Self-adaptive fuzzy terminal sliding mode control system of permanent magnet synchronous linear motor

Abstract

The invention discloses a permanent magnet synchronous linear motor self-adaptive fuzzy terminal sliding mode control system, a self-adaptive fuzzy terminal sliding mode controller further comprises a switching control law module, the switching control law module outputs a self-adaptive fuzzy switching control law, and the self-adaptive fuzzy switching control law comprises a switching gain, an adaptive fuzzy terminal sliding mode, an adaptive fuzzy terminal sliding mode and an adaptive fuzzy terminal sliding mode. The corresponding switching gain is adjusted along with the change of the sliding mode surface, and the convergence speed corresponding to the position difference and the speed difference is controlled within the finite time; according to the method, better dynamic performance is provided, and singularity points can be eliminated while the convergence speed of the system is ensured; fuzzy control and sliding mode control are combined, and the chattering phenomenon generated by sliding mode control is restrained. Through fusion of adaptive control and fuzzy nonsingular fast terminal sliding mode control, parameters are optimized and adjusted in real time, and robustness is enhanced, so that control precision is improved, influence of unknown external disturbance is reduced, and uncertainty generated by load change is reduced.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of magnetic synchronous linear motor control, and particularly relates to a permanent magnet synchronous linear motor adaptive fuzzy terminal sliding mode control system. BACKGROUND

[0002] The permanent magnet synchronous linear motor (PMLSM) is an advanced electromagnetic drive system, and its working principle is similar to that of a conventional rotating motor, but the output is linear motion instead of rotary motion. Because the permanent magnet synchronous linear motor has the characteristics of high precision and high thrust, the permanent magnet synchronous linear motor is widely applied to the fields of high-precision positioning and high-speed linear driving. However, because the permanent magnet synchronous linear motor is a multivariable and strongly coupled nonlinear time-varying system, and the friction between the slider and the track of the permanent magnet synchronous linear motor is inevitable, it is difficult to obtain an accurate mathematical model of the permanent magnet synchronous linear motor. Moreover, when the system is running, the external disturbance and load variation generated also increase the uncertainty of the system.

[0003] In order to overcome the above problems, the present application refers to the document Nonsingular Fast Terminal Sliding Mode Control for Permanent Magnet Linear Synchronous Motor via High-Order Super-Twisting Observer, and uses the nonsingular fast terminal sliding mode control (NFTSMC). The sliding mode control theory is established on the basis of modern control theory, and the main mathematical core is the Lyapunov function. The basic principle is to design a sliding mode surface, and pull the controlled system to the sliding mode surface, and make the system move along the sliding mode surface. This method can effectively cope with external disturbance and system uncertainty. In addition, the sliding mode control also combines mathematical tools such as sign function and saturation function to enhance its robustness and stability. However, the document also has disadvantages. When the state trajectory reaches the sliding mode surface, it is difficult to strictly slide along the sliding mode surface to the equilibrium point, but instead it crosses the equilibrium point on both sides to approach the equilibrium point, thereby producing chattering. This is one of the main obstacles of the sliding mode control in practical application. Secondly, for high-precision control, asymptotic stability may not achieve fast convergence without applying strong control force. The above problems need to be solved urgently. SUMMARY

[0004] The purpose of the present application is to provide a permanent magnet synchronous linear motor adaptive fuzzy terminal sliding mode control system to solve the problems proposed in the background.

[0005] In order to achieve the above object, the present application provides the following technical scheme: a permanent magnet synchronous linear motor adaptive fuzzy terminal sliding mode control system, comprising an adaptive fuzzy non-singular fast terminal sliding mode controller, the adaptive fuzzy non-singular fast terminal sliding mode controller comprising a sliding surface module and an equivalent control law module, the adaptive fuzzy terminal sliding mode controller outputting a total control law of the permanent magnet synchronous linear motor in a two-phase rotating coordinate system according to a position difference, the sliding surface module outputting a non-singular fast terminal sliding surface, and the equivalent control law module outputting an equivalent control law, the adaptive fuzzy terminal sliding mode controller further comprising a switching control law module, the switching control law module outputting an adaptive fuzzy switching control law, the adaptive fuzzy switching control law comprising a switching gain, the corresponding switching gain being adjusted with the change of the sliding surface, and the corresponding convergence speed of the position difference and the speed difference being controlled within a limited time, wherein the position difference is the difference between the actual position of the mover and the given reference position, the speed difference is the difference between the actual speed of the mover and the given reference speed, and the speed difference is the first derivative of the position difference.

[0006] Further, the switching control law module further comprises a fuzzy control module and an adaptive control module.

[0007] The expressions of the total control law, the equivalent control law and the adaptive fuzzy switching control law are as follows:

[0008] u = -1 / K m (u eq + u sw )

[0009]

[0010] In the formula, u is the total control law, u eq is the equivalent control law, u sw is the switching control law, s is the non-singular fast terminal sliding surface, B m = -B / M, K m = K f / M, F m = -F d / M, M is the mass of the mover, B is the viscous friction coefficient, K f is the electromagnetic thrust coefficient, and K f = 3πn p ψ f / 2τ, n p is the pole pair number, ψ f is the permanent magnet flux linkage, τ is the pole pitch, F d is the integrated friction and total disturbance, e1 is the difference between the actual position of the mover and the reference position, and the derivative of e1 is the position state variable of the mover, e2 is the difference between the actual speed of the mover and the reference speed, and the derivative of e2 is the speed state variable, and d is the actual position of the mover. *is the reference position of the robot, is a normal number designed, 0≤σ3<1, α, β, σ1, σ2 are parameters of the sliding mode control respectively; 0<α<100, 0<β<20, σ1<σ2, 1<σ2<2, σ2=q / p, q and p are positive odd numbers, 0<q<10, 0<p<10, sign(x) is a sign function, the switching gain includes k1, k2, and U z , wherein k1 is a first fuzzy coefficient, k2 is a second fuzzy coefficient, is a first adaptive control coefficient, U z is a second adaptive control coefficient.

