in step 2.2, the deviation value θ of the kth historical moment e (k) The method comprises the following steps:
θ e (k)＝θ d (k)-θ 0 (k)
in θ d (k) Output torsion angle of harmonic reducer at kth historical moment, θ 0 (k) The k=1, 2, …, M is the number of set historical moments, which is the output torsion angle of the memristive hysteresis model at the kth historical moment.
4. The method for controlling error compensation of a harmonic reducer by combining a memristive model with a neural network according to claim 1, wherein in step 2.3, the unit torsion angle compensation amount at the kth historical time isThe method comprises the following steps:
in θ 0 (k) The output torsion angle of the memristive hysteresis model at the kth historical moment is theta (k) which is the kthThe output torsion angles of the RBF dynamic neural network at the historical moments, k=1, 2, …, M and M are the set number of the historical moments.
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