CN105137763B - Supersonic motor robustness recursion neutral net Variable Structure Control system and method - Google Patents

Abstract

The invention relates to a robust recursive neural network sliding mode control system and method for an ultrasonic motor. The system includes a base and an ultrasonic motor disposed thereon. One side of the ultrasonic motor is connected to a photoelectric encoder, and the other The side output shaft is connected to the flywheel inertial load or DC motor, the output shaft of the flywheel inertial load or DC motor is connected to the torque sensor through a coupling, and the signal output terminals of the photoelectric encoder and torque sensor are respectively connected to the control system. The control system is composed of a robust recursive neural network sliding mode controller and an ultrasonic motor. The entire controller system is built on the sliding mode, and the smooth surface is also used as its adjustment function in the design of the robust controller. , so as to obtain better control performance. The invention not only has high control accuracy, but also has simple and compact structure and good use effect.

Description

Robust recursive neural network sliding mode control system and method for ultrasonic motor

technical field

The invention relates to the field of motor control, in particular to a robust recursive neural network sliding mode control system and method for an ultrasonic motor.

Background technique

In the design of the existing recursive neural network control system for ultrasonic motors, the total uncertainties are considered, and the total uncertainties include the cross-coupling disturbances in the driving system. In order to improve the following control effect, we design a robust recurrent neural network sliding mode control system to approximate the equivalent control in the sliding mode control system. From the experimental results of various trajectory following, we found that the system has significantly improved the motion tracking effect, and factors such as parameter changes, noise, cross-coupling interference and friction can hardly affect the motion system effect, so Lu The stick recursive neural network sliding mode control system can effectively improve the control efficiency of the system and further reduce the influence of the system on the uncertainty, so the position and speed control of the motor can obtain better dynamic characteristics.

Contents of the invention

The purpose of the present invention is to propose a robust recursive neural network sliding mode control system and method for an ultrasonic motor, which not only has high control accuracy, but also has a simple and compact structure and good use effect.

The system of the present invention is realized by the following scheme: a robust recursive neural network sliding mode control system for an ultrasonic motor, including a base and an ultrasonic motor arranged on the base, one side output shaft of the ultrasonic motor is connected to a photoelectric The encoder is connected, and the output shaft on the other side of the ultrasonic motor is connected with the flywheel inertial load or the DC motor, and the output shaft of the flywheel inertial load or the DC motor is connected with the torque sensor through an elastic coupling; The signal output end of the photoelectric encoder and the signal output end of the torque sensor are respectively connected to the control system.

Further, the control system includes an ultrasonic motor drive control circuit, the ultrasonic motor drive control circuit includes a control chip circuit and a drive chip circuit, and the signal output terminal of the photoelectric encoder is connected to the corresponding input terminal of the control chip circuit. connected, the output end of the control chip circuit is connected with the corresponding input end of the driver chip circuit to drive the driver chip circuit; the driving frequency adjustment signal output end of the driver chip circuit and the drive half-bridge circuit adjustment signal The output ends are respectively connected with the corresponding input ends of the ultrasonic motors.

The method of the present invention is realized by the following scheme: a method based on the robust recursive neural network sliding mode control system of the ultrasonic motor described above, the recursive neural network sliding mode controller is set on the control chip In the circuit, the recursive neural network sliding mode controller is established on the sliding mode, and the smooth surface is used as its adjustment function to obtain better control performance.

Further, the dynamic equation of the recursive neural network sliding mode controller can be expressed as follows:

Among them, α ₁ , α ₂ , α ₃ , α ₄ and α ₅ are all positive numbers; is the estimated value of the uncertain item H; A _p ＝-B/J, B _P ＝J/K _t >0, C _P ＝-1/J; B is the damping coefficient, J is the moment of inertia, K _t is the current factor, U(t) is the output torque of the motor, A _n is the standard value of A _p , B _n is the standard value of B _P , S(t) is the smooth surface, W is the nonlinear function, u(t) is an auxiliary control input, U _r is a robust controller, d, v and r are parameters in the neural network, F∈R ^1×K is an adjustable weight vector from the hidden layer to the output layer.