[0011] The fuzzy control module controls the output of the adaptive fuzzy switching control law by making k1 and k2 take values corresponding to the change of the absolute value of s through fuzzy control;

[0012] The adaptive control module makes U z take values corresponding to the change of the absolute value of s, take values corresponding to the change of the absolute value of s and k1, so as to control the output of the adaptive fuzzy switching control law, according to formulas (12) and (15), the second adaptive control coefficient U z and the first adaptive control coefficient

[0013]

[0014] In the formula, 0<μ<20, 0<z<1, 0<η<500, s is a nonsingular fast terminal sliding mode surface, k1 is a first fuzzy coefficient, is a first adaptive control coefficient, U z is a second adaptive control coefficient.

[0015] Further, according to the fuzzy control, the physical domain A of the absolute value of the nonsingular fast terminal sliding mode surface s is set, the physical domain A has a plurality of fuzzy sets, the input absolute value of s corresponds to the fuzzy set in the physical domain A;

[0016] According to the fuzzy control, the physical domain B of the first fuzzy coefficient k1 and the physical domain C of the second fuzzy coefficient k2 are set, the physical domain B and the physical domain C have a plurality of fuzzy sets respectively, the output first fuzzy coefficient k1 corresponds to the fuzzy set in the physical domain B, and the output second fuzzy coefficient k2 corresponds to the fuzzy set in the physical domain C;

[0017] The corresponding relationship of the fuzzy sets in A, B and C is set, so that the corresponding first fuzzy coefficient k1 and second fuzzy coefficient k2 are obtained according to the change of the absolute value of s, so as to control the corresponding convergence speed of the position difference and the speed difference in a limited time.

[0018] Further, set quantization factor q s , quantization factor q s Scale the actual physical quantity of s absolute value to input sliding surface s ly , input sliding surface s ly Fall into the physical domain A range of s absolute value; Set proportional factor q1 and q2, proportional factor q1 enlarge the first output coefficient k ly1 In the physical domain B of k1 to the first fuzzy coefficient k1 as the actual control quantity; Proportional factor q2 enlarge the second output coefficient k ly1 In the physical domain C of k2 to the second fuzzy coefficient k2 as the actual control quantity;

[0019]

[0020] In the formula: Z, PS, PM, PMB and PB are fuzzy sets of fuzzy language variables, Z represents zero, PS represents positive small, PM represents positive medium, PMB represents positive medium big; PB represents positive big;

[0021] Input sliding surface s ly Corresponding to the fuzzy set in A, determine the corresponding fuzzy set in A through the value of input sliding surface s ly , the first output coefficient k ly1 Corresponding to the fuzzy set in B, determine the corresponding first output coefficient k ly1 Through the fuzzy set in B, the second output coefficient k ly1 Corresponding to the fuzzy set in C, determine the corresponding second output coefficient k ly1 ;

[0022] When A takes PB, B takes Z, and C takes PB; When A takes PMB, B takes PS, and C takes PMB; When A takes PM, B takes PM, and C takes PM; When A takes PS, B takes PMB, and C takes PS; When A takes Z, B takes PB, and C takes Z;

[0023] Scale the corresponding k1 and k2 in the physical domain first output coefficient k ly1 And the second output coefficient k ly1 Through proportional factor q1 and q2 respectively, obtain the k1 and k2 values of the actual control quantity.

[0024] Further, the physical domain A is designed as [0, 0.1], the physical domain B is designed as [0, 1], and the physical domain C is designed as [0, 1];

[0025] The membership function of s ly As input is designed as gauss2 type input function, k ly1The membership function as the output is designed as a first output function of a triangle type, k ly1 The membership function as the output is designed as a second output function of a triangle type.

[0026] Compared with the prior art, the application has the beneficial effects that: the application provides better dynamic performance for the system through the non-singular fast terminal sliding mode control, eliminates the singular point while ensuring the convergence speed of the system, suppresses the chattering phenomenon generated by the sliding mode control through the combination of the fuzzy control and the sliding mode control, optimizes and adjusts the parameters in real time through the combination of the adaptive control and the fuzzy non-singular fast terminal sliding mode control, enhances the robustness and improves the control precision, reduces the influence of unknown external disturbances and reduces the uncertainty generated by the load change. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 The figure is a structure schematic block diagram of the adaptive fuzzy non-singular fast terminal sliding mode controller in the embodiment of the application;

[0028] Figure 2 The figure is a flow chart of the fuzzy control in the embodiment of the application;

[0029] Figure 3 The figure is a membership function graph of the absolute value of the input variable s in the embodiment of the application;

[0030] Figure 4 The figure is a membership function graph of the first fuzzy coefficient k1 of the output variable in the embodiment of the application;

[0031] Figure 5 The figure is a membership function graph of the second fuzzy coefficient k2 of the output variable in the embodiment of the application;

[0032] Figure 6 The figure is a position tracking response curve graph corresponding to the sinusoidal function in the embodiment of the application;

[0033] Figure 7 The figure is a position tracking error curve graph corresponding to the sinusoidal function in the embodiment of the application;

[0034] Figure 8 The figure is an electromagnetic thrust graph corresponding to the sinusoidal function in the embodiment of the application;

[0035] Figure 9 The figure is a PMSLM adaptive fuzzy non-singular fast terminal sliding mode control system block diagram in the embodiment of the application;

[0036] Figure 10 The figure is another structure schematic block diagram of the adaptive fuzzy non-singular fast terminal sliding mode controller in the embodiment of the application. DETAILED DESCRIPTION

[0037] Clearly, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present application.

[0038] In the description of the present application, unless otherwise specified, the meaning of "a plurality of" is two or more; the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail" and the like are based on the orientations or positional relationships shown in the drawings, and are only for the purpose of facilitating the description of the present application and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second", "third" and the like are only for the purpose of description, and cannot be understood as indicating or implying relative importance.

