Motor fuzzy PID parameter tuning method based on improved whale algorithm

Abstract

Disclosed is a motor fuzzy PID parameter tuning method based on an improved whale algorithm. The method comprises: building a brushless direct-current motor speed control system model, and using a fuzzy PID controller to perform motor speed control. A conventional whale algorithm is optimized by using a chaotic convergence factor, a fractional order, and Levy flights, so as to obtain an improved whale algorithm. Secondly, the overshoot of the system is used as a component of an ITAE performance index to obtain an improved ITAE performance index, and the improved ITAE performance index is used as a fitness function for the improved whale algorithm. Finally, the improved whale algorithm is used to optimize input and output membership functions of a fuzzy controller, so as to obtain optimal ΔKp, ΔKi, and ΔKd values, and Kp, Ki, and Kd parameters of a PID controller are tuned to implement motor speed control. The present invention addresses the difficulty of tuning parameters of conventional PID controllers and solves the problem of low precision of motor speed control, has the advantages of high anti-interference capability, little overshoot, and short adjustment time, and improves the dynamic characteristics and robustness of the controllers.

Description

A motor fuzzy PID parameter tuning method based on improved whale algorithm Technical Field

[0001] The present invention relates to the field of brushless DC motor control, and in particular to a motor fuzzy PID parameter tuning method based on an improved whale algorithm. Background Art

[0002] Brushless DC motors (BLDCMs) are a new type of motor that has rapidly matured with the development of power electronics and motor control technologies. They offer stable and reliable operation, simple structure, and multivariable, strongly coupled, and nonlinear characteristics, enabling them to meet the demands of a variety of complex operating conditions. They have broad applications and research value in fields such as industrial robotics, aerospace, and automotive manufacturing. Currently, the traditional PID control scheme is widely used. However, this traditional PID control scheme relies on specific mathematical models, resulting in poor control accuracy and slow adaptability, making it difficult to meet the requirements for precise and stable motor speed control.

[0003] Fuzzy PID control does not rely heavily on the mathematical model of the controlled object. Instead, it constructs membership functions from fuzzy subsets and makes fuzzy decisions based on a table of control rules to achieve effective control of the speed system. Therefore, fuzzy controllers offer advantages such as fast response and robustness. However, existing fuzzy controllers often rely on the experience of experts in the field and are susceptible to subjective influences, resulting in limited accuracy.

[0004] Summary of the Invention

[0005] The purpose of the present invention is to provide a motor fuzzy PID parameter tuning method based on an improved whale algorithm to solve the problems existing in the above-mentioned prior art, so that the control system has better dynamic and static performance and adaptive ability, improves the control accuracy of the system and the speed response of the motor, and reduces the overshoot of the system.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] The present invention provides a motor fuzzy PID parameter tuning method based on an improved whale algorithm.

[0008] Step (1) Establish a dual closed-loop control system model for the brushless DC motor speed. Build a simulation model in Simulink, which mainly includes modules such as current hysteresis control, BLDCM, and inverter.

[0009] Step (2) constructs a fuzzy PID controller in the brushless DC motor speed control system.

[0010] Step (2-1) The present invention adopts a two-input three-output fuzzy controller, the input of which is the deviation E and the deviation change rate E. c The output is the change in the proportional adjustment coefficient of the PID controller ΔK p , integral adjustment coefficient change ΔK i , differential adjustment coefficient change ΔK d .

[0011] In step (2-2), the input and output fuzzy subsets are both divided into 7 levels, namely: {Negative Large (NB), Negative Medium (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Medium (PM), Positive Large (PB)}, and the input and output domains are both {-3,3}.

[0012] In step (2-3), the membership function of the input quantity adopts Gaussian membership function, the output quantity NB and PB adopt S-type membership function, and the rest adopt triangular membership function.

[0013] Steps (2-4) are based on the expert experience in the database and E, E c and ΔK p , ΔK i , ΔK d relationship, establish inference rules, and formulate fuzzy rule tables.

