CN114977928A - Parameter self-tuning method for speed ring and position ring of permanent magnet synchronous servo system - Google Patents
Parameter self-tuning method for speed ring and position ring of permanent magnet synchronous servo system Download PDFInfo
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0021—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using different modes of control depending on a parameter, e.g. the speed
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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Abstract
The invention provides a parameter self-setting method for a speed ring and a position ring of a permanent magnet synchronous servo system, which obtains a parameter vector to be optimized of parameters of the position ring and a speed ring controller in the permanent magnet synchronous servo motor through a model reference self-adaptive algorithm, automatically finds the optimal parameter of the position ring and the speed ring control in the permanent magnet synchronous servo motor through a firework algorithm with improved selection strategies, realizes higher solving precision and faster convergence rate and better real-time performance of parameter setting, can make the parameters of the speed ring and the position ring controller of the permanent magnet synchronous servo system correct in time according to the state of an actual system so as to adapt to the change of the working condition of the servo system, improves the adaptability and the working performance of the servo system, carries out online adjustment on the control parameters of the speed ring and the position ring, and improves the robustness of the servo system to the parameter disturbance change, and moreover, the labor cost and the time cost are reduced, the solving precision is high, and a servo system is stable.
Description
Technical Field
The invention relates to the field of motion control, in particular to a method for automatically adjusting parameters of a speed ring and a position ring of a permanent magnet synchronous servo system.
Background
The permanent magnet synchronous servo system is widely applied to the fields of industrial automation, numerical control machines and the like, and has the characteristic of being sensitive to external disturbance signals. In order to make the servo system have good dynamic and static performances under different system parameters, the parameters of the controller of the servo system need to be properly adjusted. The requirement of parameter setting on operators is high, if the parameter setting is manually completed, the labor cost and the time cost are greatly increased, the effect is not ideal, and the instability of a servo system is caused. In order to reduce the problems caused by parameter change disturbance, the parameter on-line adjustment is performed on the PI controller after the rotational inertia information is acquired through a parameter identification algorithm, so that the robustness of the servo system to the parameter disturbance change is improved, the rotational inertia is the most critical parameter, and the identification value is the basis of the parameter self-tuning of the controller. The parameter self-tuning technology of the servo system controller can make the controller parameter of the servo drive system timely correct according to the state of an actual system so as to adapt to the change of the working condition of the servo system, and has great theoretical research value and engineering practice significance for improving the adaptability and the working performance of the servo system.
Disclosure of Invention
The invention provides a speed ring of a permanent magnet synchronous servo system and a parameter self-setting method of the speed ring, aiming at the problem that the optimal parameters of the position ring and the speed ring in the existing permanent magnet synchronous servo motor are difficult to find automatically, the parameter vector to be optimized of the parameters of the position ring and the speed ring controller in the permanent magnet synchronous servo motor is obtained through a model reference self-adaptive algorithm, the optimal parameters of the position ring and the speed ring controller in the permanent magnet synchronous servo motor are found automatically through a firework algorithm of an improved selection strategy, and the purposes of higher solving precision, higher convergence speed of parameter setting and better real-time performance are achieved.
