CN107870566A - MEMS gyroscope quick start method based on parallel estimation Hybrid Learning - Google Patents
MEMS gyroscope quick start method based on parallel estimation Hybrid Learning Download PDFInfo
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- G—PHYSICS
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
- G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only
Abstract
The invention discloses a kind of MEMS gyroscope quick start method based on parallel estimation Hybrid Learning, for solving the technical problem of existing MEMS gyroscope modal control method poor practicability.Technical scheme is to build neural network prediction error according to parallel estimation model and kinetic model first, with reference to tracking error, designs the compound adaptive law of neural network weight, corrects the weight coefficient of neutral net, realize unknown dynamic (dynamical) effective dynamic estimation；Sliding mode controller is designed according to sliding formwork hypersurface and double exponentially approaching rules simultaneously, unknown dynamic (dynamical) feedforward compensation is realized, makes detection mass vibration error Fast Convergent, and then meet the needs of gyro quickly starts.Compound adaptive law of the invention by designing neural network weight, the weight coefficient of neutral net is corrected, sliding formwork hypersurface and the sliding mode controller of double exponentially approaching rule designs is introduced, makes detection mass vibration error Fast Convergent, and then meeting the needs of gyro quickly starts, practicality is good.
Description
Technical Field
The invention relates to a mode control method of an MEMS (micro-electromechanical system) gyroscope, in particular to a quick starting method of the MEMS gyroscope based on parallel estimation composite learning.
Background
The time required for the MEMS gyroscope to reach the nominal accuracy from power-on start-up is often as long as ten and several minutes, during which the gyroscope is in a wide temperature variation environment, and various factors comprehensively affect the gyroscope output, so that the gyroscope output has large start-up drift, which is a fatal defect for some systems requiring quick start-up use. How to design a nonlinear controller to realize effective dynamic estimation of unknown dynamics of a gyroscope and quick convergence of vibration errors of a gyroscope detection mass block are two important research contents for realizing quick starting.
A Terminal sliding mode Control of Z-axis MEMS gyroscope with an object based rotation estimation (M Saif, B Ebrahimi and M Vali, american Control reference, no. 47, no. 10 of 2011) introduces a Terminal sliding mode Control into MEMS gyroscope drive Control, and a MEMS gyroscope detection mass driving shaft vibration tracking error on a sliding mode surface can be converged to zero in a limited time by constructing the Terminal sliding mode surface. However, for a system needing quick start, the Terminal sliding mode control convergence rate is limited, and the quick start of the MEMS gyroscope is difficult to realize.
Disclosure of Invention
In order to overcome the defect that the existing MEMS gyroscope modal control method is poor in practicability, the invention provides an MEMS gyroscope quick starting method based on parallel estimation composite learning. Firstly, establishing a neural network prediction error according to a parallel estimation model and a dynamics model, designing a composite adaptive law of a neural network weight by combining a tracking error, correcting a weight coefficient of the neural network, and realizing effective dynamic estimation of unknown dynamics; meanwhile, a sliding mode controller is designed according to a sliding mode hypersurface and a double-exponential approximation rule, feed-forward compensation of unknown dynamics is achieved, vibration errors of the detection mass block are converged quickly, and the requirement for quick starting of the gyroscope is met. The invention constructs a neural network prediction error according to a parallel estimation model and a dynamics model, designs a composite adaptive law of a neural network weight by combining a tracking error, corrects the weight coefficient of the neural network and realizes effective dynamic estimation of unknown dynamics. The sliding mode controller designed by the sliding mode hypersurface and double-exponential approximation rule is introduced, so that the vibration error of the detection mass block is converged quickly, the requirement of quick start of the gyroscope is further met, and the practicability is good.
The technical scheme adopted by the invention for solving the technical problems is as follows: a MEMS gyroscope quick start method based on parallel estimation composite learning is characterized by comprising the following steps:
(a) The kinetic model of the MEMS gyroscope considering the quadrature error is:
wherein m is the mass of the proof mass; omega z Inputting an angular velocity for the gyroscope;is an electrostatic driving force; x * respectively detecting the acceleration, the speed and the displacement of the mass block of the MEMS gyroscope along the driving shaft;y * acceleration, velocity and displacement of the proof mass along the detection axis, respectively; d xx ，d yy Is the damping coefficient; k is a radical of xx ，k yy Is the stiffness coefficient; d xy Is the damping coupling coefficient, k xy Is the stiffness coupling coefficient.
