CN108931919A - A kind of permanent magnetic linear synchronous motor control system and method - Google Patents

Abstract

The invention discloses a kind of permanent magnetic linear synchronous motor control system and methods, the system includes realizing the controller of Discrete-time Sliding Mode and disturbance compensation, the sensor with the interference estimator of controller formation closed loop, the position and speed for obtaining permanent magnetic linear synchronous motor, the desired signal of signal and setting that sensor obtains belongs to the input terminal for being input to interference estimator and controller, and the output end of the controller and the controlled end of permanent magnetic linear synchronous motor connect.Discretization technique of this method based on Euler, designs the discrete time model of permanent magnetic linear synchronous motor, by introducing a kind of novel Discrete-time Sliding Mode, devises based on the discrete time terminal sliding mode and disturbance compensation control device based on equivalent control method.The advantages of invention, is: greatly increasing the control precision and interference free performance of permanent magnetic linear synchronous motor, ensure that closed-loop system state can accurately and fast converge to equalization point, this method has preferably dynamic and steady-state performance.

Description

A permanent magnet synchronous linear motor control system and method

technical field

The invention relates to the technical field of motor control, in particular to a permanent magnet synchronous linear motor control system and method.

Background technique

The permanent magnet synchronous linear motor is a device that can directly convert electrical energy into linear motion without any intermediate conversion mechanism. Since the permanent magnet synchronous linear motor has many advantages such as fast speed, large thrust, and high precision, it has been successfully used in industry, military, etc. where high speed, low thrust, small displacement, and high-precision position control are required. But the permanent magnet synchronous linear motor is a typical nonlinear multivariable system, and the control performance will be affected by various nonlinear factors, such as unknown load and friction and other nonlinear factors. Recently, the control problem of permanent magnet synchronous linear motor has become an important topic in the field of permanent magnet synchronous linear motor. How to improve the control performance of permanent magnet synchronous linear motor has received some attention.

With the development of modern control theory, many nonlinear control methods are applied to the permanent magnet synchronous linear motor control system, such as adaptive compensation control, linear sliding mode control, PID control method and so on. Although these methods are robust to system parameter uncertainties and external disturbances, they have high requirements on the dynamic and steady-state performance of the system in the motor position servo system. As more and more controllers are implemented based on digital computers in practice, although continuous time control methods can be discretized through various digital forms, such as Euler discretization, the stability analysis method of closed-loop systems (the control object is continuous time, but the controller is in discrete time form) but the analysis of this method is very difficult. Therefore, it is urgent to propose a method that can improve the dynamic and steady-state performance of the system and can be directly applied to the permanent magnet synchronous linear motor.

Contents of the invention

In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a permanent magnet synchronous linear motor control system and method.

To achieve the above object, the present invention adopts the following technical solutions:

A permanent magnet synchronous linear motor control system, including a controller that realizes discrete-time synchronous film and disturbance compensation, a disturbance estimator that forms a closed loop with the controller, a sensor that obtains the position and speed of the permanent magnet synchronous linear motor, and the signal obtained by the sensor The set expected signal is also input to the disturbance estimator and the input terminal of the controller, and the output terminal of the controller is connected with the controlled terminal of the permanent magnet synchronous linear motor.

The control method of the above-mentioned control system comprises the following steps

S1, establish the mathematical model of the permanent magnet synchronous linear motor, the mathematical model is

Where x ₁ (t), y(t) is linear displacement, x ₂ (t) is linear velocity, y(t), x ₂ (t) are obtained from position and speed sensors, is the first derivative corresponding to x ₁ (t) and x ₂ (t), u(t) is the control signal output by the controller, R is the resistance of the motor, m is the mass of the motor, k _f is the force constant, k _e is the anti-electromotive force, and d represents external disturbance, which includes friction force and ripple force;

make The mathematical model simplifies to

S2. Define the core displacement tracking error of the permanent magnet synchronous linear motor as e ₁ (t)=x _r (t)-x ₁ (t), and the linear velocity tracking error as where x _r (t) is the reference value of linear displacement, The first derivative of x _r (t) represents the reference value of the linear velocity; the dynamic equation to establish the tracking error is

in is the first derivative of e ₁ (t), e ₂ (t), is the first derivative of x _r (t), is the second derivative of x _r (t);