The specific implementation content of the invention is as follows:
a method for self-tuning parameters of a speed ring and a position ring of a permanent magnet synchronous servo system comprises the following steps:
step 1: establishing a mechanical motion equation of the permanent magnet synchronous servo motor, and performing online identification on the rotary inertia of the permanent magnet synchronous servo motor by using a model reference adaptive algorithm;
step 11: establishing a mechanical motion equation of the permanent magnet synchronous servo motor according to an output electromagnetic matrix of the permanent magnet synchronous servo motor, a load matrix of the permanent magnet synchronous servo motor, the sum of a shaft of the permanent magnet synchronous servo motor and the rotational inertia of a load, a friction coefficient and the rotational angular speed of a rotor of the permanent magnet synchronous servo motor;
the permanent magnet synchronous servo system comprises a current loop, a speed loop and a position loop, the servo system detects the current of a three-phase winding of the motor and the position theta of a rotor through a current detection circuit and a position detection circuit, and calculates an exciting current component i through coordinate transformation d Torque current component i q . The difference value delta theta between the position signal command and the actual rotor position signal is used as the input of a position controller to generate a speed signal command omega, the difference value delta omega between the speed signal command and the actual speed signal is used as the input of a speed controller to generate a torque current command i qr (ii) a Torque current command i qr Excitation current command i dr The actual current signal passes through a current PI regulator to obtain a corresponding voltage command signal; the voltage command of the dq axis generates a pulse width modulation signal for controlling the inverter through park transformation and space vector pulse width modulation, so that the permanent magnet synchronous servo motor is driven;
step 12: performing online identification on the rotational inertia of the permanent magnet synchronous servo motor by using a model reference adaptive algorithm;
step 121: discretizing the mechanical motion equation of the permanent magnet synchronous servo motor in a sampling period to obtain a discrete form of the mechanical motion equation of the permanent magnet synchronous servo motor;
step 122: according to the discrete permanent magnet synchronous servo motor, a reference model of the permanent magnet synchronous servo motor is established without changing the load;
step 123: establishing an iterative model according to a Landaut algorithm and the established reference model, and identifying the moment of inertia through online identification;
step 2: obtaining initial parameter vectors to be set of the parameters of the position ring and the speed ring controller by using the online identified rotational inertia;
step 21: calculating the speed loop by using an open loop transfer function, and obtaining a speed loop controller parameter after determining the cut-off frequency and the intermediate frequency of the speed loop;
step 22: calculating the position loop by using a closed loop transfer function, and introducing a compensation coefficient field in an under-compensation state to obtain a position loop controller parameter;
step 23: and obtaining the parameter vectors to be optimized of the speed ring and the position ring according to the obtained speed ring controller parameters and the position ring controller parameters.
And step 3: and (3) establishing a performance evaluation formula for evaluating the servo system, and respectively searching the optimal parameters of the position ring and the speed ring by using a firework algorithm of an improved selection strategy based on the initial parameter vector to be set obtained in the step (2).
Step 31: in the improved strategy selection firework algorithm, the absolute error integral is taken as one item of a fitness function of the strategy improvement firework algorithm, the rise time is taken as one item of a performance evaluation index in a moderate function, and an output square item is added in the moderate function to obtain the fitness function of an evaluation servo system;
step 32: automatically optimizing the parameters of the speed ring controller and the position ring controller to be optimized by using a firework algorithm of an improved selection strategy to obtain the optimal parameters of the speed ring controller and the position ring controller;
step 321: setting a feasible region of a firework algorithm of an improved selection strategy according to the parameter search range of the speed ring and the position ring, taking the parameters of a controller of the speed ring and the position ring to be optimized as initial firework units, randomly generating the rest firework units in the feasible range, and finally generating N initial firework units;
step 322: calculating the fitness value of each firework individual according to the fitness function obtained in the step 31 to obtain the respective explosion intensity and explosion amplitude of different firework individuals;
the explosion intensity represents the number of sparks generated by explosion;
step 323: carrying out certain displacement operation on each dimension of the individual fireworks within the range of the explosion amplitude to generate explosion sparks, calculating the displacement, and updating the individual fireworks according to the calculated displacement;
step 324: carrying out Gaussian variation operation on the exploded sparks, and mapping the sparks generated by the fireworks to the feasible domain through mapping operation if the sparks are outside the feasible domain in the using process of the Gaussian variation algorithm;
step 325: taking the individual fireworks, the explosion sparks and the explosion sparks after Gaussian variation as an initial candidate set, and calculating the individual fitness in the candidate set;
step 326: adding a firework pool into an initial candidate set, wherein the firework pool is empty initially, adding the most excellent individuals in the candidate set into the firework pool in each iteration, and giving up the addition if the individuals to be added into the firework pool exist in the firework pool;
the most elegant individuals are the individuals with the minimum fitness;
step 327: if the number of times of the firework units in the next generation does not reach the set maximum number of times or is smaller than the iteration error, implementing a k-means clustering algorithm in the candidate set, randomly selecting N-1 clustering centers in the candidate set, calculating the distance between each individual in the candidate set and the clustering center, classifying each individual into a cluster where the nearest clustering center is located, if no cluster is changed, taking the N-1 clustering centers as next-generation firework units, and continuing to jump to the step 322 for the next iteration;
step 328: and if the set maximum times is reached or is smaller than the iteration error, stopping searching and outputting a final result to obtain the optimal speed ring and position ring controller parameters.