In order to improve the accuracy of mechanism analysis, the MEMS gyro dynamic model is subjected to dimensionless processing. Taking dimensionless time t * ＝ω o t, then divided by the square of the reference frequency on both sides of equation (1) simultaneouslyReference length q 0 And a detection substanceThe mass m is measured to obtain a dimensionless model of the MEMS gyroscope as
Wherein, the first and the second end of the pipe are connected with each other,
redefining the relevant system parameters as
The dimensionless model of the MEMS gyroscope is simplified to
Let A =2S-D, B = Ω 2 K, considering the parameter fluctuations caused by environmental factors and unmodeled factors, equation (4) is expressed as
The dimensionless model is composed of state variables q = [ x y =] T And control input u = [ u ] x u y ] T And (4) forming. Wherein x and y are respectively the motion displacement of the detection mass block along the driving shaft and the detection shaft after the dimensionless operation; u. u x u y Respectively representing the forces applied to the driving shaft and the detection shaft after non-dimensionalization; A. b and C are parameters of the model, and the values of the parameters are related to the structural parameters and the dynamic characteristics of the gyroscope; p is the unknown dynamics brought by uncertainty of model parameters, anΔ A, Δ B are unknown parameter fluctuations caused by environmental factors and unmodeled factors.
(b) Constructing neural networksApproximationIs provided with
Wherein, X in Is an input vector of the neural network, an Is a weight matrix of the neural network; theta (X) in ) Is an M-dimensional basis vector. The ith element of the basis vector is
Wherein, X mi ，σ i Are respectively the center and standard deviation of the Gaussian function, an
Defining an optimal estimation parameter w * Is composed of
Where ψ is a set of w.
Thus, the uncertainty term of the kinetic model is expressed as
Wherein epsilon is the approximation error of the neural network.
And the estimation error of the uncertainty term is
Wherein, the first and the second end of the pipe are connected with each other,and is provided with
(c) The dynamic reference model of the MEMS gyroscope is established as
Wherein, the first and the second end of the pipe are connected with each other,q d in order to refer to the vibration displacement signal,is q d The second derivative of (d); a. The x ，A y Reference amplitudes of the proof mass vibrating along the drive axis and the proof axis, respectively; omega x ，ω y Reference angular frequencies at which the proof mass vibrates along the drive and proof axes, respectively.
Constructing a tracking error of
e＝q-q d (12)
Selecting a slip form hypersurface
Wherein the content of the first and second substances,is the first derivative of the tracking error e; alpha and beta satisfy the Hurwitz condition; m is a unit of 1 >n 1 >0，m 2 >n 2 >, 0, and m 1 ，n 1 ，m 2 ，n 2 Are all odd numbers.
Selecting a dual-exponential approach law
Wherein k is 1 >0，k 2 >0，0<a<1，b>1。
The derivation of the sliding mode hyperboloid (13) is carried out
In combination with the dual-exponential approximation law formula (14), there are
Namely, it is
Considering equation (5), the sliding mode controller is designed as
Wherein, K s Satisfying the Hurwitz condition.
Substituting the formulae (5) and (18) into the formula (17) has
By substituting formula (19) for formula (15), there are
(d) Defining a neural network prediction error as
Wherein, the first and the second end of the pipe are connected with each other,is composed ofAn estimate of (d).
Since the parallel estimation model of equation (5) is designed as
Wherein, K z Is a positive definite matrix.
Considering sliding mode function formula (13) and neural network prediction error type (21), designing composite learning law of neural network weight as
Wherein r is 1 ，r 2 ，r 3 And δ is a positive definite matrix.
(e) The controller equation (18) and the composite learning weight update law equation (23) are obtained, and the dynamic model equation (5) of the MEMS gyroscope is returned to, and the vibration displacement and the speed of the gyroscope proof mass are tracked and controlled.
