CN110579966A - z-axis gyroscope control method based on neural network identification parameters - Google Patents
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Abstract
The application discloses a Z-axis gyroscope control method based on neural network identification parameters, which is characterized in that on the basis of obtaining micro-gyroscope tracking errors and designed sliding mode surfaces, a RBF neural network is adopted to estimate a spring parameter matrix based on the tracking errors and the sliding mode surfaces, and a micro-gyroscope control law is designed according to the sliding mode surfaces and the estimated spring parameters, so that accurate estimation of spring parameters is finally realized. The method can adopt the neural network to estimate the spring parameters under the condition that the frame of the gyroscope system is in an asymmetric structure and the spring parameters are unknown or the nominal value is inconsistent with the actual value, and completes the self-adaptive adjustment of the weight by designing the self-adaptive rule of the weight of the neural network, thereby ensuring the stability of the system and improving the measurement precision of the gyroscope.
Description
Technical Field
The invention relates to the field of automatic control systems, in particular to a Z-axis gyroscope control method based on neural network identification parameters.
background
MEMS gyroscopes are commonly used sensors for measuring angular velocity. The method is mainly applied to occasions such as navigation, mobile phones, four-axis aircrafts and the like. The operating principle of a gyroscope is based on the inertial effect of the coriolis force causing the proof mass. When an angular velocity is input, a coriolis force is generated on the micro-gyroscope which is perpendicular to both the direction of the angular velocity and the direction of the initial vibration, and whose magnitude is proportional to the input angular velocity. The required angular velocity signal can be obtained by detecting the vibration displacement caused by the Coriolis force and carrying out a series of processing such as demodulation, amplification, filtering and the like.
in fact, small manufacturing errors always exist in the manufacturing process of the micro gyroscope, so that certain deviation exists between the spring parameters of the gyroscope system and the nominal values of the spring parameters, meanwhile, the manufacturing errors can cause the problems of asymmetric structure of the micro gyroscope, misalignment of left and right driving and sensing devices, mass center deviation and the like, unnecessary cross coupling effect can be generated, system inherent interference in the form of mechanical and electrostatic force is formed, and the performance of the micro gyroscope is reduced. The traditional control method adopts self-adaptive sliding mode to estimate the system spring parameters, and the tracking effect is poor.
disclosure of Invention
In view of this, the present invention provides a method for controlling a Z-axis gyroscope based on neural network identification parameters, which aims to estimate spring parameters by using a neural network, and to design a weight adaptive rule of the neural network to complete adaptive adjustment of weights, thereby ensuring system stability.
In order to solve the technical problem, the invention provides a Z-axis gyroscope control method based on neural network identification parameters, which comprises the following steps:
1) establishing a micro-gyroscope dynamic model, and outputting a micro-gyroscope motion track according to the model;
The model is shown as follows:
In the above formula, the first and second carbon atoms are,
In the formula, q is a motion track of the gyroscope, u is a control input of the gyroscope, D is a damping parameter matrix, K is a spring parameter matrix, omega is an angular velocity parameter matrix, and D is external interference;
2) calculating a tracking error according to the motion track of the micro gyroscope obtained in the step 1), and establishing a sliding mode surface according to the tracking error;
The tracking error is shown as follows:
e＝qd-q (2)
in the above formula, e is the tracking error, qdthe reference trace is a micro gyroscope motion reference trace;
the sliding mode surface is established according to the following formula:
in the formula, S is a sliding mode surface, and lambda is a sliding mode surface parameter;
3) An RBF neural network is adopted to output an estimated spring parameter matrix according to the tracking error, and the control law of the micro gyroscope is designed according to the sliding mode surface and the estimated spring parameter matrix;
The estimated spring parameter matrix is:
In the above formula, the first and second carbon atoms are,in order to estimate the spring parameter matrix,Is the RBF neural network weight, phi1，φ2，φ3，φ4Is a Gaussian base function;
the control law of the micro gyroscope is as follows:
in the above formula, u is the control law of the micro gyroscope,is the derivative of q and is,Is qdρ is the robust term gain, sgn () is the sign function;
4) Designing a Lyapunov function based on a Lyapunov stability theory, designing an update algorithm of a RBF neural network weight according to the Lyapunov function, and applying the update algorithm to the RBF neural network to ensure that a tracking error converges to zero and ensure the stability of a system;
the Lyapunov function is as follows:
Wherein eta is1、η2、η3、η4Taking the RBF neural network weight value adaptive law gain parameter as a positive number, estimating an error for the weight;
The updating algorithm is as follows:
Wherein X and Y are displacements of the micro gyroscope on X and Y axes, S1，S2the sliding mode surface is the sliding mode surface of X and Y axes.