[0014] In step (2-5), the fuzzy controller reasoning method adopts Mamdani fuzzy reasoning method, and the defuzzification method selects the center of gravity method.

[0015] Step (3) uses the improved whale algorithm to optimize the input and output membership functions of the fuzzy controller.

[0016] Step (3-1) expresses the dimension of the whale algorithm as the optimization variable set X=(x1, x2, ..., x 81 ) T , i.e. dim = 81. All variables are encoded using real numbers, setting the population number Number and the maximum number of iterations T of the whale algorithm. max and search space area.

[0017] Step (3-2) updates the individual whale positions according to the improved whale algorithm process.

[0018] Step (3-3) After the whale position is updated, out-of-bounds processing is performed, the out-of-bounds elements are replaced, and the fitness function value of the whale individual is calculated and compared with the previous optimal fitness value. If the new value is smaller, the optimal fitness value and the optimal whale position are updated.

[0019] Step (3-4) assigns the current whale position to the input and output membership functions, and obtains ΔK through the fuzzy controller. p, ΔK i , ΔK d The parameter values ​​are passed to the PID controller, and then a co-simulation is performed with the BLDCM speed control model constructed in Simulink. The improved ITAE performance index (time multiplied by the integral of the absolute value of the error) is used as the fitness function of the whale algorithm.

[0020] Steps (3-5) are continuously updated and iterated until the number of cycles reaches the maximum number of iterations T max , the global optimal whale position is fuzzy calculated and output to the PID controller to control the motor speed.

[0021] In the optimization process of the whale algorithm, there are two main predation mechanisms (contraction and encirclement mechanism and spiral position update mechanism) and three predation strategies (prey search strategy, encirclement and predation strategy and bubble net attack strategy).

[0022] Assuming that the optimal individual whale position in the contemporary group is the prey position, each whale randomly chooses a prey search strategy, an encirclement predation strategy, or a bubble net attack strategy.

[0023] If p≥0.5, the whale population adopts a bubble net attack strategy. At this time, the whales swim along a spiral path toward the prey. The whale position update formula is as follows: X(t+1)=X * (t)+D p e bl cos(2πl)

[0024] Among them, D p =|X*(t)-X(t)| represents the distance between the whale and its prey; b is a constant representing the shape of the spiral, with a value of 1; l is a random number on [-1,1].

[0025] If |A|≤1 and p<0.5, the whale population adopts an encirclement predation strategy. At this time, the whales swim towards the whale in the optimal position. The whale position update formula is as follows: X(t+1)=X * (t)-AD D=|CX * (t)-X(t)|

[0026] In the above formula, X*(t) represents the position of the whale that achieves the global optimal solution within the population at the tth generation, X(t) represents the positions of the remaining whales at the tth iteration, and D is the bracketing step size. A and C are coefficient vectors.

[0027] If |A|>1 and p<0.5, the whale population adopts a search-for-prey strategy. In this phase, the whale swims towards a whale at a random location, and the position update formula using fractional-order Levy flight is as follows:

[0028] In the above formula, α is the step size control quantity; Levy(β) is the random search path that satisfies

[0029] Where u and v are respectively subject to the parameters σ u and σ v Normal distribution of:

[0030] Among them, σ u It can be obtained by the following formula:

[0031] Wherein, β=1.5, Γ() is the gamma function.

[0032] The present invention discloses the following technical effects: a fuzzy PID controller optimized by an improved whale algorithm enables a motor to have a faster response speed and higher control accuracy, thereby reducing the overshoot of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0034] FIG1 is a flow chart of a motor fuzzy PID parameter tuning method based on an improved whale algorithm according to the present invention;

[0035] FIG2 is a schematic diagram of a motor fuzzy PID parameter tuning method based on an improved whale algorithm according to the present invention;

[0036] FIG3 is a diagram of E and E of a motor fuzzy PID parameter tuning method based on an improved whale algorithm according to the present invention. c Membership function graph of ;

[0037] Figure 4 shows the ΔK of a motor fuzzy PID parameter tuning method based on the improved whale algorithm of the present invention. p , ΔK i , ΔK d Membership function graph of .