S3. The discrete-time model of the permanent magnet synchronous linear motor is obtained by using the Euler discretization method as

Where e ₁ (k+1) is the next moment of e ₁ (k), e ₂ (k+1) is the next moment of e ₂ (k), and h is the sampling period;

S4. Select the discrete-time terminal sliding mode as

s(k)=e ₂ (k)+c ₁ sig ^α (e ₁ (k))

Where sig ^α (e ₁ (k))=sgn(e ₁ (k))·|e ₁ (k)| ^α , |e ₁ (k)| is the absolute value of e ₁ (k), sgn(e ₁ (k)) is the sign function of e ₁ (k), c ₁ and α are parameters, c ₁ >0, 0<α<1;

S5, by using the equivalent control method s(k+1)=0, the mathematical model of the discrete-time terminal sliding mode controller u(k) that obtains the realization of the discrete-time terminal sliding mode surface S(k) is solved as

The mathematical model of the disturbance estimator for

in is the estimated value of F(k), F(k-1) is the previous moment of F(k), e ₂ (k-1) is the previous moment of e ₂ (k), u(k-1) is The previous moment of u(k), for the moment before, for the moment before

The advantage of the present invention is: the present invention is based on Euler's discretization technology, first analyzes and obtains the discrete time model of permanent magnet synchronous linear motor approximation. Then by introducing a new discrete-time sliding mode surface, a discrete-time terminal sliding mode and disturbance compensation control method based on the equivalent control method is designed. Compared with the existing control method, such as the PID control method, the present invention greatly improves the control precision and anti-interference performance of the permanent magnet synchronous linear motor. The use of the permanent magnet synchronous linear motor control method ensures that the state of the closed-loop system can converge to the equilibrium point accurately and quickly, so the permanent magnet synchronous linear motor control method has better dynamic and steady-state performance.

The feasibility of discrete-time sliding-mode and disturbance-compensated control law design is demonstrated as follows:

According to the external disturbance F(k) of the permanent magnet synchronous linear motor is bounded and satisfies |F(k)|≤d ^* , Wherein both d ^* and δ ^* are parameters and d ^* >0, δ ^* >0. From s(k+1)=h[F(k)-F(k-1)], s(k+1) is the next moment of s(k), F(k-1) is F(k) At the previous moment, the discrete-time terminal sliding mode surface s(k) is bounded as: |s(k)|≤λ=d ^* h ² =o(h ² ), where h is the sampling period, λ is a parameter and λ>0, o(h ² ) is the second-order infinitesimal of h.

where |e ₁ (∞)| is the final value of e ₁ (k), define α=2/3, express and the maximum of the two, Denotes (o(h)) ^2/α and The maximum value of the two means that |e ₁ (∞)|≤ρ=o(h ³ ), c ₁ , ρ are parameters and c ₁ >0, ρ>0, o(h ³ ) is h The third-order infinitesimal of . The displacement tracking error e ₁ (k) of the permanent magnet synchronous linear motor is bounded, and the speed tracking error e ₂ (k) of the permanent magnet synchronous linear motor is: e ₂ (k)=s(k)-c ₁ sig ^α (e ₁ (k)), the speed tracking error e ₂ (k) of the permanent magnet synchronous linear motor is also bounded.

Description of drawings

Fig. 1 is the block diagram of the permanent magnet synchronous linear motor control principle based on discrete time terminal sliding mode and disturbance compensation technology of the present invention.

Fig. 2 is the position response curve effect comparison diagram of the permanent magnet synchronous linear motor tracking step signal based on discrete time terminal sliding mode and disturbance compensation control and PID control;

Fig. 3 is the position response curve effect comparison diagram of the permanent magnet synchronous linear motor tracking sinusoidal signal based on discrete time terminal sliding mode and disturbance compensation control and PID control;

Figure 4 is a comparison diagram of the position error response curve effect of the permanent magnet synchronous linear motor tracking sinusoidal signal based on the discrete time terminal sliding mode and disturbance compensation control and PID control.

