Design method of active vibration isolation controller with self-optimized parameters

Abstract

According to the design method of the active vibration isolation controller with the self-optimized parameters, the controller parameters can be automatically generated by solving the optimization problem, the frequency band of vibration suppression of the vibration isolator can be set, targeted vibration suppression is achieved, and the stability of the vibration isolator is guaranteed. According to the method, the vibration transmissibility of the vibration isolation system is set as the cost, the phase margin is not smaller than the set minimum value and is set as the constraint, a parameter optimization problem is constructed, the parameters of the multi-order lead-lag compensator in the controller are solved, and the vibration suppression rate and the vibration isolator stability are both considered. According to the method, the problem of long adjustment time caused by manual parameter configuration of the active vibration isolation controller can be solved, and help is provided for design of the active vibration isolation controller.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration isolation, and in particular to a method for designing an active vibration isolation controller with self-optimized parameters. Background Art

[0002] Vibration significantly impacts the sensitivity and stability of precision instruments. Passive vibration isolation systems attenuate vibrations greater than the square root of two times the natural frequency. To further suppress low-frequency vibrations, active vibration isolation control technology with external energy input is employed. The active isolation actuator provides additional force, which cancels out the external vibration disturbance, achieving vibration control.

[0003] The control inputs for the active vibration isolation system's actuators are generated in real time by a controller based on vibration sensor data. The controller's design determines the system's vibration suppression capability and stability. Parameter setting is a crucial step in controller design. Currently, active vibration isolation controller parameters rely on manual tuning, increasing the system's debugging time and potentially missing optimal parameters. Therefore, designing an active vibration isolation controller that can automatically determine parameters is a key challenge in this field. Summary of the Invention

[0004] In response to the deficiencies in the prior art, the present invention provides a method for designing an active vibration isolation controller with self-optimization of parameters, which can automatically generate controller parameters by solving an optimization problem and set the frequency band of vibration suppression of the isolator, thereby achieving targeted vibration suppression and ensuring the stability of the isolator.

[0005] The technical solutions of the present invention are as follows:

[0006] The method for designing an active vibration isolation controller with self-optimization of parameters is characterized by comprising the following steps:

[0007] Step 1: Obtain the vibration transfer function of the active vibration isolation system;

[0008] Step 2: Construct the controller parameter optimization problem;

[0009] Step 3, solving the controller parameter optimization problem;

[0010] Step 4: Substitute the optimized parameters into the multi-order lead-lag compensator.

[0011] The expressions included in step 1 are as follows:

[0012]

[0013] Among them, H passive (s) is the passive vibration isolation transfer function, s is the Laplace variable, H open(s) is the open-loop transfer function of the active vibration isolation.

[0014]

[0015] Where c is the damping coefficient of the passive isolator, k is the stiffness of the passive isolator, and m is the mass of the object being isolated.

[0016] H open (s)=H seis (s)H amp (s)H c (s)H vccs (s)H vc (s)H P (s),

[0017] Among them, H seis (s) is the seismograph transfer function, H amp (s) is the transfer function of the amplifier circuit, H c (s) is the multi-order lead-lag compensator transfer function, H vccs (s) is the voltage-controlled current source transfer function, H vc (s) Transfer function from input current to output force of voice coil motor, H P (s) is the transfer function from the force acting on the isolated object to the motion velocity.

[0018] The expressions included in step 4 are as follows:

[0019]

[0020] H c (s)=G llc,1 (s)·G llc,2 (s)…G llc,κ (s),

[0021] Param=[τ κ z1 p1 … z κ p κ ]∈R 2κ+1 ,

[0022] τ κ =τ1·τ2…τ κ ,

[0023] Among them G llc (s) is the lead-lag compensator, τ is the phase compensator gain, z is the phase compensator zero, p is the phase compensator pole, τ, z and p are G llc (s) Parameters that need to be configured, H c (s) is a κ-order lead-lag compensator, κ is an integer greater than 1, G llc,1(s) is the first-order lead-lag compensator, G llc,κ (s) is the κth order lead-lag compensator, Param is H c (s) Input parameter, τ κ is the intermediate quantity, τ1 is the first phase compensator gain, is the phase compensator gain, τ κ is the κth phase compensator gain, z1 is the first phase compensator zero, z k is the kth phase compensator zero, p1 is the first phase compensator pole, R κ is the κth phase compensator pole, R 2κ+1 is a 2κ+1 vector dimension.