[0039] In the description of the present application, it should be noted that, unless otherwise specified and limited, the terms "connected", "connected" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0040] Please refer to the drawings in the specification, the present application provides a kind of technical scheme: a kind of permanent magnet synchronous linear motor adaptive fuzzy terminal sliding mode control system, including adaptive fuzzy non-singular fast terminal sliding mode controller 1, adaptive fuzzy non-singular fast terminal sliding mode controller 1 includes sliding surface module 33 and equivalent control law module 31, adaptive fuzzy terminal sliding mode controller 1 exports permanent magnet synchronous linear motor in two-phase rotating coordinate system according to position difference output total control law, sliding surface module 33 exports non-singular fast terminal sliding surface, equivalent control law module 31 exports equivalent control law, adaptive fuzzy terminal sliding mode controller 1 still includes switching control law module 34, switching control law module 34 exports adaptive fuzzy switching control law, adaptive fuzzy switching control law includes switch gain, adjusts corresponding switch gain with the change of sliding surface, controls the corresponding convergence speed of position difference and speed difference in limited time, wherein, position difference is the difference between the actual position of mover and given reference position, speed difference is the difference between the actual speed of mover and given reference speed, and speed difference is the first derivative of position difference.

[0041] In the above embodiments, as Figure 9As shown, an adaptive fuzzy terminal sliding mode control system for a permanent magnet synchronous linear motor further includes a PI regulator 2 for the current loop, an inverse Park transform module 3, an SVPWM module 4, an inverter 5, a Park transform module 6, a Clark transform module 7, a grating ruler 8, and a permanent magnet synchronous linear motor module 9. It also includes an adaptive fuzzy non-singular fast terminal sliding mode controller 1. The adaptive fuzzy non-singular fast terminal sliding mode controller 1 outputs the overall control law of the permanent magnet synchronous linear motor in a two-phase rotating coordinate system based on the position difference, such as... Figure 1 As shown, the adaptive fuzzy non-singular fast terminal sliding mode controller 1 also includes a sliding mode surface module 33, which controls the output of the non-singular fast terminal sliding mode surface based on the position difference and velocity difference; an equivalent control law module 31, which sets the first derivative of the sliding mode surface to zero and controls the output of the equivalent control law; and a switching control law module 34, which adjusts the corresponding switching gain of the adaptive fuzzy switching control law as the sliding mode surface changes, controls the convergence and expansion speeds of the position difference and velocity difference within a finite time, and outputs the adaptive fuzzy switching control law; wherein, the position difference is the difference between the actual position of the mover and the given reference position, the velocity difference is the difference between the actual velocity of the mover and the given reference velocity, and the velocity difference is the first derivative of the position difference.

[0042] The adaptive fuzzy terminal sliding mode control system for a permanent magnet synchronous linear motor includes an adaptive fuzzy non-singular fast terminal sliding mode controller 1, a PI regulator for the current loop 2, an inverse Park transform module 3, an SVPWM module 4, an inverter 5, a Park transform module 6, a Clark transform module 7, a grating ruler 8, and a permanent magnet synchronous linear motor module 9. The adaptive fuzzy non-singular fast terminal sliding mode controller 1 calculates the equivalent current of the permanent magnet synchronous linear motor in a two-phase rotating coordinate system based on the difference between the actual position and the given reference position.

[0043] The adaptive fuzzy terminal sliding mode control system for permanent magnet synchronous linear motors obtains the equivalent current of the permanent magnet synchronous linear motor in a two-phase rotating coordinate system (dq coordinate system) based on the difference between the actual position and the given reference position using an adaptive fuzzy non-singular fast terminal sliding mode controller 1. The PI regulator 2 in the current loop obtains the motor voltage d and q axis reference values ​​U. d U q ; Desired value of the d-axis component of the motor stator current (Usually set to 0) and the actual value of the d-axis component of the motor stator current fed back by the Park transformation module 32. d The difference Δi d The PI regulator 2 of the current loop obtains the motor voltage d-axis reference value U. d Motor voltage q-axis reference value U q and motor voltage d-axis reference value U dThe motor alpha, beta axis stator reference voltage U is transformed by the inverse Park transformation module 3 α , β The SVPWM module 4 is a space vector pulse width modulation module, which modulates the motor alpha, beta axis stator reference voltage U α , β to obtain a PWM wave, and the six switching devices of the inverter 5 are controlled by the PWM wave, so that the direct current power signal is inverted into a three-phase alternating current voltage to control the permanent magnet synchronous linear motor module 9; the actual value i of the motor stator current q axis component and the actual value i of the motor stator current d axis component are obtained by the motor three-phase current i q , d , a , b , c are transformed by the Clarke transformation module 7 and the Park transformation module 6; the grating ruler 8 is used to obtain the actual position d of the mover.

[0044] As shown in Figure 1 , the adaptive fuzzy nonsingular fast terminal sliding mode controller 1 includes an equivalent control law module 31, a derivation module 32, a sliding mode surface module 33, a switching control law module 34, and a gain module 35, which are used to generate a total control law The switching control law module 34 includes a fuzzy control module and an adaptive control module; the equivalent control law module 31 is used to output an equivalent control law; e1 is the difference between the actual position of the mover and the reference position, e2 is the difference between the actual speed of the mover and the reference speed, the derivation module 32 is used to derive e1 to obtain e2, the sliding mode surface module 33 is used to output a sliding mode surface s, the switching control law module 34 outputs an adaptive fuzzy switching control law through the fuzzy control module and the adaptive control module, and the switching control law module 34 outputs the adaptive fuzzy switching control law by adjusting the switching gain. In the switching control law, the switching gain is a key design parameter. The switching gain is a scalar coefficient, which is applied to the switching term and / or the discontinuous term of the switching control law. The switching control term is responsible for driving the system state to the sliding mode surface and overcoming model uncertainties, parameter variations, and external disturbances. The switching gain is used to overcome uncertainties and disturbances. Unmodeled dynamics, parameter variations, and external disturbances always exist in the system. In order to ensure the occurrence and maintenance of the sliding mode motion, the switching gain enables the control force generated by the switching term to offset or suppress the total effect of all possible uncertainties and disturbances, so as to provide a strong enough control force to drive the system state to the sliding mode surface and overcome the uncertainties and external disturbances existing in the system, ensure the robustness, and minimize the chattering and the negative effects caused by the chattering. The gain module 35 is used to generate a gain coefficient -1 / k m Further, the equivalent control law u eq and the switching control law u sw are summed and multiplied by the gain coefficient -1 / km Multiplication, get total control law u, wherein,