preferably, the control law of the micro gyroscope is designed according to the sliding mode surface and the estimated spring parameter matrix, and specifically comprises the following steps:
The first derivative of the slip form surface is:
In the above formula, the first and second carbon atoms are,Is the first derivative of S and is,is qdThe second derivative of (a);
estimating a spring parameter matrix from the RBF neural network, let saidand designing an equivalent control law of the micro gyroscope according to the estimated spring parameter matrix,
The equivalent control law is as follows:
In the above formula, ueqthe equivalent control law of the micro gyroscope;
designing a robust item of a control law according to the sliding mode surface,
The robust term of the control law is as follows:
us＝ρsgn(S) (10)
according to the equivalent control law and the robust item, designing the control law of the micro gyroscope as follows:
Compared with the prior art, the invention discloses a Z-axis gyroscope control method based on neural network identification parameters, which is characterized in that on the basis of obtaining a micro-gyroscope tracking error and a designed sliding mode surface, a spring parameter matrix is estimated by adopting an RBF neural network based on the tracking error and the sliding mode surface, a micro-gyroscope control law is designed according to the sliding mode surface and the estimated spring parameters, and finally, the accurate estimation of the spring parameters is realized. Therefore, the method can effectively compensate the manufacturing error of the micro gyroscope, effectively improve the control effect and the parameter estimation effect, and further improve the measurement precision of the micro gyroscope. The method can adopt the neural network to estimate the spring parameters under the condition that the frame of the gyro system is in an asymmetric structure and the spring parameters are unknown or the nominal value is inconsistent with the actual value, and completes the self-adaptive adjustment of the weight by designing the self-adaptive rule of the weight of the neural network, thereby ensuring the stability of the system.
Drawings
Fig. 1 is a schematic diagram of a method for controlling a Z-axis gyroscope based on neural network identification parameters according to an embodiment of the present invention.
FIG. 2 is a graph of X and Y axis position tracking curves in an embodiment of the present invention;
FIG. 3 is a graph of X and Y axis position tracking errors in an embodiment of the present invention;
FIG. 4 is a Z-axis gyroscope model spring parameter identification curve in an embodiment of the invention.
Detailed Description
for a further understanding of the invention, reference will now be made to the preferred embodiments of the present invention by way of example, and it is to be understood that the description is intended to further illustrate features and advantages of the present invention and is not intended to limit the scope of the claims which follow.
as shown in fig. 1, the present invention provides a method for controlling a Z-axis gyroscope based on neural network identification parameters, comprising the following steps:
1) Establishing a micro gyroscope dynamic model, and outputting a micro gyroscope motion track according to the model:
The mathematical model of the micro gyroscope is as follows:
wherein x and y are displacements of the Z-axis micro gyroscope in the direction of the X, Y axis, and u isx、uyfor control input of the micro-gyroscope in the direction of the X, Y axis, dxx、dyyIs the elastic coefficient, omega, of the X, Y axial springxx、ωyyis a damping coefficient in the direction of the axis of X, Y, dxy、dyx、ωxy、ωyxIs a coupling parameter, omega, due to machining errors or the likezIs the angular velocity of the mass spinning.
Writing the gyro model into a state space expression:
wherein q is1＝q，
In the formula, q is a motion track of the gyroscope, u is a control input of the gyroscope, D is a damping parameter matrix, K is a spring parameter matrix, and omega is an angular velocity parameter matrix.
Considering the external interference, the system model can be written as:
where d is external interference.
we make the following reasonable assumptions
suppose 1. the external interference exists in the upper bound, and suppose that the upper bound is D, which is a positive number. The system external interference D and the interference upper bound D meet the inequality D- | D | > delta, and delta is a small positive number.
2) calculating a tracking error according to the motion trail of the micro gyroscope obtained in the step 1), and establishing a sliding mode surface according to the tracking error:
the ideal vibration trajectory is Is the actual vibration trajectory.