[0024] The expressions included in step 2 are as follows:

[0025]

[0026] τ k =τ1·τ2…τ k ,

[0027] Cost = w T Tran,

[0028] Tran=[tran(ω1),tran(ω2),…,tran(ω n )] T ∈R n ,

[0029] w T =[w1,w2,…,w n ] T ,

[0030]

[0031] Among them H c (s) is a κ-order lead-lag compensator, κ is an integer greater than 1, τ κ is the intermediate quantity, τ1 is the first phase compensator gain, is the phase compensator gain, τ κ is the κth phase compensator gain, z1 is the first phase compensator zero, z k is the κth phase compensator zero, p1 is the first phase compensator pole, and p κ is the κth phase compensator pole, Pa * is the controller parameter optimization problem, is the minimum value operation related to the optimization problem of the controller parameter Pa, Cost is the cost of the optimization problem, st is the constraint condition, pm(ω i ) is the i-th vibration frequency ω to be suppressed iThe phase margin, i is the serial number, pm m (ω i ) is the set frequency ω i The minimum phase margin that is satisfied is is the intermediate quantity, w T is the intermediate quantity, Tran is the vibration transmissibility vector, tran(ω1) is the amplitude of the first vibration frequency ω1, tran(ω n ) is the nth vibration frequency ω n The amplitude, n is a positive integer, R n is the n-dimensional vector dimension, w1 is the weight of ω1, w n Yes n The weight of .

[0032] Step 3 includes using particle swarm optimization, genetic algorithm and simulated annealing algorithm to obtain Pa * The solution.

[0033] The expressions included in step 3 are as follows:

[0034]

[0035] where τ κ,* is τ k The optimal amount of is the optimal amount of z1, is the optimal amount of p1, It is z k The optimal amount of It is p κ The optimal amount of .

[0036] The expressions included in step 4 are as follows:

[0037]

[0038] in By using Pa * The optimal controller parameters H c (s)Optimal configuration.

[0039] The technical effects of the present invention are as follows: The present invention provides a method for designing an active vibration isolation controller with self-optimized parameters, which can automatically generate controller parameters by solving an optimization problem, and can set the frequency band of vibration suppression of the vibration isolator, thereby achieving targeted vibration suppression and ensuring the stability of the vibration isolator. This method constructs a parameter optimization problem by setting the vibration transmission rate of the vibration isolation system as a cost and the phase margin not less than the set minimum value as a constraint, and solves the parameters of the multi-order lead-lag compensator inside the controller to achieve a balance between vibration suppression rate and vibration isolator stability. This method can solve the problem of long adjustment time caused by manual parameter configuration of the active vibration isolation controller, and provides assistance for the design of active vibration isolation controllers.

[0040] The advantages of the present invention compared with the prior art are:

[0041] (1) The present invention solves the parameter optimization problem in the active vibration isolation controller. The controller parameters do not need to be manually configured and debugged, and can be obtained by solving the optimization problem.

[0042] (2) The parameter optimization problem designed in the controller of the present invention takes the vibration suppression rate as the optimization cost, and the phase margin is set to be not less than the set minimum value as a hard constraint to achieve a balance between the vibration suppression rate and the stable operation of the vibration isolation system.

[0043] (3) The parameter-free active vibration isolation controller proposed in the present invention can set the vibration frequency to be suppressed, thereby achieving vibration suppression at a specified frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The present invention is a flow chart of a method for designing an active vibration isolation controller with self-optimization of parameters. Figure 1 The method includes step 1, obtaining the vibration transfer function of the active vibration isolation system; step 2, constructing the parameter optimization problem; step 3, solving the parameter optimization problem under the set frequency range; step 4, inputting the controller parameters and outputting the control effect. DETAILED DESCRIPTION

[0045] Below is the attached figure ( Figure 1 ) and Examples illustrate the present invention.

[0046] Figure 1 This is a flow chart of the design method of the active vibration isolation controller with self-optimization of parameters according to the present invention. Figure 1 As shown in FIG, a method for designing an active vibration isolation controller with self-optimization of parameters includes the following steps: step 1, obtaining the vibration transfer function of the active vibration isolation system; step 2, constructing a controller parameter optimization problem; step 3, solving the controller parameter optimization problem; step 4, bringing the optimized parameters into a multi-order lead-lag compensator.