The invention has the beneficial effects that: the method comprises the steps of firstly, constructing a neural network prediction error according to a parallel estimation model and a dynamics model, designing a composite adaptive law of a neural network weight by combining a tracking error, correcting a weight coefficient of the neural network, and realizing effective dynamic estimation of unknown dynamics; meanwhile, a sliding mode controller is designed according to a sliding mode hypersurface and a double-exponential approximation law, the feedforward compensation of unknown dynamics is realized, the vibration error of the detection mass block is rapidly converged, and the requirement of rapidly starting the gyroscope is further met. The method constructs a neural network prediction error according to a parallel estimation model and a dynamics model, designs a composite adaptive law of the neural network weight by combining a tracking error, corrects the weight coefficient of the neural network, and realizes effective dynamic estimation of unknown dynamics. The sliding mode controller designed by the sliding mode hypersurface and double-exponential approximation law is introduced, so that the vibration error of the detection mass block is converged quickly, the requirement of quick start of the gyroscope is met, and the practicability is good.
The invention is described in detail below with reference to the drawings and the detailed description.
Drawings
FIG. 1 is a flow chart of a MEMS gyroscope fast start method based on parallel estimation composite learning according to the invention.
Detailed Description
Refer to fig. 1. The MEMS gyroscope quick starting method based on parallel estimation composite learning specifically comprises the following steps:
(a) The kinetic model of the MEMS gyroscope considering the quadrature error is:
wherein m is the mass of the proof mass; omega z Inputting an angular velocity for the gyroscope;is an electrostatic driving force; x * respectively detecting the acceleration, the speed and the displacement of the mass block of the MEMS gyroscope along the driving shaft;y * acceleration, velocity and displacement of the proof mass along the proof axis, respectively; d is a radical of xx ，d yy Is the damping coefficient; k is a radical of formula xx ，k yy Is the stiffness coefficient; d xy Is the damping coupling coefficient, k xy Is the stiffness coupling coefficient.
In order to improve the accuracy of mechanism analysis, the MEMS gyro dynamic model is subjected to dimensionless treatment. Taking dimensionless time t * ＝ω o t, then divided by the square of the reference frequency on both sides of equation (1) simultaneouslyReference length q 0 And detecting mass m of the mass block to obtain a dimensionless model of the MEMS gyroscope
Wherein, the first and the second end of the pipe are connected with each other,
redefining the relevant system parameters as
The dimensionless model of the MEMS gyroscope can be simplified to
Let A =2S-D, B = Ω 2 K, considering the parameter fluctuations due to environmental factors and unmodeled factors, equation (4) can be expressed as
The model is composed of state variables q = [ x y =] T And control input u = [ ] x u y ] T And (4) forming. Wherein x and y are respectively the motion displacement of the detection mass block along the driving shaft and the detection shaft after the dimensionless operation; u. u x u y Respectively representing the force applied to the driving shaft and the detection shaft after non-dimensionalization; A. b and C are parameters of the model, and the values of the parameters are related to the structural parameters and the dynamic characteristics of the gyroscope; p is the unknown dynamics due to uncertainty in model parameters, anΔ A, Δ B are unknown parameter fluctuations caused by environmental factors and unmodeled factors.
According to a certain model of vibrating silicon micromechanical gyroscope, selecting parameters of the gyroscope as m =0.57 × 10 -7 kg，q 0 ＝[10 -6 10 -6 ] T m，ω 0 ＝1kHz，Ω z ＝5.0rad/s，k xx ＝80.98N/m，k yy ＝71.62N/m，k xy ＝0.05N/m，d xx ＝0.429×10 -6 Ns/m，d yy ＝0.0429×10 -6 Ns/m，d xy ＝0.0429×10 -6 Ns/m, then can be calculated
(b) And (3) dynamically estimating unknown dynamics brought by uncertain model parameters by using a neural network.
Constructing neural networksApproximationIs provided with
Wherein, X in Is an input vector to the neural network, an Is a weight matrix of the neural network; theta (X) in ) For an M-dimensional basis vector, M is the number of neural network nodes, and M =5 × 5 × 3 × 3=225 is selected. The ith element of the basis vector is
Wherein X mi ，σ i Are the center and standard deviation, respectively, of the Gaussian function, anIts value is [ -20]×[-0.24 0.24]×[-10 10]×[-0.12 0.12]Optionally, in addition to σ i ＝1。
Defining an optimal estimation parameter w * Is composed of
Where ψ is a set of w.