[0038] FIG5 is an algorithm flow chart of a motor fuzzy PID parameter tuning method based on an improved whale algorithm according to the present invention; DETAILED DESCRIPTION

[0039] While various exemplary embodiments of the present invention are described in detail, this detailed description should not be considered as limiting the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0040] It should be understood that the terms described herein are intended only to describe particular embodiments and are not intended to limit the present invention. In addition, for numerical ranges herein, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. The intermediate value within any stated value or stated range, and each smaller range between any other stated value or intermediate value within the stated range, is also encompassed within the present invention. The upper and lower limits of these smaller ranges may be independently included or excluded within the scope.

[0041] Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art. Although only preferred methods and materials are described herein, any methods and materials similar or equivalent to those described herein may also be used in the practice or testing of the present invention. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods and / or materials associated with the documents. In the event of any conflict with any incorporated document, the contents of this specification shall prevail.

[0042] It will be apparent to those skilled in the art that various modifications and variations may be made to the specific embodiments described herein without departing from the scope or spirit of the invention. Other embodiments will be apparent to those skilled in the art from the description of the invention. The description and examples are intended to be illustrative only.

[0043] The words “include,” “including,” “have,” “contain,” etc. used in this document are open-ended terms, meaning including but not limited to.

[0044] In order to make the purpose, technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0045] As shown in Figure 1, a motor fuzzy PID parameter tuning method based on the improved whale algorithm specifically includes the following steps:

[0046] Step (1) Establish a brushless DC motor speed double closed-loop control system model.

[0047] A three-phase six-state brushless DC motor model is established. For ease of analysis, the following assumptions are made:

[0048] 1) The three-phase winding structure is symmetrical, and the stator current and rotor magnetic field distribution are symmetrical;

[0049] 2) The three-phase back electromotive force is a trapezoidal wave with a flat top width of 120°;

[0050] 3) Ignore armature reaction, cogging effect and magnetic circuit saturation;

[0051] 4) The motor speed remains constant during commutation;

[0052] According to the characteristics of the brushless DC motor, the voltage balance equation of the stator winding can be obtained:

[0053] In the above formula, k = A, B, C, u k is the three-phase stator winding terminal voltage, e k is the reverse electromotive force of each phase, L is the self-inductance of each phase winding, R is the phase resistance of each phase winding, i k is the phase current of each phase winding, and M is the mutual inductance between each phase winding.

[0054] The electromagnetic torque equation of the brushless DC motor is:

[0055] Where w is the mechanical angular velocity of the motor, T e is the electromagnetic torque.

[0056] The equation of motion of the brushless DC motor can be expressed as:

[0057] Where J is the moment of inertia, T L is the load torque, and B is the damping coefficient.

[0058] According to formulas (1), (2), and (3), a simulation model is built in Simulink, which mainly includes modules such as current hysteresis control, BLDCM, and inverter.

[0059] Step (2) constructs a fuzzy PID controller in the brushless DC motor speed control system, as shown in Figure 2.

[0060] Step (2-1) The present invention adopts a two-input three-output fuzzy controller, the input of which is the deviation E and the deviation change rate E. c , the output is the change of the proportional adjustment coefficient ΔK p , integral adjustment coefficient change ΔK i , differential adjustment coefficient change ΔK d .

[0061] In step (2-2), the input and output fuzzy subsets are both divided into 7 levels, namely: {Negative Large (NB), Negative Medium (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Medium (PM), Positive Large (PB)}, and the input and output domains are both {-3,3}.

[0062] In step (2-3), the membership function of the input quantity adopts Gaussian membership function, the output quantity NB and PB adopt S-type membership function, and the rest adopt triangular membership function.

[0063] By improving the whale algorithm, the input and output membership functions of the fuzzy controller are optimized to obtain ΔK p , ΔK i , ΔK d , then the K of the PID controller p , K i , K d The parameters are tuned, and the parameter tuning formula is as follows:

[0064] where K p *、K i *、K d * is the initial value of the PID controller, ΔK p , ΔK i , ΔK d is the output value of the fuzzy controller.