The meanings of the marked symbols in the figure are as follows:

1-Controller 2-Disturbance Estimator 3-Sensor 4-Permanent Magnet Synchronous Linear Motor

Detailed ways

Example 1

As shown in Figure 1, a permanent magnet synchronous linear motor control system includes a controller 1 that realizes discrete-time synchronous film and disturbance compensation, a disturbance estimator 2 that forms a closed loop with the controller, and obtains the position and The speed sensor 3, the signal obtained by the sensor 3 and the set expected signal belong to the input terminal of the disturbance estimator 2 and the controller, and the output terminal of the controller is connected with the controlled terminal of the permanent magnet synchronous linear motor 4 . The actual displacement signal x ₁ (k) and the actual speed signal x ₂ (k) of the permanent magnet synchronous linear motor 4 are measured by the sensor 3; the expected signal includes the expected displacement and speed signals, and the expected displacement and speed signals are different from the actual The displacement velocity error signal obtained by making a difference between the corresponding displacement and the error signal passes through the controller and the disturbance estimator 2 to obtain the control signal u(k) to control the permanent magnet synchronous linear motor 4 .

Example 2

Use the method of system in embodiment 1, concrete steps are as follows:

S1, establish the mathematical model of permanent magnet synchronous linear motor 4, mathematical model is

Wherein x ₁ (t), y (t) is linear displacement, x ₂ (t) is linear velocity, y (t), x ₂ (t) obtain according to position and speed sensor 3, is the first derivative corresponding to x ₁ (t) and x ₂ (t), u(t) is the control signal output by the controller, R is the resistance of the motor, m is the mass of the motor, k _f is the force constant, k _e is the anti-electromotive force, and d represents external disturbance, which includes friction force and ripple force;

make The mathematical model simplifies to

S2. Define the core displacement tracking error of the permanent magnet synchronous linear motor 4 as e ₁ (t)=x _r (t)-x ₁ (t), and the linear velocity tracking error is where x _r (t) is the reference value of linear displacement, The first derivative of x _r (t) represents the reference value of the linear velocity; the dynamic equation to establish the tracking error is

in is the first derivative of e ₁ (t), e ₂ (t), is the first derivative of x _r (t), is the second derivative of x _r (t);

S3. The discrete-time model of permanent magnet synchronous linear motor 4 obtained by Euler discretization method is

Where e ₁ (k+1) is the next moment of e ₁ (k), e ₂ (k+1) is the next moment of e ₂ (k), and h is the sampling period;

S4. Select the discrete-time terminal sliding mode as

s(k)=e ₂ (k)+c ₁ sig ^α (e ₁ (k))

Where sig ^α (e ₁ (k))=sgn(e ₁ (k))·|e ₁ (k)| ^α , |e ₁ (k)| is the absolute value of e ₁ (k), sgn(e ₁ (k)) is the sign function of e ₁ (k), c ₁ and α are parameters, c ₁ >0, 0<α<1;

S5, by using the equivalent control method s(k+1)=0, the mathematical model of the discrete-time terminal sliding mode controller u(k) that obtains the realization of the discrete-time terminal sliding mode surface S(k) is solved as

where the mathematical model of the interference estimator 2 for

in is the estimated value of F(k), F(k-1) is the previous moment of F(k), e ₂ (k-1) is the previous moment of e ₂ (k), u(k-1) is The previous moment of u(k), for the moment before, for the previous moment.

First, a discrete-time terminal sliding mode controller u(k) is designed according to the selected discrete-time terminal sliding mode surface S(k), and then a disturbance compensation controller is designed for the disturbance F(k) in u(k)

In the specific embodiment, select m=5.4kg, R=16.8ohms, k _f =130N/A, _ke =123V/m/s,

d(t)＝F _fric (t)+F _fipple (t)

F _fipple (t)＝A ₁ sin(ωx)+A ₂ sin(3ωx)+A ₃ sin(5ωx),

Wherein x is the actual displacement value of the permanent magnet synchronous linear motor 4, is the first derivative of x, F _fric (t) is the friction force, F _fipple (t) is the ripple force, f _c is the Coulomb friction coefficient and f _c =10N, f _s is the static friction coefficient and f _s =20N, f _v is the viscous friction coefficient and f _v =30N, A ₁ , A ₂ , A ₃ are parameters and the values are A ₁ =8.5, A ₂ =4.25, A ₃ =2.0, ω is the angular frequency and ω=3.14 rad/s, is the lubrication parameter and for symbol function. h=0.005 sec, c ₁ =1.5, c ₂ =1.5, α=2/3,

In order to facilitate the comparison of the multiple indicators of the permanent magnet synchronous linear motor 4 under the controller of the present invention and the permanent magnet synchronous linear motor 4 under the traditional PID control, in a specific implementation, the desired displacement reference signal is selected to have an amplitude of 200mm respectively The step signal and the sinusoidal signal with an amplitude of 5mm and a frequency of 1rad/s. And in the specific embodiment, the parameters of the traditional PID controller are selected as follows: proportional coefficient k _p =300, integral coefficient k _i =5, differential coefficient k _d =2.