The invention has the following beneficial effects:
(1) according to the method, the model reference adaptive algorithm and the firework algorithm of the improved selection strategy are combined, so that the convergence speed of parameter setting is higher and the real-time performance is better while the solving precision is higher.
(2) The invention can make the speed ring and position ring controller parameter of the permanent magnet synchronous servo system correct in time according to the state of the actual system, so as to adapt to the change of the working condition of the servo system, and improve the adaptability and working performance of the servo system.
(3) The invention carries out online adjustment on the control parameters of the speed loop and the position loop, improves the robustness of the servo system to parameter disturbance change, reduces labor cost and time cost, and has high solving precision and stable servo system.
Drawings
FIG. 1 is a flow chart of parameter self-tuning proposed by the present invention;
FIG. 2 is an equivalent control block diagram of a speed loop structure of a PMSM permanent magnet synchronous servo motor servo system;
FIG. 3 is an equivalent control block diagram of a position loop structure of a PMSM permanent magnet synchronous servo motor servo system;
FIG. 4 is a flowchart of the optimization execution of the parameters of the firework algorithm;
FIG. 5 is a flowchart of the k-means clustering algorithm for selecting next-generation firework individuals.
Detailed Description
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and therefore should not be considered as a limitation to the scope of protection. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
In the description of the present invention, it is to be noted that, unless otherwise explicitly specified or limited, the terms "disposed," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in a specific case to those of ordinary skill in the art.
Example 1:
the embodiment provides a parameter self-tuning method for a speed ring and a position ring of a permanent magnet synchronous servo system, which comprises three stages, wherein in the first stage, a mechanical motion equation of a permanent magnet synchronous servo motor is established, and the rotational inertia of the permanent magnet synchronous servo motor is identified on line by using a model reference self-adaptive algorithm; in the second stage, the initial parameter vectors to be optimized of a speed ring and a position ring of the permanent magnet servo system are obtained according to the online identified rotational inertia; and in the third stage, the initial parameter vectors to be optimized of the speed ring and the position ring are used as initial firework individuals, and the optimal speed ring and position ring parameters are obtained by optimizing the firework algorithm of the improved selection strategy.
The working principle is as follows: in the embodiment, a model reference adaptive algorithm and a firework algorithm of an improved selection strategy are combined, the parameter vector to be optimized of the parameters of the position ring and the speed ring controller in the permanent magnet synchronous servo motor is obtained through the model reference adaptive algorithm, the optimal parameter of the position ring and the speed ring controller in the permanent magnet synchronous servo motor is automatically found through the firework algorithm of the improved selection strategy, and the purposes that the convergence speed of parameter setting is higher and the real-time performance is better while the solving precision is higher are achieved.
Example 2:
in this embodiment, the implementation steps of three stages are described as steps on the basis of embodiment 1.