Thus, the uncertainty term of the kinetic model can be expressed as
Wherein epsilon is the approximation error of the neural network.
And the estimated error of the uncertainty term is
Wherein the content of the first and second substances,and is
(c) And designing a sliding mode controller according to the sliding mode hypersurface and the double-exponential approximation rule to realize the feedforward compensation of unknown dynamics.
Establishing a dynamic reference model of the MEMS gyroscope as follows
Wherein the content of the first and second substances,q d in order to refer to the vibration displacement signal,is q d The second derivative of (a); a. The x ，A y Reference amplitudes of the proof mass vibrating along the drive axis and the detection axis, respectively, and A x ＝10μm，A y ＝0.12μm；ω x ，ω y Vibrating along drive and sense axes, respectively, for the sense massReference angular frequency, and ω x ＝2000rad/s，ω y ＝2000rad/s。
Constructing a tracking error of
e＝q-q d (12)
Selecting a slip form hypersurface
Wherein the content of the first and second substances,is the first derivative of the tracking error e; alpha and beta satisfy the Hurwitz condition and take the values as m 1 >n 1 >0，m 2 >n 2 >, 0, and m 1 ，n 1 ，m 2 ，n 2 Are all odd numbers, and take the value of m 1 ＝3，n 1 ＝1，m 2 ＝5，n 2 ＝3。
Selecting a dual-exponential approach law
Wherein k is 1 >0，k 2 >0，0<a<1，b>, 1, value of k 1 ＝20，k 2 ＝20，a＝0.5，b＝10。
Derivation of the sliding-mode hyperboloid (13) is then
In combination with the dual-exponential approximation law formula (14), there are
Namely, it is
Considering equation (5), the sliding mode controller can be designed as
Wherein, K s Satisfy the Hurwitz condition and take the value as
Substituting the formulae (5) and (18) into the formula (17) has
By substituting formula (19) for formula (15), there are
(d) And (4) considering the tracking error and the neural network prediction error, and designing a composite learning law of the neural network weight.
Defining a neural network prediction error as
Wherein the content of the first and second substances,is composed ofAn estimate of (d).
Since the parallel estimation model of equation (5) can be designed
Wherein, K z Is a positive definite matrix, takes a value of
Considering sliding mode function formula (13) and neural network prediction error type (21), designing composite learning law of neural network weight as
Wherein r is 1 ，r 2 ，r 3 δ is a normal number and takes the value r respectively 1 ＝0.2，r 2 ＝5，r 3 ＝2，δ＝15。
(e) The controller equation (18) and the composite learning weight update law equation (23) are obtained, and the dynamic model equation (5) of the MEMS gyroscope is returned to, and the vibration displacement and the speed of the gyroscope proof mass are tracked and controlled.
This invention is not described in detail and is within the ordinary knowledge of a person skilled in the art.
