CN113219821A - Proportional-integral sliding mode surface fuzzy sliding mode position control method for numerical control machine tool - Google Patents
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Abstract
The invention discloses a fuzzy sliding mode position control method for a numerical control machine tool of a proportional-integral sliding mode surfacedThe position error e (t); then designing a proportional-integral sliding mode surface switching function, and taking a switching function s (t) in sliding mode control as the input of a fuzzy system; further designing a fuzzy controller, and carrying out defuzzification on the system by adopting a gravity center algorithm to obtain fuzzy controller output u (t); and finally, inputting a position output signal u (t) of the position controller of the mechanical numerical control machine tool into the numerical control system, and feeding back the position angle output by the mechanical numerical control machine tool system to the input end. The fuzzy sliding mode control based on the proportional-integral sliding mode surface replaces the traditional PID servo control system, so that the tracking precision and the response performance of the position are improved, and the control requirements of high speed, high precision and large output power in a motion control system are met.
Description
Technical Field
The invention relates to a fuzzy sliding mode position control method for a numerical control machine tool with a proportional-integral sliding mode surface, and belongs to the field of position control of mechanical numerical control machine tools.
Background
The mechanical numerical control machine tool is the foundation of manufacturing industry and the strategic foundation of national development and joy, and the numerical control device is the core component in the numerical control machine tool and determines the functions and the performance of the numerical control machine tool. With the vigorous development of the manufacturing industry, higher requirements are put forward on the aspects of the technical indexes, the comprehensive performance, the reliability and the like of the numerical control device, and the development of the monitoring level of the technical indexes and the comprehensive performance of the numerical control device is promoted. Under the background of the rapid development of domestic numerical control devices and the research and development of numerical control devices in China, the control performance of the numerical control devices is urgently needed to be improved.
The main reason why the control system in the numerical control device is prone to failure is that the self-nonlinear characteristics of the motor and the gear in the numerical control system cause the self-parameter value of the system to deviate, so that the machined workpiece is low in precision and cannot be used.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a fuzzy sliding mode position control method for a numerical control machine with a proportional-integral sliding mode surface, which is used for applying the fuzzy sliding mode control of the sliding mode surface with the proportional-integral sliding mode surface to the position control of the mechanical numerical control machine, so that the processing precision is improved, the influence of human errors on the product quality is eliminated, the production condition is improved, and the industrial production efficiency is improved.
In order to achieve the purpose, the invention adopts the technical scheme that: a proportional-integral sliding mode surface fuzzy sliding mode position control method for a numerical control machine tool comprises the following steps;
the method comprises the following steps: firstly, analyzing a nonlinear system of the mechanical numerical control machine tool, extracting an actual feedback value theta of the position of the mechanical numerical control machine tool, and obtaining a position expected value theta of the mechanical numerical control machine tooldThe position error e (t);
step two: designing a proportional-integral sliding mode surface switching function, and taking a switching function s (t) in sliding mode control as the input of a fuzzy system;
step three: designing a fuzzy controller, wherein a fuzzy rule base is constructed according to experience, so that the number of fuzzy rules is greatly reduced; performing defuzzification on the system by adopting a gravity center algorithm to obtain fuzzy controller output u (t);
step four: and inputting a position output signal u (t) of the mechanical numerical control machine tool position controller into the numerical control system, and feeding back the position angle output by the mechanical numerical control machine tool system to an input end.