[0045] The application is based on the traditional sliding mode control, adopts the non-singular fast terminal sliding mode control, can provide better dynamic performance for the system, and can eliminate the singular point while ensuring the convergence speed of the system; in the process of converging to the equilibrium point, the high-frequency switching motion is made near the sliding surface to converge to the equilibrium point, and finally the chattering is formed; based on the chattering phenomenon generated by the sliding mode control, the application introduces the method of combining fuzzy control and sliding mode control to achieve the effect of suppressing chattering.

[0046] Optionally, the switching control law module 34 further comprises a fuzzy control module and an adaptive control module;

[0047] The expressions of the total control law, the equivalent control law and the adaptive fuzzy switching control law are:

[0048] u = -1 / K m (u eq + u sw )

[0049]

[0050] In the formula: u is the total control law, u eq is the equivalent control law, u sw is the switching control law, s is the non-singular fast terminal sliding surface, B m = -B / M, K m = K f / M, F m = -F d / M, M is the mass of the mover, B is the viscous friction coefficient, K f is the electromagnetic thrust coefficient, and K f = 3πn p ψ f / 2τ, n p is the number of pole pairs, ψ f is the permanent magnet flux, τ is the pole pitch, F d is the integrated friction and total disturbance e1 is the difference between the actual position of the mover and the reference position, and the derivative is the position state variable of the mover, e2 is the difference between the actual speed of the mover and the reference speed, and the derivative is the speed state variable, d is the actual position of the mover, d *is the reference position of the motion, σ3 is a normal number designed, 0 < σ3 < 1, α, β, σ1, σ2 are parameters of the sliding mode control respectively, 0 < α < 100, 0 < β < 20, σ1 < σ2, 1 < σ2 < 2, σ2 = q / p, q and p are positive odd numbers, 0 < q < 10, 0 < p < 10, sign(x) is a sign function, the switching gain includes k1, k2, and U z , wherein k1 is a first fuzzy coefficient, k2 is a second fuzzy coefficient, is a first adaptive control coefficient, U z is a second adaptive control coefficient.

[0051] The fuzzy control module adjusts k1 and k2 to take values corresponding to the change of the absolute value of s through fuzzy control, so as to control the output of the adaptive fuzzy switching control law.

[0052] The adaptive control module adjusts U z to take values corresponding to the change of the absolute value of s, to take values corresponding to the change of the absolute value of s and k1, so as to control the output of the adaptive fuzzy switching control law, according to formulas 12 and 15, the second adaptive control coefficient U z and the first adaptive control coefficient

[0053]

[0054] In the formula, 0 < μ < 20, 0 < z < 1, 0 < η < 500, s is a non-singular fast terminal sliding mode surface, k1 is a first fuzzy coefficient, is a first adaptive control coefficient, U z is a second adaptive control coefficient.

[0055] In the above embodiment, let The expression of the total control law, the equivalent control law and the adaptive fuzzy switching control law is:

[0056] u = -1 / K m (u eq + u sw )

[0057]

[0058] The switching control law module 34 further includes a fuzzy control module 38, which adjusts k1 and k2 to take values corresponding to the change of the absolute value of s respectively based on fuzzy control, so as to adjust the adaptive fuzzy switching control law; an adaptive control module, which adjusts U and U z to take values corresponding to the change of s respectively, so as to perform adaptive control on the adaptive fuzzy switching control law.

[0059] According to the position difference and the speed difference, a non-singular fast terminal sliding mode surface is obtained, and the expression of the non-singular fast terminal sliding mode surface is:

[0060]

[0061] Wherein, e1 and e2 represent the position difference and the speed difference of the mover; α, β, σ1, σ2 are parameters of the sliding mode control respectively; 0 < α < 100, 0 < β < 20, σ1 < σ2, 1 < σ2 < 2, σ2 = q / p; q and p are positive odd numbers, 0 < q < 10, 0 < p < 10; sign(x) is a sign function.

[0062] Further comprising a permanent magnet synchronous linear motor module 9, used to obtain the operating parameters of the permanent magnet synchronous linear motor and the position difference and the speed difference, obtain the mathematical model of the permanent magnet synchronous linear motor, and the mathematical model of the permanent magnet synchronous linear motor is:

[0063]

[0064] Wherein, d is the actual position of the mover; is the acceleration of the mover; M is the mass of the mover; B is the viscous friction coefficient; K f is the electromagnetic thrust coefficient, K f = 3πn p ψ f / 2τ; n p is the number of pole pairs; ψ f is the magnetic linkage of the permanent magnet; τ is the pole pitch; i q is the motor current; F d is the integration of the friction and the total disturbance.

[0065] Based on the mathematical model of the permanent magnet synchronous linear motor, the state equation of the permanent magnet synchronous linear motor system is generated, and The state equation is:

[0066]

[0067] Wherein, B m =-B / M; K m =K f / M; F m =-F d / M; e1 is the difference between the actual position of the mover and the reference position, and the derivative is the position state variable of the mover; e2 is the difference between the actual speed of the mover and the reference speed, and the derivative is the speed state variable; is the equivalent current of the permanent magnet synchronous linear motor in the two-phase rotating coordinate system according to the position difference, d * is the reference position.