[0065] Steps (2-4) formulate a fuzzy rule table. The fuzzy rules are shown in Table 1:

[0066] Table 1

[0067] In step (2-5), the fuzzy controller reasoning method adopts Mamdani fuzzy reasoning method, and the defuzzification method selects the center of gravity method.

[0068] Step (3) uses the improved whale algorithm to optimize the input and output membership functions of the fuzzy controller.

[0069] The membership function curve of the speed error E is shown in Figure 3. The membership function to be optimized is expressed as x1, x2, ..., x1 in the range of [-3, 3]. 12 Similarly, this is also the definition of the error change rate E c A method for optimizing parameters of the membership function.

[0070] Proportional adjustment coefficient change ΔK p The membership function curve is shown in Figure 4. The membership function to be optimized is expressed as x in the range of [-3,3]. 25 , x 26 ,…,x 43 Similarly, this also defines the output as the change in the integral adjustment coefficient ΔK i and the differential adjustment coefficient change ΔK d A method for optimizing parameters of the membership function.

[0071] In summary, the optimized parameters of the fuzzy controller are shown in Table 2.

[0072] Table 2 Membership function optimization parameters

[0073] As shown in Table 1, the total number of parameters that need to be optimized in the fuzzy controller is 81. The definition of the optimization parameters is as follows: X = (x1, x2, ..., x 81 ) T

[0074] Combined with the calculation process of the improved whale algorithm, as shown in Figure 5, the following is the basic process of optimizing the membership function:

[0075] Step (3.1) expresses the dimension of the whale algorithm as the optimization variable set X = (x1, x2, ..., x 81 ) T , i.e. dim = 81. All variables are encoded using real numbers, setting the population number Number and the maximum number of iterations T of the whale algorithm. max and search space area.

[0076] Step (3.2) updates the position of individual whales according to the whale optimization algorithm process.

[0077] After the whale position is updated in step (3.3), out-of-bounds processing is performed, the out-of-bounds elements are replaced, and the fitness function value of the whale individual is calculated and compared with the previous optimal fitness value. If the new value is smaller, the optimal fitness value and the optimal whale position are updated.

[0078] Step (3.4) decodes the whale individual at the current optimal position and outputs the relevant parameters of the membership function to the fuzzy controller. Then, a joint simulation is performed with the BLDCM speed control model constructed in Simulink, and the improved ITAE index (time multiplied by the integral of the absolute value of the error) is used as the fitness function of the whale algorithm.

[0079] Step (3.5) is continuously updated and iterated until the number of cycles reaches the maximum number of iterations T max , the globally optimal whale position is decoded and directly output as the optimization parameter of the membership function.

[0080] Figure 1 is a flow chart of the improved whale algorithm for optimizing the fuzzy controller's membership function. The whale algorithm's optimization process employs two main predation mechanisms (a contraction and encirclement mechanism and a spiral position update mechanism) and three predation strategies (a prey search strategy, an encirclement and encirclement strategy, and a bubble net attack strategy).

[0081] Assuming that the optimal individual whale position in the contemporary group is the prey position, each whale randomly chooses a prey search strategy, an encirclement predation strategy, or a bubble net attack strategy.

[0082] If p≥0.5, the whale population adopts a bubble net attack strategy. At this time, the whales swim along a spiral path toward the prey. The whale position update formula is as follows: X(t+1)=X * (t)+D p e bl cos(2πl) (5)

[0083] Among them, D p =|X*(t)-X(t)| represents the distance between the whale and its prey; b is a constant representing the shape of the spiral, with a value of 1; l is a random number on [-1,1].