Preferably, the principle of the present invention is further as follows:

The dynamic equation of the ultrasonic motor drive system can be written as:

Where A _p ＝-B/J, B _P ＝J/K _t >0, C _P ＝-1/J; B is the damping coefficient, J is the moment of inertia, K _t is the current factor, T _f (v) is the friction Resistance torque, T _L is the load torque, U(t) is the output torque of the motor, θ _r (t) is the position signal measured by the photoelectric encoder.

Now assume that the parameters of the system are known, and the external force interference, cross-coupling interference and friction do not exist, then the standard model of the motor is shown in the following formula:

Among them, A _n is the standard value of A _p , and B _n is the standard value of B _P.

If there are uncertain items (such as the system parameter value deviates from the standard value or the system has external force disturbance, cross-coupling disturbance and friction torque, etc.), the dynamic equation of the control system is modified to:

Among them, C _n is the standard value of C _P , ΔA, ΔB, and ΔC represent small changes, and D(t) is the total uncertainty item, which is defined as:

Here we assume that the boundary of the total set of uncertain items is known, such as |D(t)|≤ρ, and ρ is a given normal number item. In order to avoid unpredictable uncertain terms in the motor, we use a robust recursive neural network sliding mode control system to control the system.

In order to achieve the purpose of control, it is to find a control law so that the state variable θ _r (t) can follow the reference command θ _m (t).

Define following error e(t)=θ _m (t)-θ _r (t) (5)

Where θ _m (t) represents the motion control command of the motor.

The smooth surface is defined as:

where λ is a positive constant value. Differentiate S(t) with respect to t, using (3), we can get:

When designing a sliding mode control system, it is first necessary to obtain the equivalent control force of the system on the smooth surface. This equivalent control force can be obtained by the following formula:

Putting formula (7) into formula (8), we can get

Solution (9), one of the solutions is as follows:

now that Then the dynamic characteristics of the sliding mode of the system are expressed as follows when t≥0:

After choosing an appropriate λ value, the dynamic characteristics required by the system, such as rise time, overshoot and stabilization time, can be simply designed as a second-order system. If the parameters of the system are determined, formula (11) will not hold true, and the stability of the system will be destroyed. In order to ensure the stability of the system under the above circumstances, the robust recursive neural network sliding mode controller design based on the control design is carried out below.

From (6), (7) and (8), the ideal equivalent control law (9) can be modified as:

Where W is a nonlinear function, which is defined as follows:

In order to approximate the ideal equivalent control law, it is designed as follows:

U _eq (t) = Wu (t) (14)

where u(t) is an auxiliary control input.

Substituting (14) into (12), the closed-loop system becomes

In actual control, u(t) can be a PID controller, and its design rules are as follows:

where K _S , K _P and _KI are control gains. We can choose K _P and K _I as follows:

K _P =K _S ×2λ; K _I =K _S ×λ ² (17)

Substituting formula (17) into formula (18), we can get

u(t)＝-K _S S(t) (18)

From equation (18), the new closed-loop control system can be obtained again as follows:

We define the Lyapunov function as follows:

Substituting equation (20) into equation (19) after differentiating it with respect to time, we can get:

because so is negative semidefinite, that is, V ₁ (S(t))≤V ₁ (S(0)), where S(t) is bounded.

hypothetical function and the integral function Γ ₁ (t) are both time variables,

V ₁ (S(0)) is bounded and V ₁ (S(t)) is a bounded non-increasing function, so the following results can be obtained:

Because Γ ₁ is also bounded, according to Barbara's auxiliary theorem, Therefore, when S(t)→0, t→∞, so it can be determined that the control design is stable, so the tracking error of the control system converges to 0 when S(t)→0.

Further, a robust recursive neural network design is carried out:

In formula (13), the influence of many uncertainties of the nonlinear function W is considered, such as the change of mechanical parameters, external noise, cross-coupling effect between shafts and friction, etc. Since the change of system parameters is not easy to obtain and an exact value of noise, cross-coupling effects and friction cannot be obtained, in practical applications, these uncertain items are difficult to know in advance, so formula (14) is almost is not possible. Therefore, we propose a controller such as equation (24) to approximate the nonlinear function W:

in As an intelligent controller, it can be used to learn the nonlinear function W, which is defined as follows:

in is the recurrent neural network output, and U _r is the robust controller. recurrent neural network Can be used to learn nonlinear equations. Due to the uncertainty of the system, we design a robust controller _Ur to compensate W and difference between.