[0068] The adaptive fuzzy nonsingular fast terminal sliding mode control system adopted by the application obtains equivalent currents of the permanent magnet synchronous linear motor in a two-phase rotating coordinate system (d-q coordinate system) according to a difference between an actual position and a given reference position

[0069] Further, the adaptive fuzzy nonsingular fast terminal sliding mode controller 1 is used to obtain a total control law, an equivalent control law and a switching control law through a nonsingular fast terminal sliding surface and a mathematical model of the permanent magnet synchronous linear motor;

[0070] Let The expression of the total control law, the equivalent control law and the first switching control law is:

[0071]

[0072] Wherein, u is the total control law; u eq is the equivalent control law; u qh is the first switching control law; λ1, λ2 and σ3 are normal numbers designed, and 0 < σ3 < 1;

[0073] The first fuzzy coefficient k1 and the second fuzzy coefficient k2 are set for the switching control law to generate a fuzzy switching control law, and a functional relationship between the first fuzzy coefficient, the second fuzzy coefficient and the sliding surface is established, so that the first fuzzy coefficient and the second fuzzy coefficient change accordingly with the change of the sliding surface;

[0074] The fuzzy switching control law, and the expression of the fuzzy switching control law is:

[0075]

[0076] Wherein, in order to weaken the chattering, a fuzzy control module is designed, the input variable is the absolute value of the sliding surface s, and the output variable is set as the first fuzzy coefficient k1 and the second fuzzy coefficient k2.

[0077] The adaptive control module is used to generate an adaptive fuzzy switching control law through the fuzzy switching control law, so as to control the position of the system, increase the convergence speed of the system far away from the sliding surface, reduce the convergence speed when close to the sliding surface, and suppress the chattering of the sliding surface.

[0078] The formula 12 and the formula 15 are substituted into the formula 6, and the expression of the adaptive fuzzy switching control law is obtained as:

[0079] u = -1 / K m (u eq + u sw )

[0080]

[0081] wherein: μ is a constant greater than 0; 0<z<1; η is a constant and greater than 0; is the upper limit estimation value of parameter λ1; λ2=U z is the adaptive control of λ2.

[0082] The approaching law of the sliding mode control can guarantee the quality of the system state point movement, and is also the main factor of the chattering phenomenon generated by the system, when the state point is far away from the sliding mode surface, the appropriate approaching law can make the system have a faster approaching speed, and accelerate the dynamic response of the system; when the phase point moves to the sliding mode surface, the approaching speed is rapidly reduced to zero, so as to guarantee that the phase point stays on the surface, and realizes the adaptive control through the fuzzy switching control law; since the permanent magnet synchronous linear motor itself is a nonlinear time-varying system, when the system is running, there are unknown external disturbances, and the load variation also increases the uncertainty, aiming at the above problems, the adaptive control is designed to optimize and adjust the parameters in real time, enhance the robustness, and improve the control precision, the method combining the non-singular fast terminal sliding mode control, the fuzzy control and the adaptive control is adopted, the convergence speed of the system is guaranteed, the chattering is suppressed, and the purpose of improving the position precision is realized.

[0083] The traditional exponential approaching law of the sliding mode control is expressed as:

[0084]

[0085] Wherein, ε>0, k>0; -εsign(s) is the constant speed approaching law, and -ks is the exponential approaching law.

[0086] Since the traditional pure exponential approaching law cannot converge to the sliding mode surface in a limited time, the constant speed approaching term is added, and the purpose is to ensure that when s approaches 0, the approaching speed is ε instead of 0. Although the limited time convergence problem can be solved by adding the constant speed approaching term, the approaching speed to the sliding mode surface is mainly determined by the design value of the parameter k, which makes the increase of the approaching speed and the reduction of the sliding chattering contradictory.

[0087] By integrating the formula from 0 to t, wherein s(t)=0

[0088] t * =1 / k[ln[s(0)+ε / l]-lnε / k}——formula (11);

[0089] From the above formula, the approach speed increases with the increase of k value, if a faster approach speed is obtained, k should take a larger value, but when the system reaches the sliding surface, a larger k value will lead to overshoot, and then increase the chattering of the system on the sliding surface. In order to make the convergence speed of the system far away from the sliding surface large enough, the convergence speed when approaching the sliding surface is small, and the chattering of the sliding surface is suppressed. The present application carries out adaptive control on the equal speed approach law and the exponential approach law respectively.

[0090] Step a, the following function is designed:

[0091]

[0092] Wherein, μ is a constant greater than 0; 0 < z < 1.

[0093] The convergence speed of the system far away from the sliding surface is large enough, and the convergence speed when approaching the sliding surface is small.

[0094] Step b, based on Lyapunov theorem, the Lyapunov function is selected as follows:

[0095]

[0096] Wherein: η is a constant greater than 0; N represents the upper limit value of parameter λ1, represents the upper limit estimate value of parameter λ1, represents the estimation error.

[0097] Derive the formula with respect to time:

[0098]

[0099] Let The adaptive law is obtained as follows:

[0100]

[0101] Therefore, the adaptive fuzzy nonsingular fast terminal sliding mode controller is designed as:

[0102] u = -1 / K m (u eq +u sw )

[0103]

[0104] The stability of the designed controller is proved as follows:

[0105] The Lyapunov function is selected as follows:

[0106]

[0107] Differentiating the formula with respect to time, we have:

[0108]

[0109] Substituting the above formula, we have:

[0110]

[0111] If the condition is satisfied Then:

[0112]

[0113] Therefore, the adaptive fuzzy nonsingular fast terminal sliding mode controller satisfies the condition That is, the closed-loop system is stable, and

[0114] A sine function with an amplitude of 0.2m and a frequency of 1Hz is set as the reference position. At 5s, the load is suddenly changed from 200N to 400N.