Defining the tracking error of the micro gyroscope as:
e＝qd-q (15)
according to the tracking error, designing a sliding mode surface as follows:
Wherein, λ is sliding mode surface parameter, and is taken as second-order diagonal matrix, and the diagonal element is positive number.
3) an estimated spring parameter matrix is output according to the tracking error by adopting an RBF neural network, and the control law of the micro gyroscope is designed according to the sliding mode surface and the estimated spring parameter matrix:
not considering external interference, derivation is carried out on the sliding mode surface and the derivative of the sliding mode surface is madeAn equivalent control law of
in the above formula, ueqIs an equivalent control law of the micro gyroscope,is the derivative of q and is,is qdA derivative of (a);
according to the sliding mode surface, a robust item of a control law is designed as follows:
us＝ρsgn(S) (18)
in the above formula, usthe robust term of the control law of the micro gyroscope is shown, rho is the gain of the robust term, and sgn () is a sign function;
in the case where the system model is completely known, the final control law can be designed to be
Wherein u is the control law of the micro gyroscope.
since the control law contains the matrix K of the spring parameters of the micro-gyroscope, in the actual case, K is an unknown parameter or an error exists between the known nominal value and the actual value. Therefore, the control law is difficult to implement. The RBF neural network can be used to approximate the micro-gyroscope spring parameter matrix K.
Taking the estimated value of a spring parameter matrix K of the micro gyroscope asestimating all parameters in a spring parameter matrix of the micro gyroscope by utilizing a neural network, wherein the estimated value is as follows:
WhereinIs a weight of the neural network, phi1，φ2，φ3，φ4is a gaussian basis function.
assumption 2. there is an optimal weight when using neural networks to approximate the system spring parametersSatisfy the requirement of σ1，σ2，σ3，σ4Is an approximation error, and the approximation error is bounded, i.e., satisfies | σ1|＜σ1d，|σ2|＜σ2d，|σ3|＜σ3d，|σ4|＜σ4d，σ1d，σ2d，σ3d，σ4dFor the upper bound of the approximation error, the approximation error of the neural network can be theoretically such that the upper bound σ of the approximation error is1d，σ2d，σ3d，σ4dapproaching 0.
Spring coefficient matrixcan be used forexpressed as:
using the estimated value of the spring parameter to replace the actual value thereof for control force design, and designing the control law into
whereinfor the estimated values of the spring parameters of the micro-gyroscope, the estimated deviation isThe controller is as shown in figure 1.
4) Designing a Lyapunov function based on a Lyapunov stability theory, designing an update algorithm of a RBF neural network weight according to the Lyapunov function, and applying the update algorithm to the RBF neural network to ensure that a tracking error converges to zero and ensure the stability of a system;
the Lyapunov function is
wherein S is a slip form surface eta1、η2、η3、η4Taking the weight adaptive rate gain parameter of the neural network as a positive number, The error is estimated for the weight.
the derivation is carried out to obtain
Bringing the control law into the above formula to obtain
Is finished to obtain
According to the design, the updating algorithm is
wherein X and Y are displacements of the micro gyroscope on X and Y axes, S1，S2the sliding mode surface is the sliding mode surface of X and Y axes.
substituting the Lyapunov stability theory updating algorithm into (25) to obtain
The gain of the robust term is slightly larger than the upper interference bound, which is known from hypothesis 1 and hypothesis 2
The stability was demonstrated.
5) Computer simulation experiment
according to the Z-axis gyroscope control method based on the neural network identification parameters, computer simulation experiments are carried out on the control method in MATLAB/SIMULINK. The Z-axis gyroscope parameters for the simulation experiment were as follows:
m＝1.8×10-7kg，kxx＝63.955N/m，kyy＝95.92N/m，kxy＝12.779N/m，
dxx＝1.8×10-6N·s/m，dyy＝1.8×10-6N·s/m，dxy＝3.6×10-7N·s/m
The unknown input angular velocity is assumed to be Ωz100 rad/s. The reference length is selected as q01 μm, reference frequency ω01000Hz, after non-dimensionalization, the parameters of the micro gyroscope are as follows:
ωx 2＝355.3，ωy 2＝532.9，ωxy＝70.99，dxx＝0.01，dyy＝0.01，dxy＝0.002，Ω＝0.1
taking X as the initial state of the controlled object0＝[0.7 0 0.7 0]reference trackrandom interference with amplitude of 1
Coefficient of sliding form
The parameters of the neural network parameter identification part are taken as follows: eta1＝30，η2＝5，η3＝5，η4＝70
The robust gain value for the fixed robust gain is set to: ρ 50
FIG. 2 is a graph of X and Y axis position tracking performance in an embodiment of the present invention; wherein the dotted line is the actual trajectory and the solid line is the ideal trajectory. As can be seen from the figure, the controlled trajectory can well track the ideal trajectory.