Claims (1)
1. A MEMS gyroscope quick start method based on parallel estimation composite learning is characterized by comprising the following steps:
(a) The kinetic model of the MEMS gyroscope considering the quadrature error is:
wherein m is the mass of the proof mass; omega z Inputting an angular velocity for the gyroscope;is an electrostatic driving force; x * respectively detecting the acceleration, the speed and the displacement of the mass block of the MEMS gyroscope along the driving shaft;y * acceleration, velocity and displacement of the proof mass along the detection axis, respectively; d is a radical of xx ，d yy Is the damping coefficient; k is a radical of xx ，k yy Is the stiffness coefficient; d xy Is the damping coupling coefficient, k xy Is the stiffness coupling coefficient;
in order to improve the accuracy of mechanism analysis, carrying out dimensionless treatment on the MEMS gyro dynamic model; taking dimensionless time t * ＝ω o t, then divided by the square of the reference frequency on both sides of equation (1) simultaneouslyReference length q 0 And detecting the mass m of the mass block to obtain a dimensionless model of the MEMS gyroscope as
Wherein the content of the first and second substances,
redefining the relevant system parameters as
The dimensionless model of the MEMS gyroscope is simplified to
Let A =2S-D, B = Ω 2 K, considering the parameter fluctuation caused by environmental factors and unmodeled factors, the formula (4) is expressed as
The dimensionless model is composed of state variables q = [ x y =] T And control input u = [ ] x u y ] T Forming; wherein x and y are respectively the motion displacement of the detection mass block along the driving shaft and the detection shaft after the dimensionless operation; u. of x u y Respectively representing the force applied to the driving shaft and the detection shaft after non-dimensionalization; A. b and C are parameters of the model, and the values of the parameters are related to the structural parameters and the dynamic characteristics of the gyroscope; p is the unknown dynamics brought by uncertainty of model parameters, anDelta A and delta B are unknown parameter fluctuation caused by environmental factors and unmodeled factors;
(b) Constructing neural networksApproximationIs provided with
Wherein, X in Is an input vector to the neural network, an Is a weight matrix of the neural network; theta (X) in ) Is an M-dimensional basis vector; the ith element of the basis vector is
Wherein X mi ，σ i Are respectively the center and standard deviation of the Gaussian function, an
Defining an optimal estimation parameter w * Is composed of
Where ψ is a set of w;
thus, the uncertainty term of the kinetic model is expressed as
Wherein epsilon is an approximation error of the neural network;
and the estimation error of the uncertainty term is
Wherein the content of the first and second substances,and is provided with
(c) The dynamic reference model of the MEMS gyroscope is established as
Wherein, the first and the second end of the pipe are connected with each other,q d in order to refer to the vibration displacement signal,is q d The second derivative of (d); a. The x ，A y Reference amplitudes of the proof mass vibrating along the drive axis and the detection axis, respectively; omega x ，ω y Reference angular frequencies of the proof mass vibrating along the drive shaft and the proof shaft respectively;
constructing a tracking error of
e＝q-q d (12)
Selecting a slip form hypersurface
Wherein, the first and the second end of the pipe are connected with each other,is the first derivative of the tracking error e; alpha and beta satisfy the Hurwitz condition; m is a unit of 1 >n 1 >0，m 2 >n 2 >, 0, and m 1 ，n 1 ，m 2 ，n 2 Are all odd numbers;
selecting a dual-exponential approach law
Wherein k is 1 >0，k 2 >0，0<a<1，b>1；
The derivation of the sliding mode hyperboloid (13) is carried out
In combination with the dual-exponential approximation law formula (14), there are
Namely that
Considering equation (5), the sliding mode controller is designed as
Wherein, K s Meets the Hurwitz condition;
substituting the formulae (5) and (18) into the formula (17) has
By substituting formula (19) for formula (15) there are
(d) Defining a neural network prediction error as
Wherein the content of the first and second substances,is composed ofAn estimated value of (d);
since the parallel estimation model of equation (5) is designed as
Wherein, K z Is a positive definite matrix;
considering sliding mode function formula (13) and neural network prediction error (21), designing composite learning law of weight of neural network as
Wherein r is 1 ，r 2 ，r 3 δ is a positive definite matrix;
(e) The obtained controller equation (18) and the complex learning weight update law equation (23) are returned to the dynamic model equation (5) of the MEMS gyroscope, and the vibration displacement and the speed of the gyroscope proof mass are tracked and controlled.
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| CN110456809A (en) * | 2019-07-30 | 2019-11-15 | 哈尔滨工程大学 | A kind of structure changes integrated controller design method reducing AUV roll and pitch |
| CN110456809B (en) * | 2019-07-30 | 2022-07-15 | 哈尔滨工程大学 | Design method of variable-structure integrated controller for reducing AUV (autonomous Underwater vehicle) rolling and pitching |
| CN110579966A (en) * | 2019-09-23 | 2019-12-17 | 南通大学 | z-axis gyroscope control method based on neural network identification parameters |
| CN110579966B (en) * | 2019-09-23 | 2022-02-01 | 南通大学 | Z-axis gyroscope control method based on neural network identification parameters |
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