Preferably, the position error e (t) in the step one is calculated by:
identifying the structure, parameters and model of the control system according to the input and output data of the system to obtain a position servo system model, wherein the model expression is as follows:
θ(k)＝f[θ(k-1)，θ(k-2)，…θ(k-n)，θd(k-1)，θd(k-2)，…θd(k-m)] (1)
in the formula, theta is output by the system position angle; thetadInputting a system position angle instruction; n is the system order; m is the output order; k is a position loop parameter;
and simultaneously carrying out time series discretization treatment to obtain a difference equation expression of the formula (1):
in the formula, aiAnd bjAre identified model parameters, where i is [1, n ]]J is [1, m ]]Is an integer of (1);
through the identification of the model structure and the parameters, a grid search algorithm and a recursive least square method can be combined to identify the model structure and the parameters of a control system, and finally a mathematical model of the position servo system of the mechanical numerical control machine tool can be obtained; the angle of the control position of the mechanical numerical control machine tool can be expressed as:
in the formula, f and g are unknown nonlinear functions in the mechanical numerical control machine tool; d (t) is the interference suffered by the mechanical numerical control machine tool in the operation process, and the tracking error is as follows:
e(t)＝θ(t)-θd(t) (4)
in the formula, theta is output by the system position angle; thetadAnd inputting a system position angle instruction.
Preferably, the proportional-integral sliding mode surface switching function in the second step is as follows:
wherein K is a non-zero constant, K1And K2Is a non-zero normal number;
when the sliding mode control is in an ideal state, the following conditions are shown:
by determining K1And K2The tracking error e (t) and its derivative approach zero; compared with the traditional PID controller of a mechanical numerical control machine tool, the switching function s (t) can be used as the input of the fuzzy controller, and the control input u (t) can be used as the output of the fuzzy system, so that a single-input single-output (SISO) fuzzy system is formed.
Preferably, the fuzzy controller design method in step three is as follows:
the fuzzy controller is an important part of the system, and fuzzy mathematics is taken as a theoretical support; firstly, a proportional integral sliding mode surface switching function s (t) of the position control quantity of a cutter of the mechanical numerical control machine tool is used as fuzzy input (wherein the fuzzy input is specifically described by a corresponding fuzzy language), and then a control rule of a fuzzy controller is designed according to a fuzzy relation with empirical design; finally, developing a fuzzy decision mechanism according to the control rule obtained by reasoning, thereby obtaining a fuzzy control quantity u (t);
the fuzzy rule form of the fuzzy controller is as follows:
Rule i:IF s is Fs i THEN u is ai (8)
in the formula, Fs iAnd ai(i ═ 1,2, m) is the fuzzy set of inputs and outputs, respectively;
according to expert experience, the following 5 fuzzy rules can be established in the fuzzy control system:
(6)If(s is NB)then(u is PB)
(7)If(s is NS)then(u is PS)
(8)If(s is Z)then(u is Z)
(9)If(s is PS)then(u is NS)
(10)If(s is PB)then(u is NB)
wherein the membership functions of s and u take "negative big" (NB), "Negative Small (NS)," zero (Z), "positive small (PB)," Positive Big (PB) ". The fuzzy definition rule is as follows: if s is NB (negative large), u is PS (positive large); if s is NS (negative small), u is PS (positive small); if s is Z (zero), u is Z (zero); if s is PS (plus or minus), u is NS (plus or minus); if s is PB (negative large), u is NB (negative large);
finally, developing a fuzzy decision mechanism according to the obtained control rule; the gravity center method is that the gravity center of the area enclosed by the membership function curve and the abscissa is taken as the final output value of the fuzzy inference; performing defuzzification by adopting a gravity center method to obtain the output of a controller as follows:
in the formula, ωiIs the degree of membership, a, postulated in the ith ruleiThe degree of membership of the conclusion in the ith rule.
Preferably, in the fourth step, the position output signal u (t) of the position controller of the mechanical numerical control machine tool is input into the numerical control system, and the position angle output by the mechanical numerical control machine tool system is fed back to the input end, so that the position and speed double closed-loop control is realized.
The invention has the beneficial effects that: the position control method of the proportional-integral sliding mode surface is used for replacing PID control of a traditional mechanical numerical control machine tool, the method has a good effect on inhibiting buffeting in the running process of a numerical control system, and when parameters of the numerical control system drift or external interference exists, the system robustness can be maintained, the precision of a processing device is improved, the influence of human errors on product quality is eliminated, the production condition is improved, and the industrial production efficiency is improved.