The working principle is as follows: the embodiment provides a method for self-tuning parameters of a speed ring and a position ring of a permanent magnet synchronous servo system, which specifically comprises the following steps:
step 1: establishing a mechanical motion equation of the permanent magnet synchronous servo motor, and performing online identification on the rotary inertia of the permanent magnet synchronous servo motor by using a model reference adaptive algorithm;
step 11: establishing a mechanical motion equation of the permanent magnet synchronous servo motor according to an output electromagnetic matrix of the permanent magnet synchronous servo motor, a load matrix of the permanent magnet synchronous servo motor, the sum of a shaft of the permanent magnet synchronous servo motor and load rotational inertia, a friction coefficient and the rotation angular speed of a rotor of the permanent magnet synchronous servo motor;
the permanent magnet synchronous servo system comprises a current loop, a speed loop and a position loop, the servo system detects the current of a three-phase winding of the motor and the position theta of a rotor through a current detection circuit and a position detection circuit, and an exciting current component id and a torque current component iq are calculated through coordinate transformation. The difference value delta theta between the position signal command and the actual rotor position signal is used as the input of a position controller to generate a speed signal command omega, and the difference value delta omega between the speed signal command and the actual speed signal is used as the input of a speed controller to generate a torque current command iqr; the torque current instruction iqr, the exciting current instruction idr and the actual current signal pass through a current PI regulator to obtain corresponding voltage instruction signals; the voltage command of the dq axis generates a pulse width modulation signal for controlling the inverter through park transformation and space vector pulse width modulation, so that the permanent magnet synchronous servo motor is driven;
step 12: performing online identification on the rotational inertia of the permanent magnet synchronous servo motor by using a model reference adaptive algorithm;
step 121: discretizing the mechanical motion equation of the permanent magnet synchronous servo motor in a sampling period to obtain a discrete form of the mechanical motion equation of the permanent magnet synchronous servo motor;
step 122: according to the discrete permanent magnet synchronous servo motor, a reference model of the permanent magnet synchronous servo motor is established without changing the load;
step 123: establishing an iterative model according to a Landaut algorithm and the established reference model, and identifying the moment of inertia through online identification;
step 2: obtaining initial parameter vectors to be set of the parameters of the position ring and the speed ring controller by using the online identified rotational inertia;
step 21: calculating the speed loop by using an open loop transfer function, and obtaining a speed loop controller parameter after determining the cut-off frequency and the intermediate frequency of the speed loop;
step 22: calculating the position loop by using a closed loop transfer function, and introducing a compensation coefficient field in an under-compensation state to obtain a position loop controller parameter;
step 23: and obtaining the parameter vectors to be optimized of the speed ring and the position ring according to the obtained speed ring controller parameters and the position ring controller parameters.
And step 3: and (3) establishing a performance evaluation formula for evaluating the servo system, and respectively searching the optimal parameters of the position ring and the speed ring by using a firework algorithm of an improved selection strategy based on the initial parameter vector to be set obtained in the step (2).
Step 31: in the improved strategy selection firework algorithm, absolute error integral is taken as one item of a fitness function of the improved strategy firework algorithm, rising time is taken as one item of a performance evaluation index in a moderate function, and an output square item is added in the moderate function to obtain the fitness function of an evaluation servo system;
step 32: as shown in fig. 4, which is a flow chart of optimizing execution of parameters of a firework algorithm, parameters of a speed loop controller and a position loop controller to be optimized are automatically optimized by using the firework algorithm with an improved selection strategy to obtain optimal parameters of the speed loop controller and the position loop controller;
step 321: setting a feasible region of a firework algorithm of an improved selection strategy according to the parameter search range of the speed ring and the position ring, taking the parameters of a controller of the speed ring and the position ring to be optimized as initial firework units, randomly generating the rest firework units in the feasible range, and finally generating N initial firework units;
step 322: calculating the fitness value of each firework individual according to the fitness function obtained in the step 31 to obtain the respective explosion intensity and explosion amplitude of different firework individuals;
the explosion intensity represents the number of sparks generated by explosion;
step 323: carrying out certain displacement operation on each dimension of the individual fireworks within the range of the explosion amplitude to generate explosion sparks, calculating the displacement, and updating the individual fireworks according to the calculated displacement;
step 324: carrying out Gaussian variation operation on the exploded sparks, and mapping the sparks generated by the fireworks to the feasible domain through mapping operation if the sparks are outside the feasible domain in the using process of the Gaussian variation algorithm;
step 325: using the firework individual, the explosion spark and the explosion spark after Gaussian variation as an initial candidate set, and calculating the individual fitness in the candidate set;
step 326: adding a firework pool into an initial candidate set, wherein the firework pool is empty initially, adding the most excellent individuals in the candidate set into the firework pool in each iteration, and giving up the addition if the individuals to be added into the firework pool exist in the firework pool;
the most elegant individuals are the individuals with the minimum fitness;
step 327: if the number of times of the firework units in the next generation does not reach the set maximum number of times or is smaller than the iteration error, implementing a k-means clustering algorithm in the candidate set, randomly selecting N-1 clustering centers in the candidate set, calculating the distance between each individual in the candidate set and the clustering center, classifying each individual into a cluster where the nearest clustering center is located, if no cluster is changed, taking the N-1 clustering centers as next-generation firework units, and continuing to jump to the step 322 for the next iteration;
step 328: and if the set maximum times is reached or is smaller than the iteration error, stopping searching and outputting a final result to obtain the optimal speed ring and position ring controller parameters.