[0047] The expressions included in step 1 are as follows:

[0048]

[0049] Among them, H passive (s) is the passive vibration isolation transfer function, s is the Laplace variable, H open (s) is the open-loop transfer function of the active vibration isolation.

[0050]

[0051] Where c is the damping coefficient of the passive isolator, k is the stiffness of the passive isolator, and m is the mass of the object being isolated.

[0052] H open (s)=H seis (s)H amp (s)H c (s)H vccs (s)H vc (s)H P (s),

[0053] Among them, H seis (s) is the seismograph transfer function, H amp (s) is the transfer function of the amplifier circuit, H c (s) is the multi-order lead-lag compensator transfer function, H vccs (s) is the voltage-controlled current source transfer function, H vc (s) Transfer function from input current to output force of voice coil motor, H P (s) is the transfer function from the force acting on the isolated object to the motion velocity.

[0054] The expressions included in step 4 are as follows:

[0055]

[0056] H c (s)=G llc,1 (s)·G llc,2 (s)…G llc,κ (s),

[0057] Param=[τ κ z1 p1 … z κ p κ ]∈R 2κ+1 ,

[0058] τ κ =τ1·τ2…τ κ ,

[0059] Among them G llc (s) is the lead-lag compensator, τ is the phase compensator gain, z is the phase compensator zero, p is the phase compensator pole, τ, z and p are G llc (s) Parameters that need to be configured, H c (s) is a κ-order lead-lag compensator, κ is an integer greater than 1, G llc,1 (s) is the first-order lead-lag compensator, G llc,κ (s) is the κth order lead-lag compensator, Param is H c (s) Input parameter, τ κis the intermediate quantity, τ1 is the first phase compensator gain, is the phase compensator gain, τ κ is the κth phase compensator gain, z1 is the first phase compensator zero, z κ is the κth phase compensator zero, p1 is the first phase compensator pole, and p κ is the κth phase compensator pole, R 2κ+1 is a 2κ+1 vector dimension.

[0060] The expressions included in step 2 are as follows:

[0061]

[0062] τ κ =τ1·τ2…τ κ ,

[0063] Cost = w T Tran,

[0064] Tran=[tran(ω1),tran(ω2),…,tran(ω n )] T ∈R n ,

[0065] w T =[w1,w2,…,w n ] T ,

[0066]

[0067] Among them H c (s) is a k-order lead-lag compensator, κ is an integer greater than 1, τ k is the intermediate quantity, τ1 is the first phase compensator gain, is the phase compensator gain, τ k is the kth phase compensator gain, z1 is the first phase compensator zero point, z κ is the κth phase compensator zero, p1 is the first phase compensator pole, and p κ is the κth phase compensator pole, Pa * is the controller parameter optimization problem, is the minimum value operation related to the optimization problem of the controller parameter Pa, Cost is the cost of the optimization problem, st is the constraint condition, pm(ω i ) is the i-th vibration frequency ω to be suppressed i The phase margin, i is the serial number, pm m (ω i ) is the set frequency ω i The minimum phase margin that is satisfied is is the intermediate quantity, w T is the intermediate quantity, Tran is the vibration transmissibility vector, tran(ω1) is the amplitude of the first vibration frequency ω1, tran(ω n ) is the nth vibration frequency ω n The amplitude, n is a positive integer, R n is the n-dimensional vector dimension, w1 is the weight of ω1, w n Yes n The weight of .

[0068] Step 3 includes using particle swarm optimization, genetic algorithm and simulated annealing algorithm to obtain Pa * The solution.

[0069] The expressions included in step 3 are as follows:

[0070]

[0071] where τ κ,* is τ κ The optimal amount of is the optimal amount of z1, is the optimal amount of p1, It is z κ The optimal amount of It is p κ The optimal amount of .

[0072] The expressions included in step 4 are as follows:

[0073]

[0074] in By using Pa * The optimal controller parameters H c (s)Optimal configuration.

[0075] The present invention relates to a method for designing an active vibration isolation controller with self-optimized parameters. The controller parameters are automatically generated by solving an optimization problem, and the frequency band of vibration suppression of the vibration isolator can be set to achieve targeted vibration suppression and ensure the stability of the vibration isolator. The method constructs a parameter optimization problem by setting the vibration transmission rate of the vibration isolation system as a cost and the phase margin not less than a set minimum value as a constraint, and solves the parameters of the multi-order lead-lag compensator inside the controller to achieve a balance between vibration suppression rate and vibration isolator stability. The present invention can solve the problem of long adjustment time caused by manual parameter configuration of the active vibration isolation controller, and provides assistance for the design of active vibration isolation controllers.