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FIG. 1 is a control strategy diagram of a fuzzy sliding mode position control method for a numerical control machine tool with a proportional-integral sliding mode surface according to the invention;
fig. 2 is a position and speed tracking change curve of the fuzzy sliding mode position control method for the numerical control machine tool with the proportional-integral sliding mode surface.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood, however, that the description herein of specific embodiments is only intended to illustrate the invention and not to limit the scope of the invention.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs, and the terms used herein in the specification of the present invention are for the purpose of describing particular embodiments only and are not intended to limit the present invention.
As shown in fig. 1 and fig. 2, a fuzzy sliding mode position control method for a numerical control machine tool with a proportional-integral sliding mode surface comprises the following steps;
the method comprises the following steps: firstly, analyzing a nonlinear system of the mechanical numerical control machine tool, extracting an actual feedback value theta of the position of the mechanical numerical control machine tool, and obtaining a position expected value theta of the mechanical numerical control machine tooldThe position error e (t);
step two: designing a proportional-integral sliding mode surface switching function, and taking a switching function s (t) in sliding mode control as the input of a fuzzy system;
step three: designing a fuzzy controller, wherein a fuzzy rule base is constructed according to experience, so that the number of fuzzy rules is greatly reduced; performing defuzzification on the system by adopting a gravity center algorithm to obtain fuzzy controller output u (t);
step four: and inputting a position output signal u (t) of the mechanical numerical control machine tool position controller into the numerical control system, and feeding back the position angle output by the mechanical numerical control machine tool system to an input end.
In this embodiment, the position error e (t) in the first step is calculated by:
identifying the structure, parameters and model of the control system according to the input and output data of the system to obtain a position servo system model, wherein the model expression is as follows:
θ(k)＝f[θ(k-1),θ(k-2),…θ(k-n),θd(k-1),θd(k-2),…θd(k-m)] (1)
in the formula, theta is output by the system position angle; thetadInputting a system position angle instruction; n is the system order; m is the output order; k is a position loop parameter;
and simultaneously carrying out time series discretization treatment to obtain a difference equation expression of the formula (1):
in the formula, aiAnd bjAre identified model parameters, where i is [1, n ]]J is [1, m ]]Is an integer of (1);
through the identification of the model structure and the parameters, a grid search algorithm and a recursive least square method can be combined to identify the model structure and the parameters of a control system, and finally a mathematical model of the position servo system of the mechanical numerical control machine tool can be obtained; the angle of the control position of the mechanical numerical control machine tool can be expressed as:
in the formula, f and g are unknown nonlinear functions in the mechanical numerical control machine tool; d (t) is the interference suffered by the mechanical numerical control machine tool in the operation process, and the tracking error is as follows:
e(t)＝θ(t)-θd(t) (4)
in the formula, theta is output by the system position angle; thetadAnd inputting a system position angle instruction.
In this embodiment, the proportional-integral sliding mode surface switching function in step two is:
wherein K is a non-zero constant, K1And K2Is a non-zero normal number;
when the sliding mode control is in an ideal state, the following conditions are shown:
by determining K1And K2The tracking error e (t) and its derivative approach zero; compared with the traditional PID controller of a mechanical numerical control machine tool, the switching function s (t) can be used as the input of the fuzzy controller, and the control input u (t) can be used as the output of the fuzzy system, so that a single-input single-output (SISO) fuzzy system is formed.