[0115] The parameters of the permanent magnet synchronous linear motor are: R s = 2.6Ω; L s = 0.0267H; ψ f = 0.24Wb; τ = 0.018m; n p = 2 pairs; M = 6.6kg; B = 0.2N·s / m.

[0116] The parameters of the controller are: α = 20; β = 1; σ1 = 9 / 7; σ2 = 5 / 3; σ3 = 1 / 3; λ1 = 50; λ2 = 100; q s = 1; q1 = 5; q2 = 500; U G = 120; η = 5; n = 0.7.

[0117] According to the controller, the position control of the permanent magnet synchronous linear motor is carried out, and the simulation curve is as follows Figure 6 , Figure 7 , Figure 8 .

[0118] Optionally, according to the fuzzy control, the physical domain A of the absolute value of the nonsingular fast terminal sliding mode surface s is set, the physical domain A has a plurality of fuzzy sets, and the input absolute value of s corresponds to the fuzzy set in the physical domain A;

[0119] ​According to the fuzzy control, the physical domain B of the first fuzzy coefficient k1 and the physical domain C of the second fuzzy coefficient k2 are set, the physical domain B and the physical domain C each have a plurality of fuzzy sets, the output first fuzzy coefficient k1 corresponds to the fuzzy set in the physical domain B, and the output second fuzzy coefficient k2 corresponds to the fuzzy set in the physical domain C.

[0120] The corresponding relationship of the fuzzy sets in A, B and C is set, so that the corresponding first fuzzy coefficient k1 and the second fuzzy coefficient k2 are obtained according to the change of the absolute value of s, so as to control the convergence speed of the position difference and the speed difference in a limited time.

[0121] In the above embodiment, based on the fuzzy control, the corresponding value adjustment adaptive fuzzy switching control law is performed on k1 and k2 respectively according to the change of the absolute value of s, based on the fuzzy domain division and the controller calculation capability, the physical domain of the absolute value of s, the physical domain of the first fuzzy coefficient k1 and the physical domain of the second fuzzy coefficient k2 are determined.

[0122] Optionally, a quantization factor q is set s , the quantization factor q s , the actual physical quantity of the absolute value of s is scaled as the input sliding surface s ly , the input sliding surface s ly falls into the physical domain A of the absolute value of s; the proportional factors q1 and q2 are set, the proportional factor q1 amplifies the first output coefficient k ly1 in the physical domain B of k1 as the first fuzzy coefficient k1 as the actual control quantity; the proportional factor q2 amplifies the second output coefficient k ly1 in the physical domain C of k2 as the second fuzzy coefficient k2 as the actual control quantity.

[0123]

[0124] In the formula, Z, PS, PM, PMB and PB are respectively fuzzy sets of fuzzy language variables, Z represents zero, PS represents positive small, PM represents positive medium, PMB represents positive medium big, and PB represents positive big.

[0125] The input sliding surface s ly corresponds to the fuzzy set in A, the corresponding fuzzy set in A is determined through the value of the input sliding surface s ly , the first output coefficient k ly1 corresponds to the fuzzy set in B, the corresponding first output coefficient k ly1 is determined through the fuzzy set in B, the second output coefficient k ly1 corresponds to the fuzzy set in C, and the corresponding second output coefficient k ly1 is determined through the fuzzy set in C.

[0126] When A takes PB, B takes Z, and C takes PB; when A takes PMB, B takes PS, and C takes PMB; when A takes PM, B takes PM, and C takes PM; when A takes PS, B takes PMB, and C takes PS; when A takes Z, B takes PB, and C takes Z.

[0127] The first output coefficient k in the theoretical domain ly1 Second output coefficient k ly1 The actual control quantities k1 and k2 are obtained by proportionally amplifying them using scaling factors q1 and q2, respectively.

[0128] In the above embodiments, a quantization factor q is set. s Quantization factor q s This is used to scale the actual physical quantity of the absolute value of s to the physical domain range of the absolute value of s in fuzzy control; setting scaling factors q1 and q2, scaling factor q1 is used to scale up the standardized value in the physical domain of k1 output by fuzzy inference to the actual control quantity; scaling factor q2 is used to scale up the standardized value in the physical domain of k2 output by fuzzy inference to the actual control quantity.

[0129] s = {Z, PS, PM, PMB, PB}

[0130] k1 = {Z, PS, PM, PMB, PB}

[0131] k2 = {Z, PS, PM, PMB, PB} — Formula (8);

[0132] Where Z, PS, PM, PMB, and PB are fuzzy linguistic variables, Z represents zero, PS represents positive small, PM represents positive medium, PMB represents positive medium large, and PB represents positive large.

[0133] Table 1

[0134]

[0135] As shown in Table 1, the actual physical quantity of the absolute value of s is determined by the quantization factor q. s The values ​​of k1 and k2 in the fuzzy control are scaled proportionally to the physical domain of the absolute value of s. When the absolute value of s is PB, k1 is Z and k2 is PB; when the absolute value of s is PMB, k1 is PS and k2 is PMB; when the absolute value of s is PM, k1 is PM and k2 is PM; when the absolute value of s is PS, k1 is PMB and k2 is PS; when the absolute value of s is Z, k1 is PB and k2 is Z. The corresponding standardized values ​​of k1 and k2 in the physical domain are then scaled proportionally by scaling factors q1 and q2 to obtain the actual control values ​​of k1 and k2.

[0136] Since a finer division of the fuzzy universe of discourse, i.e., more sub-elements in the fuzzy set, results in higher control accuracy, but too many elements complicate the entire calculation process and place higher demands on the controller's memory. Conversely, too few elements significantly reduce accuracy. Therefore, considering both control accuracy and computational complexity, and based on the fuzzy universe of discourse division and the controller's computational capabilities, the ranges for the physical universe of discourse, the first fuzzy coefficient, and the second fuzzy coefficient are determined. The specific fuzzy sets of each variable in this invention are shown in Formula 8.