Other parts of this embodiment are the same as those of embodiment 1, and thus are not described again.
Example 3:
the present embodiment describes a method for self-tuning parameters of a speed loop and a position loop of a permanent magnet synchronous servo system in a specific embodiment based on any one of the above embodiments 1-2.
The working principle is as follows: the embodiment provides a parameter self-tuning method for a speed ring and a position ring of a permanent magnet synchronous servo system, which specifically comprises the following steps:
step S1: establishing a mechanical motion equation of the permanent magnet synchronous servo motor, and performing online identification on the rotary inertia of the permanent magnet synchronous servo motor by using a model reference adaptive algorithm;
the specific steps of step S1 are:
step S11: establishing a mechanical motion equation of the permanent magnet synchronous servo motor;
the permanent magnet synchronous servo system is a three-loop control system comprising a current loop, a speed loop and a position loop. The servo system detects the three-phase winding current of the motor and the rotor position theta through the current detection circuit and the position detection circuit, and calculates the exciting current component i through coordinate transformation d Torque current component i q . The difference delta theta between the position signal command and the actual rotor position signal is used as the input of the position controller to generate a speed signal command omega * . The difference value delta omega between the speed signal command and the actual speed signal is used as the input of the speed controller to generate a torque current command i qr (ii) a Torque current command i qr Excitation current command i dr The actual current signal passes through a current PI regulator to obtain a corresponding voltage command signal; the voltage instruction of the dq axis generates a pulse width modulation signal for controlling the inverter through inverse Park conversion and SVPWM modulation, so that the permanent magnet synchronous servo motor is driven
The mechanical motion equation of the permanent magnet synchronous servo motor is
In the formula (1), T e Is the motor outputting an electromagnetic torque, T L The torque is the load torque of the motor, J is the sum of the motor shaft and the load moment of inertia, B is the friction coefficient, and omega is the rotation angular velocity of the motor rotor.
Step S12: performing online identification on the rotational inertia of the permanent magnet synchronous servo motor by using a model reference adaptive algorithm;
machinery for permanent magnet synchronous servo motorEquation of motion (1) over a sample period T s Discretizing to obtain the following discrete form of the motor motion equation.
In actual operation of the motor, the possibility of drastic changes within one control cycle is small, and therefore the load can be considered approximately constant. Let, then the reference model be
ω(k)＝2ω(k-1)-ω(k-2)+a(k)(ΔT e (k)-BΔω(k)) (3)
Then the estimation model is
The following iterative formula can be designed according to Landau algorithm
In equation (5), β is an adaptive gain greater than 0, the convergence rate is faster as β is larger, and the convergence accuracy is higher as β is smaller, and 1 in the denominator is to prevent a case where the divisor is 0, so that the iteration diverges. Through the parameter identification method, identify
Then, due to the sampling period T s Is a known quantity and therefore identifies the moment of inertia J.
Step S2: and obtaining initial parameter vectors to be set of the position ring and speed ring controller parameters by using the online identified rotational inertia.
The specific steps of step S2 are:
step S21: and obtaining the initial parameter vector to be set of the speed ring.
In a servo system, the bandwidth of a current inner ring is far higher than the cut-off frequency of a speed ring, so the current inner ring can be approximately equivalent to a first-order inertia link, meanwhile, the corresponding small inertia link is processed approximately in engineering, the obtained speed ring equivalent control chart is shown in figure 2, and the open-loop transfer function of the speed ring after the approximate processing is determined to be
In the formula (6), the reaction mixture is,
the amplitude-frequency characteristic analysis of the velocity open loop shows that the cut-off frequency omega of the velocity loop is determined sc After the sum frequency width h is adjusted, the parameters of the speed loop PI controller can be obtained
In the formula (7), K T Is a torque coefficient.
Step S22: and obtaining an initial parameter vector to be set of the position ring.