Further, carry out recursive neural network design:

A three-layer recurrent neural network includes an input layer, a hidden layer and an output layer, and uses a Gaussian function as its trigger function, expressed by the following formula:

y=W _RNN (x,d,v,r,F)≡F (26)

where y is a recurrent neural network with a single output; F∈R ^1×K is an adjustable weight vector from the hidden layer to the output layer; k is the number of nodes in the hidden layer; T∈R ^K×1 is the output of the hidden layer vector; is the input vector of the recurrent neural network; v _ik and d _ik are the center and width of the Gaussian function respectively; r _k is the internal feedback gain; its weight value can be expressed as follows:

For the recurrent neural network of formula (26), it can uniformly approximate a nonlinear function, even a time-varying equation. Due to its approximate properties, an ideal recurrent neural network controller can be used To learn this nonlinear function W, W can be expressed as follows:

Where ε is the minimum reconstruction error; d ^* , v ^* and r ^* are the parameters d, v and r optimized in the recursive neural network, respectively. Therefore, the following formula can be obtained

in with All are optimized parameters estimated on the condition of adapting the algorithm. Then subtract (29) from (28), the approximation error It is defined as follows:

in with We use a linearization method to convert the nonlinear recursive neural network function into a partially linear form, and get The extended equation for :

in T ^* is the optimization parameter of T; is the estimated parameter of T ^* ;

_Onv ∈R ^j×1 is the vector of the higher order part.

Then substitute formula (31) into formula (30):

in is an uncertain item. According to the equations (12, 15, 18, 24, 30 and 32), the dynamic equation can be expressed as follows:

Among them, α ₁ , α ₂ , α ₃ , α ₄ and α ₅ are all positive numbers; is the estimated value of the uncertain term H.

Use the Lyapunov function:

Further differentiating equation (40) with respect to time and using equation (32), the following equation can be obtained:

If Equation (34-37) is the adaptive law of the recursive neural network, the robust controller design is Equation (38), and its estimation algorithm is Equation (39), then (41) can be re-modified as the following equation:

is a semi-negative definite, that is,

This proves that S(t), with are bounded values. command function It can be integrated over time to get:

because is a bounded value and is a non-increasing bounded value, so the result is as follows:

is a bounded value. Proved by Barbara's auxiliary theorem So when S(t)→0, then t→∞.

We use a recurrent neural network sliding mode controller to control the rotation angle of the motor rotor.

Compared with the prior art, the present invention uses the robust recursive neural network sliding mode control system of the ultrasonic motor, the system has a significant improvement in the motion tracking effect and the parameter changes, noise, cross-coupling interference and friction, etc. Factors can hardly affect the effect of the motion system, so the robust recursive neural network sliding mode control system can effectively improve the control efficiency of the system, further reduce the influence of the system on uncertainty, and improve the accuracy of control , better dynamic characteristics can be obtained. In addition, the device has reasonable design, simple and compact structure, low manufacturing cost, strong practicability and broad application prospects.

Description of drawings

Fig. 1 is a schematic structural diagram of an embodiment of the present invention.

Fig. 2 is a schematic diagram of the control circuit of the embodiment of the present invention.

[Description of main component symbols]

In the figure: 1 is the photoelectric encoder, 2 is the fixed bracket of the photoelectric encoder, 3 is the output shaft of the ultrasonic motor, 4 is the ultrasonic motor, 5 is the fixed bracket of the ultrasonic motor, 6 is the output shaft of the ultrasonic motor, 7 is the flywheel inertia load or DC Motor, 8 is flywheel inertial load or DC motor output shaft, 9 is elastic coupling, 10 is torque sensor, 11 is torque sensor fixing bracket, 12 is base, 13 is control chip circuit, 14 is drive chip circuit , 15, 16, 17 are the A, B, Z phase signals output by the photoelectric encoder, 18, 19, 20, 21 are the driving frequency adjustment signals generated by the driver chip circuit, and 22 are the driving half-bridge circuit adjustment signals generated by the driver chip circuit Signals, 23, 24, 25, 26, 27, 28 are the signals of the drive chip circuit generated by the control chip circuit, and 29 is the ultrasonic motor drive control circuit.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1, the present embodiment provides a kind of ultrasonic motor robust recursive neural network sliding mode control system, including a base 12 and an ultrasonic motor 4 located on the base 12, the ultrasonic motor 4 The output shaft 3 on one side is connected with the photoelectric encoder 1, the output shaft 6 on the other side of the ultrasonic motor is connected with the flywheel inertial load or the DC motor 7, and the output shaft 8 of the flywheel inertial load or the DC motor 7 is elastically The coupling 9 is connected with the torque sensor 10; the signal output end of the photoelectric encoder 1 and the signal output end of the torque sensor 10 are respectively connected to the control system.