[0084] If |A|≤1 and p<0.5, the whale population adopts an encirclement predation strategy. At this time, the whales swim towards the whale in the optimal position. The whale position update formula is as follows: X(t+1)=X * (t)-AD (6) D=|CX * (t)-X(t)| (7)

[0085] In the above formula, X*(t) represents the position of the whale individual that achieves the global optimal solution in the population when searching to the tth generation, X(t) represents the position of the remaining whale individuals at the tth iteration, and D is the encirclement step size. A and C are coefficient vectors, and the calculation formula is: A=2ar1-a(8) C=2r2(9)

[0086] Among them, a is the chaos convergence factor, r1 and r2 are random numbers in [0,1], T max is the maximum number of iterations, h t =1-2(h t-1 ) 2 , and h t ∈[0,1], h0≠0.5.

[0087] If |A|>1 and p<0.5, the whale population adopts a search-for-prey strategy. In this phase, the whale swims towards a whale at a random location, and the position update formula using fractional-order Levy flight is as follows: X(t+1)=X(t)+(X * (t)-X(t))·α·Levy(β) (11)

[0088] In the above formula, α is the step size control quantity; Levy(β) is the random search path that satisfies

[0089] Where u and v are respectively subject to the parameters σ u and σ v The normal distribution, σ u and σ v The definition of u~N(0,σ u2 ) (12) v~N(0,σ v 2 ) (13) σ v =1 (15)

[0090] Usually, the value of β in the formula is 3 / 2.

[0091] In the process of searching for prey, since the position of an individual in previous generations will affect its position in the current generation, the present invention introduces a storage strategy based on fractional order expansion to improve the global optimization ability of WOA.

[0092] The specific expression of fractional calculus is as follows:

[0093] Where α is the order, T is the period, r is the cutoff order, and Γ() is the gamma function.

[0094] Combined with formula (15), taking the truncation order r = 4, formula (10) can be expressed as

[0095] At the same time, the evolution factor f is introduced into the formula to correct the order α, and the fractional order is adaptively adjusted using the whale position information. The adjustment formula is as follows:

[0096] in

[0097] In the above formula,

[0098] Among them, d ix is the average distance from the best whale individual to other whale individuals in the population, d g is the average distance from the global best position to other whales, d max and d min For all d ix The maximum and minimum values ​​in .

[0099] The fitness function of the whale algorithm in step (3.4) is shown in formula (21).

[0100] Where t is the system simulation time, e(t) is the error between the expected output speed and the actual output speed, and k is the penalty coefficient.

[0101] In this example of the improved whale algorithm, the population size Number = 50, the maximum number of iterations T max= 500, dimension dim = 81. In this example, a dual closed-loop mode is used for brushless DC motor speed control (the inner loop is a current hysteresis loop, and the outer loop is a speed loop). In the fuzzy controller, the expected output speed is subtracted from the actual output speed to obtain the error and the rate of change of the error. In the simulation model, the improved ITAE index is used as the fitness function. The improved whale algorithm is used to iteratively optimize the fuzzy controller's membership function to obtain the optimal PID controller parameter values.

[0102] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A motor fuzzy PID parameter tuning method based on an improved whale algorithm, characterized in that: The following steps are involved: Step (1) building a brushless DC motor speed double closed-loop control system model, using a fuzzy PID controller to control the motor in the simulation model, determining fuzzy input and output, establishing fuzzy sets, domains and membership functions, designing fuzzy rules, and determining fuzzy reasoning methods and defuzzification methods; Step (2) takes the output and input membership functions of the fuzzy controller as optimization objects, optimizes the membership function using the improved whale algorithm, outputs the optimal membership function shape, and uses fuzzy rules to adjust the parameters of the PID controller online to achieve control of the motor speed.

2. The method according to claim 1, characterized in that The fuzzy controller in step (1) is a two-input and three-output system, with the inputs being the error E and the rate of change of the error E. c The output is the change in the proportional adjustment coefficient of the PID controller ΔK p , integral adjustment coefficient change ΔK i and the differential adjustment coefficient change ΔK d .

3. The method according to claim 2, characterized in that The domain of the input and output quantities is divided into 7 levels, and the fuzzy sets are: negative large NB, negative medium NM, negative small NS, zero ZO, positive small PS, positive medium PM, and positive large PB. The membership function of the input quantity adopts Gaussian membership function, the output quantity NB and PB adopt S-type membership function, and the rest adopt triangular membership function.