FIG. 3 is a graph of X and Y axis position tracking error in an embodiment of the present invention; as can be seen from the figure, the tracking error can converge to 0 very quickly.
FIG. 4 is a Z-axis gyroscope model spring parameter identification curve in an embodiment of the present invention; wherein, the solid line is the true value of the spring parameter, and the dotted line is the approximate value of the neural network to the spring parameter; as can be seen from the figure, the neural network can well approximate the system spring parameters in real time.
as can be seen from the simulation diagrams, the control method provided by the invention can well realize track tracking, can effectively estimate the spring parameters of the system under the condition that the spring parameters of the system are unknown, and ensures the stability of the system.
while there have been shown and described what are at present considered the fundamental principles and essential features of the invention and its advantages, it will be apparent to those skilled in the art that the invention is not limited to the details of the foregoing exemplary embodiments, but is capable of other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (2)
1. A Z-axis gyroscope control method based on neural network identification parameters is characterized by comprising the following steps:
1) Establishing a micro-gyroscope dynamic model, and outputting a micro-gyroscope motion track according to the model;
the model is shown as follows:
In the above formula, the first and second carbon atoms are,
In the formula, q is a motion track of the gyroscope, u is a control input of the gyroscope, D is a damping parameter matrix, K is a spring parameter matrix, omega is an angular velocity parameter matrix, and D is external interference;
2) calculating a tracking error according to the motion track of the micro gyroscope obtained in the step 1), and establishing a sliding mode surface according to the tracking error;
the tracking error is shown as follows:
e＝qd-q；
in the above formula, e is the tracking error, qdthe reference trace is a micro gyroscope motion reference trace;
the sliding mode surface is established according to the following formula:
In the formula, S is a sliding mode surface, and lambda is a sliding mode surface parameter;
3) An RBF neural network is adopted to output an estimated spring parameter matrix according to the tracking error, and the control law of the micro gyroscope is designed according to the sliding mode surface and the estimated spring parameter matrix;
The estimated spring parameter matrix is:
In the above formula, the first and second carbon atoms are,In order to estimate the spring parameter matrix,is the RBF neural network weight, phi1，φ2，φ3，φ4Is a Gaussian base function;
The control law of the micro gyroscope is as follows:
in the above formula, u is the control law of the micro gyroscope,Is the derivative of q and is,Is qdρ is the robust term gain, sgn () is the sign function;
4) Designing a Lyapunov function based on a Lyapunov stability theory, designing an update algorithm of a RBF neural network weight according to the Lyapunov function, and applying the update algorithm to the RBF neural network to ensure that a tracking error converges to zero and ensure the stability of a system;
The Lyapunov function is as follows:
Wherein eta is1、η2、η3、η4Taking the RBF neural network weight value adaptive law gain parameter as a positive number, estimating an error for the weight;
The updating algorithm is as follows:
Wherein X and Y are displacements of the micro gyroscope on X and Y axes, S1，S2the sliding mode surface is the sliding mode surface of X and Y axes.
2. the control method according to claim 1, wherein a control law of the micro-gyroscope is designed according to the sliding-mode surface and the estimated spring parameter matrix, specifically:
the first derivative of the slip form surface is:
In the above formula, the first and second carbon atoms are,Is the first derivative of S and is,Is qdthe second derivative of (a);
estimating a spring parameter matrix from the RBF neural network, let saidand designing an equivalent control law of the micro gyroscope according to the estimated spring parameter matrix,
the equivalent control law is as follows:
In the above formula, ueqThe equivalent control law of the micro gyroscope;
Designing a robust item of a control law according to the sliding mode surface,
the robust term of the control law is as follows:
us＝ρsgn(S)
According to the equivalent control law and the robust item, designing the control law of the micro gyroscope as follows:
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