The ultrasonic motor 4 , photoelectric encoder 1 , and torque sensor 10 are respectively fixed on the base 12 via the ultrasonic motor fixing bracket 5 , the photoelectric encoder fixing bracket 2 , and the torque sensor fixing bracket 11 .

As shown in Figure 2, in this embodiment, the control system includes an ultrasonic motor drive control circuit 29, the ultrasonic motor drive control circuit 29 includes a control chip circuit 13 and a drive chip circuit 14, the photoelectric encoder 1 The signal output end is connected with the corresponding input end of described control chip circuit 13, and the output end of described control chip circuit 13 is connected with the corresponding input end of described driver chip circuit 14, to drive described driver chip circuit 14; The driving frequency adjustment signal output end of the driving chip circuit 14 and the driving half-bridge circuit adjustment signal output end are respectively connected to the corresponding input ends of the ultrasonic motor 4 . The drive chip circuit 14 generates a drive frequency adjustment signal and a drive half-bridge circuit adjustment signal to control the frequency, phase and on-off of the two-phase PWM output A and B of the ultrasonic motor. The start and stop of the ultrasonic motor is controlled by turning on and off the output of the PWM wave; the optimal operating state of the motor is adjusted by adjusting the frequency of the output PWM wave and the phase difference between the two phases.

This embodiment also provides a method based on the robust recursive neural network sliding mode control system of the ultrasonic motor described above, wherein the recursive neural network sliding mode controller is set in the control chip circuit, The recursive neural network sliding mode controller is established on the sliding mode, and the smooth surface is used as its adjustment function to obtain better control performance.

In this embodiment, the dynamic equation of the recursive neural network sliding mode controller can be expressed as follows:

Among them, α ₁ , α ₂ , α ₃ , α ₄ and α ₅ are all positive numbers; is the estimated value of the uncertain item H; A _p ＝-B/J, B _P ＝J/K _t >0, C _P ＝-1/J; B is the damping coefficient, J is the moment of inertia, K _t is the current factor, U(t) is the output torque of the motor, A _n is the standard value of A _p , B _n is the standard value of B _P , S(t) is the smooth surface, W is the nonlinear function, u(t) is an auxiliary control input, U _r is a robust controller, d, v and r are parameters in the neural network, F∈R ^1×K is an adjustable weight vector from the hidden layer to the output layer.

Preferably, the principle of this embodiment is further as follows:

The dynamic equation of the ultrasonic motor drive system can be written as:

Where A _p ＝-B/J, B _P ＝J/K _t >0, C _P ＝-1/J; B is the damping coefficient, J is the moment of inertia, K _t is the current factor, T _f (v) is the friction Resistance torque, T _L is the load torque, U(t) is the output torque of the motor, θ _r (t) is the position signal measured by the photoelectric encoder.

Now assume that the parameters of the system are known, and the external force interference, cross-coupling interference and friction do not exist, then the standard model of the motor is shown in the following formula:

Among them, A _n is the standard value of A _p , and B _n is the standard value of B _P.

If there are uncertain items (such as the system parameter value deviates from the standard value or the system has external force disturbance, cross-coupling disturbance and friction torque, etc.), the dynamic equation of the control system is modified to:

Among them, C _n is the standard value of C _P , ΔA, ΔB, and ΔC represent small changes, and D(t) is the total uncertainty item, which is defined as:

Here we assume that the boundary of the total set of uncertain items is known, such as |D(t)|≤ρ, and ρ is a given normal number item. In order to avoid unpredictable uncertain terms in the motor, we use a robust recursive neural network sliding mode control system to control the system.