[0137] In the above embodiments, the physical domain A is designed as [0, 0.1], the physical domain B is designed as [0, 1], and the physical domain C is designed as [0, 1].

[0138] With s ly The membership function used as input is designed as a Gaussian type input function, k ly1 The membership function for the output is designed as a triangular first output function, k ly1 The membership function used as the output is designed as a triangular second output function.

[0139] In the above embodiments, the fuzzy rules of the present invention are designed as follows: when the sliding surface approaches positive or negative infinity, the first fuzzy coefficient approaches the upper limit of the value range, and the second fuzzy coefficient approaches the lower limit of the value range; when the sliding surface approaches zero from positive or negative infinity, the first fuzzy coefficient gradually decreases, while the second fuzzy coefficient gradually increases; when the sliding surface approaches zero, the second fuzzy coefficient approaches the upper limit of the value range, and the first fuzzy coefficient approaches the lower limit of the value range.

[0140] Understandably, when the variable s approaches positive or negative infinity, k1 should be larger to improve the system's dynamic response, allowing the system to approach the sliding surface more quickly. Simultaneously, k2 should not be too large to avoid excessive damping. As the variable s approaches zero from positive or negative infinity, k1 gradually decreases while k2 gradually increases to ensure the system's rapid response. When the variable s approaches zero, k2 should be relatively large to ensure the system's adjustment speed, while k1 decreases to reduce chattering.

[0141] Determine the quantization factor q s And scaling factors q1 and q2; where the quantization factor scales the actual physical quantity proportionally to the domain of fuzzy control; the scaling factor amplifies the standardized value output by fuzzy inference proportionally to the actual control quantity. The quantization factor and scaling factor should not be too large, as this will lead to actuator saturation or system oscillation; nor should they be too small, as this will result in insufficient control and slow response; in this embodiment, the preferred quantization factor is q1. s The values ​​of the scaling factors q1 and q2 are: q s =1; q1=5; q2=500.

[0142] In this embodiment, as shown in Figure 10 , the switching control law module 34 includes a first calculation module 36, a second calculation module 37, a fuzzy control module 38, a fourth calculation module 41, a fifth calculation module 40, a sixth calculation module 42, and a seventh calculation module 39. The sliding surface s obtained by the sliding surface module 33 is input into the first calculation module 36, and the function obtained after calculation is input into the second calculation module 37 and fused with the quantization factor q s . ly The function s obtained after fusion calculation is input into the fuzzy control module 38 for fuzzy calculation to obtain a first output coefficient k ly1 and a second output coefficient k ly1 . The first output coefficient k ly1 and the second output coefficient k ly1 are input into the fourth calculation module 41 and the fifth calculation module 40, respectively, and fused with the corresponding proportional factor q1 and q2 to obtain a first fuzzy coefficient k1 and a second fuzzy coefficient k2. The function U output by the sixth calculation module 42 is multiplied with the first fuzzy coefficient k1, and the function U z output by the seventh calculation module 39 is multiplied with the second fuzzy coefficient k2. The calculation results are added to obtain the output function u sw .

[0143] The input function of the membership function is designed as gauss2, as shown in Figure 3 . The first output function and the second output function are both designed as triangles, as shown in Figure 4 and 5 .

[0144] Let the fuzzy set A i , the fuzzy set B i , and the fuzzy set C i . The input function is the membership function of the fuzzy set A i , the first output function is the membership function of the fuzzy set B i , and the second output function is the membership function of the fuzzy set C i . The form of the fuzzy rule is as follows:

[0145] R i : if s is A i , then k1 is B i , k2 is C i ——equation (9).

[0146] For example, as shown in Figure 3 , the horizontal coordinate of the input function is the absolute value of s fused with the quantization factor q s . The s lyThe physical domain is [0, 0.1], and the ordinate represents the membership degree; for example... Figure 4 As shown, the x-axis of the first output function is the first output coefficient k. ly1 The physical domain is [0, 1], and the ordinate is the membership degree; for example Figure 5 As shown, the x-axis of the second output function represents the second output coefficient k. ly1 The physical domain is [0, 1], with the ordinate representing the membership degree. The abscissa corresponding to a membership degree of 0.5 is the transition point of the fuzzy set, which divides the physical domain into multiple intervals. For example, when the absolute value of s falls into the first interval of the physical domain and its membership degree is greater than 0.5, the corresponding fuzzy set A is... i For Z, by referring to Table 1, we can find that the first output coefficient k ly1 The corresponding fuzzy set B i For PB, the first output coefficient k corresponding to a membership degree greater than 0.5 is PB. ly1 An interval of the physical domain is used as the output of k1; the second output coefficient k ly1 The corresponding fuzzy set C i Let Z be the second output coefficient k corresponding to a membership degree greater than 0.5. ly1 An interval of the physical domain is used as the output of k2.

[0147] like Figure 2 As shown, the fuzzy control process involves: determining the input and output variables; defining the universe of discourse and fuzzy sets based on the input and output variables; determining the quantization factor and scaling factor; determining the membership function; designing fuzzy rules based on the expected changes in the input and output variables; determining the fuzzy inference system based on the above; defuzzifying through the fuzzy inference system; judging whether the defuzzification result meets expectations; if not, redesigning the quantization factor and scaling factor; if the result meets expectations, completing the design of the fuzzy control algorithm.

[0148] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A permanent magnet synchronous linear motor adaptive fuzzy terminal sliding mode control system, comprising an adaptive fuzzy nonsingular fast terminal sliding mode controller (1), the adaptive fuzzy nonsingular fast terminal sliding mode controller (1) comprising a sliding surface module (33) and an equivalent control law module (31), the adaptive fuzzy terminal sliding mode controller (1) outputting a total control law of a permanent magnet synchronous linear motor in a two-phase rotating coordinate system according to a position difference, the sliding surface module (33) outputting a nonsingular fast terminal sliding surface, and the equivalent control law module (31) outputting an equivalent control law, characterized in that, The adaptive fuzzy terminal sliding mode controller (1) further comprises a switching control law module (34) which outputs an adaptive fuzzy switching control law, the adaptive fuzzy switching control law comprising switching gains, the corresponding switching gains being adjusted with the change of the sliding mode surface to control the corresponding convergence speed of the position difference and the speed difference in a limited time, wherein the position difference is the difference between the actual position of the mover and the given reference position, and the speed difference is the difference between the actual speed of the mover and the given reference speed, the speed difference being the first derivative of the position difference.