Because the expected cut-off frequency of the speed loop is far higher than that of the position loop, the closed-loop transfer function of the speed loop can be equivalent to a first-order inertia element G sc (s). A control block diagram of a position loop structure adopting feedforward composite control is shown in FIG. 3, and the closed loop transfer function of the position loop obtained from FIG. 3 is
In the formula (8), K v A closed loop equivalent gain for speed.
If speed feedforward is not introduced, the speed feedforward coefficient is known to be 0, so the closed loop transfer function of the position loop is simplified to be
In order to ensure that the position response does not generate overshoot, the formula (9) is a critical damping second-order system, and the calculation formula of the damping ratio xi is
By bringing equations (9) and (10) into equation (8), it can be found that the error transfer function of the position loop is
When the position command is given as a ramp, the position loop steady state error can be expressed as
To make the position loop steady state error 0, there is K PF ＝1/K v 。
The feedforward controller is usually designed in an under-compensation state, a compensation coefficient field 0 < lambda < 0.9 is introduced, and the parameters of the position loop controller are obtained as
Therefore, the parameter vectors to be optimized of the speed loop and the position loop can be respectively determined according to the formula (7) and the formula (12), wherein the parameter vector to be optimized of the speed loop is [ K ] ps ，K is ]The position ring has a parameter vector to be optimized of [ K ] PP ，K PF ]。
Step S3: and (3) establishing a performance evaluation formula for evaluating the servo system, and respectively searching the optimal parameters of the position ring and the speed ring by using a firework algorithm of an improved selection strategy based on the initial parameter vector to be set obtained in the step (2).
The specific steps of the step 3 are as follows:
step S31: establishing a performance evaluation formula
In the firework algorithm for improving the selection strategy, the following absolute error integral IAE is adopted as one item of a fitness function of the firework optimizing algorithm, on the basis, the input square item is added to achieve the purpose of limiting input, and meanwhile, the rise time is used as one item of a performance evaluation index.
In formula (13), ω 1 ，ω 2 ，ω 3 Is a weight, t u For rise time, e (t) is error, u (t) is controller output.
In order to prevent the system stability from being influenced by the generation of overshoot, the performance evaluation index is as follows under the condition of the existing overshoot
In formula (14), ω 4 Is a weight, and ω 4 ＞＞ω 1 。
Step S32: and optimizing the parameters of the controller by using a firework algorithm of an improved selection strategy.
Using a firework algorithm to carry out parameter optimization operation so as to respectively determine optimal speed ring and position ring controller parameters, wherein the algorithm comprises the following specific steps:
step S321: setting a feasible region omega for fireworks algorithm optimization according to the parameter searching range, and obtaining an initial firework individual X according to the step 2 0 And randomly generating the rest initial firework individuals X in the feasible region range i (i is more than or equal to 1 and less than or equal to N-1) to finally generate X 0 ，X 1 ，X 2 ，…，X N-1 And N initial firework units.
Step S322: and calculating the fitness value of each firework individual according to the determined fitness function, obtaining the respective explosion intensity, explosion amplitude and displacement of different firework individuals, and executing the operation of generating explosion sparks by displacement. In the firework algorithm, an explosion operator is divided into three formulas of explosion intensity, explosion amplitude and displacement operation generated by explosion.
1) The explosion intensity represents the number of sparks generated by explosion, and the formula for calculating the explosion intensity is
In formula (15), X i Is the current firework S i Is the number of sparks generated by the ith fireworks, m is a constant for limiting the total number of sparks generated, Y max Is the firework individual fitness value with the worst fitness function in the current firework individual, f (X) i ) Is the fitness value of the ith firework individual, and epsilon is a minimal constant avoiding the denominator being zero.
2) The formula for calculating the explosion amplitude is
In the formula (16), A i Is the amplitude of the ith firework explosion,
is a constant representing the maximum explosion amplitude, Y min Is the firework individual fitness value with the optimal fitness function in the current firework individual, f (X) i ) Is the fitness value of the ith firework individual, and epsilon is a minimal constant avoiding the denominator being zero.