4. The method according to claim 2, wherein the proportional adjustment coefficient K of the PID controller in step (1) is p , integral adjustment coefficient K i and differential adjustment coefficient K d Adjust the parameters. The parameter adjustment formula is: where K p *、K i *、K d * is the initial value of the PID controller, ΔK p , ΔK i , ΔK d is the output value of the fuzzy controller.

5. The method according to claim 2, characterized in that In step (1), based on the expert experience in the database and E, E c and ΔK p , ΔK i , ΔK d The relationship between them is established, reasoning rules are established, and a fuzzy rule table is formulated. The fuzzy controller reasoning method adopts the Mamdani fuzzy reasoning method, and the defuzzification method selects the center of gravity method.

6. The method according to claim 1, characterized in that In step (2), the improved whale algorithm is used to optimize the input and output membership functions of the fuzzy controller, which specifically includes the following steps: Step (3) represents the dimension of the whale algorithm as the optimization variable set X=(x1, x2, ..., x 81 ) T , i.e. dim = 81, all variables are encoded using real numbers, set the population number Number and the maximum number of iterations T of the whale algorithm max and search space area; Step (4) updating the individual whale positions according to the improved whale algorithm process; Step (5) After the whale position is updated, the out-of-bounds processing is performed, the out-of-bounds elements are replaced, and the fitness function value of the whale individual is calculated and compared with the previous optimal fitness value. If the new value is smaller, the optimal fitness value and the optimal whale position are updated; Step (6) assigns the current whale position to the input and output membership functions, and obtains ΔK through the fuzzy controller. p , ΔK i , ΔK d The parameter values are passed to the PID controller, and then a co-simulation is performed with the BLDCM speed control model built in Simulink. The improved ITAE performance index (time multiplied by the integral of the absolute value of the error) is used as the fitness function of the whale algorithm. Step (7) continues to update and iterate until the number of cycles reaches the maximum number of iterations T max , the global optimal whale position is fuzzy calculated and output to the PID controller to control the motor speed.

7. The method according to claim 6, characterized in that The step (6) improves the ITAE performance index to: Where t is the system simulation time, e(t) is the error between the expected output speed and the actual output speed, and k is the penalty coefficient.

8. The method according to claim 6, characterized in that The whale algorithm has two main predation mechanisms in its optimization process: the shrinking and encircling mechanism and the spiral position updating mechanism; and three predation strategies: the prey search strategy, the encircling and encircling predation strategy, and the bubble net attack strategy. Assuming that the optimal individual whale position in the contemporary group is the prey position, each whale randomly chooses a prey search strategy, an encirclement predation strategy, or a bubble net attack strategy; If p ≥ 0.5, the whale population adopts a bubble net attack strategy. At this time, the whales swim towards the prey along a spiral path. The whale position update formula is as follows: X(t+1)=X * (t)+D p e bl cos(2πl) Among them, D p =|X * (t)-X(t)| represents the distance between the whale and the prey; b is a constant representing the shape of the spiral, with a value of 1; l is a random number on [-1,1]; If |A|≤1 and p<0.5, the whale population adopts an encirclement predation strategy. At this time, the whales swim towards the whale in the optimal position. The whale position update formula is as follows: X(t+1)=X * (t)-AD D=|CX * (t)-X(t)| In the above formula, X * (t) represents the position of the whale individual that achieves the global optimal solution in the population at the tth generation, X(t) represents the position of the remaining whale individuals at the tth iteration, and D is the bracketing step size. A and C are coefficient vectors; If |A|>1 and p<0.5, the whale population adopts a search-for-prey strategy. In this phase, the whale swims towards a whale at a random location, and the position update formula using fractional-order Levy flight is as follows: In the above formula, α is the step size control quantity; Levy(β) is the random search path that satisfies Where u and v are respectively subject to the parameters σ u and σ v Normal distribution of: Among them, σ u It can be obtained by the following formula: Wherein, β=1.5, Γ() is the gamma function.

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