In order to achieve the purpose of control, it is to find a control law so that the state variable θ _r (t) can follow the reference command θ _m (t).

Define following error e(t)=θ _m (t)-θ _r (t) (5)

Where θ _m (t) represents the motion command of the motor.

The smooth surface is defined as:

where λ is a positive constant value. Differentiate S(t) with respect to t, using (3), we can get:

When designing a sliding mode control system, it is first necessary to obtain the equivalent control force of the system on the smooth surface. This equivalent control force can be obtained by the following formula:

Putting formula (7) into formula (8), we can get

Solution (9), one of the solutions is as follows:

now that Then the dynamic characteristics of the sliding mode of the system are expressed as follows when t≥0:

After choosing an appropriate λ value, the dynamic characteristics required by the system, such as rise time, overshoot and stabilization time, can be simply designed as a second-order system. If the parameters of the system are determined, formula (11) will not hold true, and the stability of the system will be destroyed. In order to ensure the stability of the system under the above circumstances, the robust recursive neural network sliding mode controller design based on the control design is carried out below.

From (6), (7) and (8), the ideal equivalent control law (9) can be modified as:

Where W is a nonlinear function, which is defined as follows:

In order to approximate the ideal equivalent control law, it is designed as follows:

U _eq (t) = Wu (t) (14)

where u(t) is an auxiliary control input.

Substituting (14) into (12), the closed-loop system becomes

In actual control, u(t) can be a PID controller, and its design rules are as follows:

where K _S , K _P and _KI are control gains. We can choose K _P and K _I as follows:

K _P =K _S ×2λ; K _I =K _S ×λ ² (17)

Substituting formula (17) into formula (18), we can get

u(t)＝-K _S S(t) (18)

From equation (18), the new closed-loop control system can be obtained again as follows:

We define the Lyapunov function as follows:

Substituting equation (20) into equation (19) after differentiating it with respect to time, we can get:

because so is negative semidefinite, that is, V ₁ (S(t))≤V ₁ (S(0)), where S(t) is bounded.

hypothetical function and the integral function Γ ₁ (t) are both time variables,

V ₁ (S(0)) is bounded and V ₁ (S(t)) is a bounded non-increasing function, so the following results can be obtained:

Because Γ ₁ is also bounded, according to Barbara's auxiliary theorem, Therefore, when S(t)→0, t→∞, so it can be determined that the control design is stable, so the tracking error of the control system converges to 0 when S(t)→0.

Further, a robust recursive neural network design is carried out:

In formula (13), the influence of many uncertainties of the nonlinear function W is considered, such as the change of mechanical parameters, external noise, cross-coupling effect between shafts and friction, etc. Since the change of system parameters is not easy to obtain and an exact value of noise, cross-coupling effects and friction cannot be obtained, in practical applications, these uncertain items are difficult to know in advance, so formula (14) is almost is not possible. Therefore, we propose a controller such as equation (24) to approximate the nonlinear function W:

in As an intelligent controller, it can be used to learn the nonlinear function W, which is defined as follows:

in is the recurrent neural network output, and U _r is the robust controller. recurrent neural network Can be used to learn nonlinear equations. Due to the uncertainty of the system, we design a robust controller _Ur to compensate W and difference between.

Further, carry out recursive neural network design:

A three-layer recurrent neural network includes an input layer, a hidden layer and an output layer, and uses a Gaussian function as its trigger function, expressed by the following formula:

y=W _RNN (x,d,v,r,F)≡F (26)

where y is a recurrent neural network with a single output; F∈R ^1×K is an adjustable weight vector from the hidden layer to the output layer; k is the number of nodes in the hidden layer; T∈R ^K×1 is the output of the hidden layer vector; is the input vector of the recurrent neural network; v _ik and d _ik are the center and width of the Gaussian function respectively; r _k is the internal feedback gain; its weight value can be expressed as follows:

For the recurrent neural network of formula (26), it can uniformly approximate a nonlinear function, even a time-varying equation. Due to its approximate properties, an ideal recurrent neural network controller can be used To learn this nonlinear function W, W can be expressed as follows:

Where ε is the minimum reconstruction error; d ^* , v ^* and r ^* are the parameters d, v and r optimized in the recursive neural network, respectively. Therefore, the following formula can be obtained

in with All are optimized parameters estimated on the condition of adapting the algorithm. Then subtract (29) from (28), the approximation error It is defined as follows:

in with We use a linearization method to convert the nonlinear recursive neural network function into a partially linear form, and get The extended equation for :

in T ^* is the optimization parameter of T; is the estimated parameter of T ^* ;

_Onv ∈R ^j×1 is the vector of the higher order part.