[0076] The present invention relates to a method for designing a parameter self-optimizing active vibration isolation controller, comprising the following steps:

[0077] Step (1): Obtain the vibration transfer function of the active vibration isolation system.

[0078] Step (2): Construct the controller parameter optimization problem.

[0079] Step (3): Solve the controller parameter optimization problem.

[0080] Step (4): Substitute the optimized parameters into the multi-order lead-lag compensator.

[0081] The vibration transfer function H in step (1) close (s) is composed of the passive vibration isolation transfer function and the transfer function of the active vibration isolation device, and its expression is as follows:

[0082]

[0083] Among them, H passive (s) is the transfer function of passive vibration isolation, s is the Laplace variable, H open (s) is the transfer function of the active vibration isolation open loop.

[0084] The expression of the passive vibration isolation transfer function is as follows:

[0085]

[0086] Where c is the damping coefficient of the passive isolator, k is the stiffness of the passive isolator, and m is the mass of the object being isolated.

[0087] The expression of the active vibration isolation open-loop transfer function is as follows:

[0088] H open (s)=H seis (s)H amp (s)H c (s)H vccs (s)H vc (s)H P (s) (3)

[0089] Among them, H seis (s) is the transfer function of the seismograph, H amp (s) is the transfer function of the amplifier circuit, H c (s) is the transfer function of the multi-order lead-lag compensator, H vccs (s) is the transfer function of the voltage-controlled current source, H vc (s) Transfer function from input current to output force of voice coil motor and H P (s) is the transfer function from the force acting on the isolated object to the motion velocity.

[0090] The expression of the lead-lag compensator is as follows:

[0091]

[0092] Among them, τ is the gain of the compensator, z is the zero point, and p is the pole, which are the parameters that need to be configured for the compensator.

[0093] For the κ-order lead-lag compensator H c The expression is:

[0094] H c (s)=G llc,1 (s)·G llc,2 (s)…G llc,k (s) (5)

[0095] Among them, G llc,i represents the i-th lead-lag compensator.

[0096] The input parameters Param for defining the κ-order lead-lag compensator are:

[0097] Param=[τ κ z1 p1 … z κ p κ ]∈R 2κ+1 (6)

[0098] Among them, τ κ =τ1·τ2…τ κ , τ i 、z i and p i are the gain, zero, and pole of the i-th phase compensator, respectively.

[0099] The controller parameter optimization problem in step (2) includes three parts: vibration suppression frequency band, optimization problem cost and phase margin constraint. The vibration suppression frequency band Ω is defined as:

[0100] Ω=[ω1,ω2,…,ω n ] T ∈R n (7)

[0101] Among them, ω i is the i-th vibration frequency to be suppressed.

[0102] The cost of the optimization problem is defined as:

[0103] Cost = w T ·Tran (8)

[0104] Among them, Tran=[tran(ω1),tran(ω2),…,tran(ω n )] T ∈Rn is the vibration transmissibility vector, tran(ω i ) represents the formula (1) at frequency ω i The amplitude of the corresponding frequency is the vibration transmissibility. n ] T ,w i is the weight corresponding to the i-th vibration frequency.

[0105] Define the phase margin constraint as:

[0106]

[0107] Among them, pm m (ω i ) indicates setting ω i The minimum phase margin that the frequency must meet, pm(ω i ) represents the formula (1) at frequency ω i The phase margin,

[0108] Combining formulas (5), (6), (7), (8) and (9), the controller parameter optimization problem can be constructed as follows:

[0109]

[0110] in, It is the optimal solution to the optimization problem, that is, it satisfies the minimum cost and phase margin constraints, and is the optimal parameter corresponding to the κ-order phase compensator in formula (5).

[0111] The controller parameter optimization problem in step (3) can be solved by using particle swarm optimization, genetic algorithm and simulated annealing algorithm to obtain the optimal controller parameter Pa in formula (10): * .

[0112] In step (4), the optimized parameters are introduced into the multi-order lead-lag compensator, which is formulated as follows:

[0113]

[0114] in, The κ-order phase compensator in formula (5) is substituted into formula (10) to solve the optimization problem Pa * expression.