In this embodiment, the method for designing the fuzzy controller in step three includes:
the fuzzy controller is an important part of the system, and fuzzy mathematics is taken as a theoretical support; firstly, a proportional integral sliding mode surface switching function s (t) of the position control quantity of a cutter of the mechanical numerical control machine tool is used as fuzzy input (wherein the fuzzy input is specifically described by a corresponding fuzzy language), and then a control rule of a fuzzy controller is designed according to a fuzzy relation with empirical design; finally, developing a fuzzy decision mechanism according to the control rule obtained by reasoning, thereby obtaining a fuzzy control quantity u (t);
the fuzzy rule form of the fuzzy controller is as follows:
Rule i:IF s is Fs i THEN u is ai (8)
in the formula, Fs iAnd ai(i ═ 1,2, m) is the fuzzy set of inputs and outputs, respectively;
according to expert experience, the following 5 fuzzy rules can be established in the fuzzy control system:
(11)If(s is NB)then(u is PB)
(12)If(s is NS)then(u is PS)
(13)If(s is Z)then(u is Z)
(14)If(s is PS)then(u is NS)
(15)If(s is PB)then(u is NB)
wherein the membership functions of s and u take "negative big" (NB), "Negative Small (NS)," zero (Z), "positive small (PB)," Positive Big (PB) ". The fuzzy definition rule is as follows: if s is NB (negative large), u is PS (positive large); if s is NS (negative small), u is PS (positive small); if s is Z (zero), u is Z (zero); if s is PS (plus or minus), u is NS (plus or minus); if s is PB (negative large), u is NB (negative large);
finally, developing a fuzzy decision mechanism according to the obtained control rule; the gravity center method is that the gravity center of the area enclosed by the membership function curve and the abscissa is taken as the final output value of the fuzzy inference; performing defuzzification by adopting a gravity center method to obtain the output of a controller as follows:
in the formula, ωiIs the degree of membership, a, postulated in the ith ruleiThe degree of membership of the conclusion in the ith rule.
In this embodiment, in the fourth step, the position output signal u (t) of the position controller of the mechanical numerical control machine is input to the numerical control system, and the position angle output by the mechanical numerical control machine is fed back to the input end, so as to implement the position and speed dual closed-loop control.
The simulation result of the invention is shown in fig. 2, and fig. 2 is a change curve of position, speed value and expected value in the position control of the fuzzy sliding mode for the mechanical numerical control machine based on the proportional-integral sliding mode surface. According to simulation results, in the dynamic operation process, the position angle and the speed of the fuzzy sliding mode control can quickly track an expected ideal value, and the error between the position angle and the speed and an actual value is small. Meanwhile, the fuzzy sliding mode position control method for the numerical control machine tool with the proportional-integral sliding mode surface can quickly track and reach an expected position point, and has strong robustness.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents or improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A proportional integral sliding mode surface fuzzy sliding mode position control method for a numerical control machine is characterized by comprising the following steps;
the method comprises the following steps: firstly, analyzing a nonlinear system of the mechanical numerical control machine tool, extracting an actual feedback value theta of the position of the mechanical numerical control machine tool, and obtaining a position expected value theta of the mechanical numerical control machine tooldThe position error e (t);
step two: designing a proportional-integral sliding mode surface switching function, and taking a switching function s (t) in sliding mode control as the input of a fuzzy system;
step three: designing a fuzzy controller, wherein a fuzzy rule base is constructed according to experience, so that the number of fuzzy rules is greatly reduced; performing defuzzification on the system by adopting a gravity center algorithm to obtain fuzzy controller output u (t);
step four: and inputting a position output signal u (t) of the mechanical numerical control machine tool position controller into the numerical control system, and feeding back the position angle output by the mechanical numerical control machine tool system to an input end.
2. The method for controlling the fuzzy sliding mode position of the numerical control machine tool with the proportional-integral sliding mode surface according to claim 1, wherein the position error e (t) in the first step is calculated by the following method:
identifying the structure, parameters and model of the control system according to the input and output data of the system to obtain a position servo system model, wherein the model expression is as follows:
θ(k)＝f[θ(k-1),θ(k-2),…θ(k-n),θd(k-1),θd(k-2),…θd(k-m)] (1)
in the formula, theta is output by the system position angle; thetadInputting a system position angle instruction; n is the system order; m is the output order; k is a position loop parameter;
and simultaneously carrying out time series discretization treatment to obtain a difference equation expression of the formula (1):
in the formula, aiAnd bjAre identified model parameters, where i is [1, n ]]J is [1, m ]]Is an integer of (1);
through the identification of the model structure and the parameters, a grid search algorithm and a recursive least square method can be combined to identify the model structure and the parameters of a control system, and finally a mathematical model of the position servo system of the mechanical numerical control machine tool can be obtained; the angle of the control position of the mechanical numerical control machine tool can be expressed as:
in the formula, f and g are unknown nonlinear functions in the mechanical numerical control machine tool; d (t) is the interference suffered by the mechanical numerical control machine tool in the operation process, and the tracking error is as follows:
e(t)＝θ(t)-θd(t) (4)
in the formula, theta is output by the system position angle; thetadAnd inputting a system position angle instruction.