Then substitute formula (31) into formula (30):

in is an uncertain item. According to the equations (12, 15, 18, 24, 30 and 32), the dynamic equation can be expressed as follows:

Among them, α ₁ , α ₂ , α ₃ , α ₄ and α ₅ are all positive numbers; is the estimated value of the uncertain term H.

Use the Lyapunov function:

Further differentiating equation (40) with respect to time and using equation (32), the following equation can be obtained:

If Equation (34-37) is the adaptive law of the recursive neural network, the robust controller design is Equation (38), and its estimation algorithm is Equation (39), then (41) can be re-modified as the following equation:

is a semi-negative definite, that is,

This proves that S(t), with are bounded values. command function It can be integrated over time to get:

because is a bounded value and is a non-increasing bounded value, so the result is as follows:

is a bounded value. Proved by Barbara's auxiliary theorem So when S(t)→0, then t→∞.

We use a recurrent neural network sliding mode controller to control the rotation angle of the motor rotor.

The above descriptions are only preferred embodiments of the present invention, and all equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope of the present invention.

Claims (1)

1. The utility model provides an ultrasonic motor robustness recursion formula neural network slip modal control system, includes the base and locates the ultrasonic motor on the base, its characterized in that: an output shaft at one side of the ultrasonic motor is connected with a photoelectric encoder, an output shaft at the other side of the ultrasonic motor is connected with a flywheel inertial load or a direct current motor, and an output shaft of the flywheel inertial load or the direct current motor is connected with a torque sensor through an elastic coupling; the signal output end of the photoelectric encoder and the signal output end of the torque sensor are respectively connected to a control system;

the control system comprises an ultrasonic motor drive control circuit, the ultrasonic motor drive control circuit comprises a control chip circuit and a drive chip circuit, the signal output end of the photoelectric encoder is connected with the corresponding input end of the control chip circuit, and the output end of the control chip circuit is connected with the corresponding input end of the drive chip circuit so as to drive the drive chip circuit; the driving frequency adjusting signal output end of the driving chip circuit and the driving half-bridge circuit adjusting signal output end are respectively connected with the corresponding input ends of the ultrasonic motor;

the recursive neural network sliding mode controller is arranged in the control chip circuit, is established on a sliding mode and takes a smooth surface as an adjusting function of the controller so as to obtain better control efficiency;

wherein, the dynamic equation of the recursive neural network sliding mode controller is expressed as follows:

α therein₁，α₂，α₃，α₄And α₅Are all positive numbers;is an estimate of the uncertainty term H; a. the_p＝-B/J,B_P＝J/K_t＞0,C_P-1/J; b is damping coefficient, J is moment of inertia, K_tFor the current factor, U (t) is the output torque of the motor, A_nIs A_pThe standard value of B_nIs B_PThe standard value of (S), (t) is a smooth surface, W is a nonlinear function, U (t) is an auxiliary control input, U_rIs a robust controller, d, v and R are all parameters in a neural network, F ∈ R^1×KIs an adjustable weight vector from the hidden layer to the output layer;

wherein,representing the error of the actual value of F from the estimated value;denotes the estimated value of F, F ∈ R^1×KIs an adjustable weight vector from the hidden layer to the output layer;to representThe first derivative of (a);an estimate value representing T; t is Represents the matrix of coefficient of partial derivatives of theta to the variable d,T＝[Θ₁Θ₂…Θ_m]，Θ₁Θ₂…Θ_mfor each vector in T; t is_vRepresents the matrix of coefficient of partial derivatives of theta to the variable v,T_rrepresents the matrix of coefficient of partial derivatives of theta over the variable r, representation matrixTransposing;to representThe first derivative of (a);representing the error of the actual value of d from the estimated value;representing the error of the actual value of v from the estimated value;representing the error of the actual value of r from the estimated value;to representThe first derivative of (a);to representThe first derivative of (a).