In a specific implementation, the expected displacement signal x _r (k) of the permanent magnet synchronous linear motor 4 is used as an input signal, and the actual displacement signal x ₁ (k) of the permanent magnet synchronous linear motor 4 is measured by the sensor 3 for measuring displacement; the expected displacement The displacement error signal obtained by difference between the signal and the actual displacement signal passes through the controller and the disturbance estimator 2 to obtain the control signal u(k) to control the permanent magnet synchronous linear motor 4, so that the actual position can quickly and accurately track the desired position.

As shown in Figures 2 to 4, they are comparison diagrams of the displacement tracking curve effects of the step signal and the sinusoidal signal under the controller of the present invention and the traditional PID control respectively when the disturbance is compensated. It can be seen from the figure that the present invention can improve the anti-interference performance of the permanent magnet synchronous linear motor 4, and make the control method of the permanent magnet synchronous linear motor 4 have better stability and convergence, so the position signal obtained by the sensor 3 can be quickly , Accurately track the upper reference position signal.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the present invention. within the scope of protection.

Claims (2)

1. a kind of permanent magnetic linear synchronous motor control system, which is characterized in that including realizing discrete time synovial membrane and disturbance compensation Controller (1), with controller (1) formed closed loop interference estimator (2), obtain permanent magnetic linear synchronous motor (4) position The desired signal of the signal and setting that obtain with the sensor (3) of speed, sensor (3), which belongs to, is input to interference estimator (2) It is connect with the output end of the input terminal of controller (1), the controller (1) with the controlled end of permanent magnetic linear synchronous motor (4).

2. the control method of control system as described in claim 1, which is characterized in that include the following steps

S1, the mathematical model for establishing permanent magnetic linear synchronous motor (4), mathematical model are

Wherein x₁(t), y (t) is linear displacement, x₂It (t) is linear speed, y (t), x₂(t) according to position and speed sensor (3) It obtains,For x₁(t)、x₂(t) corresponding first derivative, u (t) are the control signals of controller (1) output, and R is The resistance of motor, m are the quality of motor, k_fIt is force constant, k_eIt is counter electromotive force power, d indicates that external interference, external interference include Frictional force and ripple power；

It enablesMathematical model is reduced to

S2, the core displacement tracking error for defining permanent magnetic linear synchronous motor (4) are e₁(t)=x_r(t)-x₁(t), linear speed Tracking error isWherein x_rIt (t) is the reference value of linear displacement,For x_r(t) single order is led Number indicates the reference value of linear speed；The kinetics equation for establishing tracking error is

WhereinIt is e₁(t), e₂(t) first derivative,It is x_r(t) first derivative,It is x_r(t) two Order derivative；

S3, use Euler's discretization method obtain permanent magnetic linear synchronous motor (4) discrete time model for

Wherein e₁It (k+1) is e₁(k) subsequent time, e₂It (k+1) is e₂(k) subsequent time, h are the sampling periods；

S4, select discrete time terminal sliding mode for

S (k)=e₂(k)+c₁sig^α(e₁(k))

Wherein sig^α(e₁(k))=sgn (e₁(k))·|e₁(k)|^α, | e₁(k) | it is e₁(k) absolute value, sgn (e₁It (k)) is e₁ (k) sign function, c₁, α be parameter, c₁0,0 < α < 1 of >；

S5, by using equivalent control method s (k+1)=0, solve accomplished discrete time terminal sliding mode face S (k) from Dissipate time TSM control device (1) u (k) mathematical model be

The wherein mathematical model of interference estimator (2)For

WhereinFor the estimated value of F (k), F (k-1) is the previous moment of F (k), e₂It (k-1) is e₂(k) previous moment, u (k-1) previous moment for being u (k),ForPrevious moment,ForPrevious moment.