3) Generating explosion sparks, performing certain displacement operation on each dimension of the firework individual within the range of the explosion amplitude, updating all the firework individual according to the calculated displacement, and calculating according to the formula
In the formula (17), rand (0, A) i ) Representing a uniformly randomly generated one within the amplitude of the explosionThe number of the cells is equal to or greater than the total number of the cells,
is the current position of the ith firework in the k dimension.
Step S323: carrying out Gaussian variation operation on the sparks generated after the explosion to ensure the diversity of the firework individual set, wherein the calculation formula of the Gaussian variation is
In the formula (18), the reaction mixture,
is a varied spark of the gaussian type,
is the current position of the ith firework in the k dimension, g is a random number obeying Gaussian distribution, and g-N (1, 1).
Step S324: if the sparks generated by the firework individual bodies are positioned outside the feasible region omega in the algorithm implementation process, the sparks are mapped back to the feasible region through a mapping formula
In the formula (19), the reaction mixture is,
is the position of the ith spark outside the feasible region in the k dimension;
and
representing the upper and lower boundary positions of the k-th dimension, respectively.
Step S325: and implementing a selection strategy, selecting N fireworks in a candidate set as the next generation of fireworks, wherein an initial candidate set consists of fireworks, explosion sparks and Gaussian variation sparks, simultaneously introducing the concept of a firework pool in order to improve the searching capability of an optimal solution, recording the most excellent individuals generated in each iteration, wherein the most excellent individuals are the fireworks individuals with the minimum fitness, the firework pool is empty initially, the individuals in the firework pool in each subsequent iteration are added into the candidate set, and if the individuals to be added into the firework pool exist in the firework pool, the individuals are abandoned. In order to improve the global search capability of the algorithm, the best individuals in the candidate set are directly added and reserved to the next generation, N-1 clustering centers are selected as the rest next generation individuals in the candidate set by using a k-means clustering algorithm, the process of implementing the k-means clustering algorithm is shown in figure 5, and the calculation formula in the k-means clustering algorithm is
d(X i ，X j )＝||X i -X j || 2 (20)
In the formula (20), d (X) i ，X j ) Showing individual fireworks X i And X j The euclidean distance between.
Step S326: when the algorithm reaches the set maximum times or is smaller than the iteration error, stopping searching and outputting a final result to obtain a final accurate controller parameter, otherwise, continuing to jump to the step S322: the next iteration is performed.
The method uses a firework algorithm with an improved selection strategy to perform parameter self-setting work, identifies the rotary inertia by using a model reference self-adaptive algorithm, and obtains the initial value of the parameter to be set by using the rotary inertia, so that the algorithm can be quickly positioned to a position close to the global optimal performance, has good local optimal search performance in subsequent accurate search, and improves the actual efficiency of searching for the parameters of a position ring and a speed ring PI in the permanent magnet synchronous servo motor.
The other parts of this embodiment are the same as those of the above embodiments 1-2, and thus are not described again.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications and equivalent variations of the above embodiments according to the technical spirit of the present invention are included in the scope of the present invention.
Claims (8)
1. A method for self-tuning parameters of a speed ring and a position ring of a permanent magnet synchronous servo system is characterized by comprising three stages, wherein a mechanical motion equation of a permanent magnet synchronous servo motor is established in the first stage, and the rotational inertia of the permanent magnet synchronous servo motor is identified on line by using a model reference self-adaptive algorithm; in the second stage, the initial parameter vectors to be optimized of a speed ring and a position ring of the permanent magnet servo system are obtained according to the online identified rotational inertia; and in the third stage, the initial parameter vectors to be optimized of the speed ring and the position ring are used as initial firework individuals, and the optimal speed ring and position ring parameters are obtained by optimizing the firework algorithm of the improved selection strategy.
2. The method for self-tuning the parameters of the speed ring and the position ring of the permanent magnet synchronous servo system according to claim 1, wherein the specific operation of performing online identification on the rotational inertia of the permanent magnet synchronous servo motor by using the model reference adaptive algorithm in the first stage is as follows: firstly discretizing a mechanical motion equation of the permanent magnet synchronous servo motor in a sampling period to obtain a discrete form of the mechanical motion equation of the permanent magnet synchronous servo motor, then establishing a reference model of the permanent magnet synchronous servo motor according to the discrete form of the mechanical motion equation without changing the load of the permanent magnet synchronous servo motor, and finally carrying out online identification on the rotary inertia according to a Landau algorithm.