[0115] Any content not described in detail in this specification is prior art known to those skilled in the art. It should be noted that the above description is intended to help those skilled in the art understand the present invention, but does not limit the scope of protection of the present invention. Any equivalent substitution, modification, improvement, and / or simplification of the above description that does not depart from the essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A design method for an active vibration isolation controller with self-optimization of parameters, characterized in that: The following steps are involved: Step 1: Obtain the vibration transfer function of the active vibration isolation system; Step 2: Construct the controller parameter optimization problem; Step 3, solving the controller parameter optimization problem; Step 4: Substitute the optimized parameters into the multi-order lead-lag compensator.

2. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 1, characterized in that: The expressions included in step 1 are as follows: Among them, H passive (s) is the passive vibration isolation transfer function, s is the Laplace variable, H open (s) is the open-loop transfer function of the active vibration isolation.

3. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 2, characterized in that: The included expressions are as follows: Where c is the damping coefficient of the passive isolator, k is the stiffness of the passive isolator, and m is the mass of the object being isolated.

4. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 2, characterized in that: The included expressions are as follows: H open (s)=H seis (s)H amp (s)H c (s)H vccs (s)H vc (s)H P (s), Among them, H seis (s) is the seismograph transfer function, H amp (s) is the transfer function of the amplifier circuit, H c (s) is the multi-order lead-lag compensator transfer function, H vccs (s) is the voltage-controlled current source transfer function, H vc (s) Transfer function from input current to output force of voice coil motor, H P (s) is the transfer function from the force acting on the isolated object to the motion velocity.

5. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 1, characterized in that: The expressions included in step 4 are as follows: H c (s)=G llc,1 (s)·G llc,2 (s)…G llc,κ (s), Param=[τ k z1 p1 … z κ p κ ]∈R 2κ+1 , t κ =τ1·τ2…τ κ , Among them G llc (s) is the lead-lag compensator, τ is the phase compensator gain, z is the phase compensator zero, p is the phase compensator pole, τ, z and p are G llc (s) Parameters that need to be configured, H c (s) is a τ-order lead-lag compensator, κ is an integer greater than 1, G llc,1 (s) is the first-order lead-lag compensator, G llc,κ (s) is the κth order lead-lag compensator, Param is H c (s) Input parameter, τ κ is the intermediate quantity, τ1 is the first phase compensator gain, is the phase compensator gain, τ k is the κth phase compensator gain, z1 is the first phase compensator zero, z κ is the κth phase compensator zero, p1 is the first phase compensator pole, and p κ is the κth phase compensator pole, R 2κ+1 is a 2κ+1 vector dimension.

6. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 1, characterized in that: The included expressions are as follows: The included expressions in step 2 are as follows: t κ =τ1·τ2…τ κ , Cost=w T ·Tran, Tran=[tran(ω1),tran(ω2),…,tran(ω n )] T ∈R n , In T =[w1,w2,…,w n ] T , Among them H c (s) is a κ-order lead-lag compensator, κ is an integer greater than 1, τ k is the intermediate quantity, v1 is the first phase compensator gain, is the phase compensator gain, τ k is the κth phase compensator gain, z1 is the first phase compensator zero, z κ is the κth phase compensator zero, p1 is the first phase compensator pole, and p κ is the κth phase compensator pole, Pa * is the controller parameter optimization problem, is the minimum value operation related to the optimization problem of the controller parameter Pa, Cost is the cost of the optimization problem, st is the constraint condition, pm(ω i ) is the i-th vibration frequency ω to be suppressed i The phase margin, i is the serial number, pm m (ω i ) is the set frequency ω i The minimum phase margin that is satisfied is is the intermediate quantity, w T is the intermediate quantity, Tran is the vibration transmissibility vector, tran(ω1) is the amplitude of the first vibration frequency ω1, tran(ω n ) is the nth vibration frequency ω n The amplitude, n is a positive integer, R n is the n-dimensional vector dimension, w1 is the weight of ω1, w n Yes n The weight of .

7. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 6, characterized in that: Step 3 includes using particle swarm optimization, genetic algorithm and simulated annealing algorithm to obtain Pa * The solution.

8. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 6, characterized in that: The expressions included in step 3 are as follows: where τ κ,* is τ κ The optimal amount of is the optimal amount of z1, is the optimal amount of p1, It is z κ The optimal amount of It is p κ The optimal amount of .

9. The method for designing an active vibration isolation controller with self-optimization of parameters according to claim 8, characterized in that: The expressions included in step 4 are as follows: in By using Pa * The optimal controller parameters H c (s)Optimal configuration.

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