2. The adaptive fuzzy terminal sliding mode control system of a permanent magnet synchronous linear motor according to claim 1, wherein, The switching control law module (34) further comprises a fuzzy control module and an adaptive control module. The expressions of the total control law, the equivalent control law and the adaptive fuzzy switching control law are as follows: u = -1 / K m (u eq +u sw ) where: u is the total control law, u eq is the equivalent control law, u sw is the switching control law, s is the nonsingular fast terminal sliding mode surface, B m =-B / M, K m =K f / M, F m =-F d / M, M is the mover mass, B is the viscous friction coefficient, K f is the electromagnetic thrust coefficient, and K f =3πn p ψ f / 2τ, n p is the number of pole pairs, ψ f is the permanent magnet flux linkage, τ is the pole pitch, F d is the integration of the friction force and the total disturbance, e1 is the difference between the actual position and the reference position of the mover, and its derivative is the position state variable of the mover, e2 is the difference between the actual speed and the reference speed of the mover, and its derivative is the speed state variable, d is the actual position of the mover, d * is the reference position of the mover, σ3 is a designed positive constant, 0 < σ3 < 1, α, β, σ1, σ2 are the parameters of the sliding mode control respectively; 0 < α < 100, 0 < β < 20, σ1 < σ2, 1 < σ2 < 2, σ2 = q / p, q and p are both positive odd numbers, 0 < q < 10, 0 < p < 10, sign(x) is the sign function, and the switching gains include k1, k2, and U z , where, k1 is the first fuzzy coefficient, k2 is the second fuzzy coefficient, is the first adaptive control coefficient, U z is the second adaptive control coefficient; The fuzzy control module controls the output of the adaptive fuzzy switching control law by making k1 and k2 take corresponding values with the change of the absolute value of s through fuzzy control; The adaptive control module makes U z With the change of s absolute value, the corresponding value, With the change of s absolute value and k1, the corresponding value is obtained, to control the output of adaptive fuzzy switching control law, according to formula (12) and (15), the second adaptive control coefficient U z And the first adaptive control coefficient In the formula, 0<μ<20, 0<z<1, 0<η<500, s is a non-singular fast terminal sliding mode surface, k1 is a first fuzzy coefficient, A first adaptive control coefficient, U z is a second adaptive control coefficient.

3. The adaptive fuzzy terminal sliding mode control system of a permanent magnet synchronous linear motor according to claim 2, wherein, Comprising: a physical domain A of the absolute value of s is set according to the fuzzy control, the physical domain A having a plurality of fuzzy sets, the input absolute value of s corresponding to the fuzzy sets in the physical domain A; a physical domain B of the first fuzzy coefficient k1 and a physical domain C of the second fuzzy coefficient k2 are set according to the fuzzy control, the physical domain B and the physical domain C respectively having a plurality of fuzzy sets, the output first fuzzy coefficient k1 corresponding to the fuzzy sets in the physical domain B, and the output second fuzzy coefficient k2 corresponding to the fuzzy sets in the physical domain C; the corresponding relationship of the fuzzy sets in A, B and C is set, so that the corresponding first fuzzy coefficient k1 and the second fuzzy coefficient k2 are obtained according to the change of the absolute value of s to control the corresponding convergence speed of the position difference and the speed difference in a limited time.

4. The adaptive fuzzy terminal sliding mode control system of a permanent magnet synchronous linear motor according to claim 3, wherein, Comprising: Setting quantization factor q s , quantization factor q s Scaling the actual physical quantity of s absolute value to input sliding surface s ly , input sliding surface s ly Fall into the physical domain A range of s absolute value; set proportional factor q1 and q2, proportional factor q1 will k1 in the physical domain B of the first output coefficient k ly1 Amplify as the first fuzzy coefficient k1 as the actual control quantity; proportional factor q2 will k2 in the physical domain C of the second output coefficient k ly1 Amplify as the second fuzzy coefficient k2 as the actual control quantity; wherein Z, PS, PM, PMB and PB are respectively fuzzy sets of fuzzy language variables, Z represents zero, PS represents positive small, PM represents positive medium, PMB represents positive medium big, and PB represents positive big; input sliding surface s ly corresponding to the fuzzy set in A, the value of the input sliding surface s ly determines the corresponding fuzzy set in A, the first output coefficient k ly1 corresponding to the fuzzy set in B, the corresponding first output coefficient k lyl is determined by the fuzzy set in B, the second output coefficient k ly1 corresponding to the fuzzy set in C, the corresponding second output coefficient k ly1 is determined by the fuzzy set in C; when A takes PB, B takes Z, and C takes PB; when A takes PMB, B takes PS, and C takes PMB; when A takes PM, B takes PM, and C takes PM; when A takes PS, B takes PMB, and C takes PS; when A takes Z, B takes PB, and C takes Z; The corresponding k1 and k2 are scaled by the first output coefficient k ly1 and the second output coefficient k ly1 respectively by the scaling factors q1 and q2 to obtain the k1 and k2 values of the actual control quantities.

5. The adaptive fuzzy terminal sliding mode control system of a permanent magnet synchronous linear motor according to claim 4, wherein, Comprising: the physical domain A is designed as [0, 0.1], the physical domain B is designed as [0, 1], and the physical domain C is designed as [0, 1]; s ly The input membership function is designed as a gauss2 type input function, k ly1 The output membership function is designed as a triangular first output function, k ly1 The output membership function is designed as a triangular second output function.

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