3. The method for self-tuning the parameters of the speed ring and the position ring of the permanent magnet synchronous servo system according to claim 2, wherein the specific operations of obtaining the initial parameter vectors to be optimized of the speed ring and the position ring of the permanent magnet synchronous servo system in the second stage are as follows: determining the cut-off frequency and the intermediate frequency of the speed ring by using the open-loop transfer function of the speed ring to obtain the initial parameter vector of the speed ring controller to be optimized; and introducing a compensation coefficient field into the obtained online identified rotary inertia in an under-compensation state by using a closed loop transfer function of the position ring to obtain an initial position ring controller parameter vector to be optimized.
4. The method for self-tuning the parameters of the speed ring and the position ring of the permanent magnet synchronous servo system according to claim 3, wherein the third stage specifically comprises the following steps:
step 1: setting a feasible region of a firework algorithm of an improved selection strategy according to the parameter search range of the speed ring and the position ring, taking the initial to-be-optimized parameter vectors of the speed ring and the position ring controller as initial firework units, randomly generating the rest firework units in the feasible range, and finally generating N initial firework units;
step 2: calculating respective explosion intensity and explosion amplitude of different firework individuals, and performing displacement operation on each dimension of the firework individuals in an explosion range to generate explosion sparks;
and step 3: carrying out Gaussian variation operation on the explosion sparks to generate Gaussian variation sparks, and mapping the Gaussian variation sparks outside the feasible region back to the feasible region through mapping operation;
and 4, step 4: using the firework individual, the explosion spark and the Gaussian variation spark as an initial candidate set, and calculating the individual fitness in the candidate set;
and 5: adding a firework pool into the initial candidate set, and adding the individual with the minimum fitness in the candidate set into the firework pool in each iteration;
step 6: if the number of times of the firework units does not reach the set maximum number of times or is smaller than the iteration error, selecting the rest N-1 individuals according to a k-means clustering algorithm, taking the N-1 clustering centers as the next-generation firework individuals, and skipping to the step 2 for next iteration; and if the set maximum times is reached or is smaller than the iteration error, stopping searching and outputting a final result to obtain the optimal speed ring and position ring controller parameters.
5. The method for self-tuning the parameters of the speed ring and the position ring of the permanent magnet synchronous servo system according to claim 4, wherein the step 4 of establishing the fitness function for calculating the fitness of the individuals in the candidate set comprises the following specific operations: in the improved strategy selection firework algorithm, the absolute error integral is taken as one item of a fitness function of the strategy improvement firework algorithm, the rise time is taken as one item of a performance evaluation index in the fitness function, and an output square item is added in the fitness function to obtain the fitness function of the evaluation servo system.
6. The method for self-tuning the parameters of the speed ring and the position ring of the permanent magnet synchronous servo system according to claim 4, wherein the rest N-1 individuals are selected according to a k-means clustering algorithm in the step 6, and the specific operation of taking the N-1 clustering centers as the next-generation firework individuals comprises the following steps: randomly selecting N-1 clustering centers in the candidate set, calculating the distance between each individual in the candidate set and the clustering center, classifying each individual into the cluster where the closest clustering center is located, and taking the N-1 clustering centers as next-generation firework individuals if no cluster is changed.
7. The method for self-tuning the parameters of the speed ring and the position ring of the permanent magnet synchronous servo system according to claim 4, wherein the explosion intensity is the number of explosion sparks.
8. The method for self-tuning the parameters of the speed ring and the position ring of the permanent magnet synchronous servo system according to claim 1, wherein the specific operations of establishing the mechanical motion equation of the permanent magnet synchronous servo motor in the first stage are as follows: and establishing a mechanical motion equation of the permanent magnet synchronous servo motor according to an output electromagnetic matrix of the permanent magnet synchronous servo motor, a load matrix of the permanent magnet synchronous servo motor, the sum of a shaft of the permanent magnet synchronous servo motor and load rotational inertia, a friction coefficient and the rotation angular speed of a rotor of the permanent magnet synchronous servo motor.
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