3. The method for controlling the fuzzy sliding mode position of the proportional-integral sliding mode surface numerical control machine according to claim 1, wherein the proportional-integral sliding mode surface switching function in the second step is as follows:
wherein K is a non-zero constant, K1And K2Is a non-zero normal number;
when the sliding mode control is in an ideal state, the following conditions are shown:
by determining K1And K2The tracking error e (t) and its derivative approach zero; compared with the traditional PID controller of a mechanical numerical control machine tool, the switching function s (t) can be used as the input of the fuzzy controller, and the control input u (t) can be used as the output of the fuzzy system, so that a single-input single-output (SISO) fuzzy system is formed.
4. The method for controlling the fuzzy sliding mode position of the proportional-integral sliding mode surface numerical control machine according to claim 1, wherein the method for designing the fuzzy controller in the third step is as follows:
the fuzzy controller is an important part of the system, and fuzzy mathematics is taken as a theoretical support; firstly, a proportional integral sliding mode surface switching function s (t) of the position control quantity of a cutter of the mechanical numerical control machine tool is used as fuzzy input (wherein the fuzzy input is specifically described by a corresponding fuzzy language), and then a control rule of a fuzzy controller is designed according to a fuzzy relation with empirical design; finally, developing a fuzzy decision mechanism according to the control rule obtained by reasoning, thereby obtaining a fuzzy control quantity u (t);
the fuzzy rule form of the fuzzy controller is as follows:
Rule i:IF s is Fs iTHEN u is ai (8)
in the formula, Fs iAnd ai(i ═ 1,2, m) is the fuzzy set of inputs and outputs, respectively;
according to expert experience, the following 5 fuzzy rules can be established in the fuzzy control system:
(1)If(s is NB)then(u is PB)
(2)If(s is NS)then(u is PS)
(3)If(s is Z)then(u is Z)
(4)If(s is PS)then(u is NS)
(5)If(s is PB)then(u is NB)
wherein the membership functions of s and u take "negative big" (NB), "Negative Small (NS)," zero (Z), "positive small (PB)," Positive Big (PB) ". The fuzzy definition rule is as follows: if s is NB (negative large), u is PS (positive large); if s is NS (negative small), u is PS (positive small); if s is Z (zero), u is Z (zero); if s is PS (plus or minus), u is NS (plus or minus); if s is PB (negative large), u is NB (negative large);
finally, developing a fuzzy decision mechanism according to the obtained control rule; the gravity center method is that the gravity center of the area enclosed by the membership function curve and the abscissa is taken as the final output value of the fuzzy inference; performing defuzzification by adopting a gravity center method to obtain the output of a controller as follows:
in the formula, ωiIs the degree of membership, a, postulated in the ith ruleiThe degree of membership of the conclusion in the ith rule.
5. The method for controlling the position of the fuzzy sliding mode for the numerical control machine tool with the proportional-integral sliding mode surface according to claim 1, wherein in the fourth step, a position output signal u (t) of a position controller of the mechanical numerical control machine tool is input into a numerical control system, and a position angle output by the mechanical numerical control machine tool system is fed back to an input end to realize position-speed double closed-loop control.
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| CN114355842A (en) * | 2021-12-28 | 2022-04-15 | 中国航空工业集团公司北京长城航空测控技术研究所 | Position and force control switching method and system for electro-hydraulic servo loading system |
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