A data-driven method for simultaneous estimation of parameters and states of electromechanical systems

Abstract

The present invention discloses a data-driven method for simultaneously estimating parameters and states of an electromechanical system, which belongs to the field of electromechanical system control. First, a control model of an electromechanical servo system is established according to the mechanism and dynamic equations; then, based on the control model, an extended state observer with model parameters is proposed. When the convergence of the extended state observer is guaranteed, the parameter estimation error can be stably estimated from the extended state, and it is used to construct an adaptive parameter estimation law for the electromechanical system. Compared with the traditional method, the present invention does not require additional sensors, and only needs to know the information of the system input and system output to complete the accurate estimation of the system state and system parameters. There is no requirement for the control signal and the controller. The estimated dynamics can quickly converge to their true values, with fast convergence speed and high estimation accuracy.

Description

Technical Field

[0001] The invention belongs to the field of electromechanical system control, and in particular to a data-driven electromechanical system parameter and state simultaneous estimation method. Background Art

[0002] Electromechanical systems are widely used in various industries due to their unique advantages, including aerospace, CNC machine tools, national defense, industrial robots, etc. However, in some electromechanical system control fields, due to the strong nonlinearity of the system and the small number of sensors, the unknown state and dynamic parameters of the system are difficult to obtain directly.

[0003] Many researchers have proposed many methods for the state estimation of electromechanical systems. Some methods use differentiators plus disturbance observers to estimate the unmeasured states and unknown disturbances of electromechanical systems. However, the convergence of the state estimates obtained using these methods is difficult to guarantee under some conditions. The extended state observer (ESO) is a high-gain observer that treats disturbances as extended states. It can estimate unmeasured states and unknown disturbances simultaneously. However, the traditional extended state observer ignores the model parameters of the system, and the state estimation error is large under some conditions.

[0004] For the parameter estimation problem of electromechanical systems, some researchers use methods such as least squares method and sliding mode observer method. However, in some electromechanical systems, only the position information of the system can be measured by sensors, and the error of parameters estimated using traditional methods is large. Other researchers use other methods to accurately estimate the system parameters, but these methods require specially designed controllers and continuous signal excitation conditions to ensure the accuracy of parameter estimation, which cannot be met in many scenarios. Summary of the invention

[0005] The technical problem solved by the present invention is to provide a data-driven method for simultaneously estimating the parameters and states of an electromechanical system. In view of the state estimation problem of the electromechanical system, the present invention proposes an extended state observer that takes into account the model parameters on the basis of the mathematical model of the electromechanical system, and accurately estimates the system parameter error based on the estimation of unmeasured states and unknown disturbances. In view of the parameter estimation problem of the electromechanical system, based on the extended state observer, the present invention proposes a data-driven parameter estimation adaptive law. Compared with traditional methods, the state and parameter estimation method proposed by the present invention has the characteristics of fast convergence speed and small estimation error.

[0006] The technical solution to achieve the purpose of the present invention is:

[0007] A data-driven method for simultaneously estimating parameters and states of an electromechanical system, comprising:

[0008] Step 1: Establish the mathematical model of the electromechanical system, that is, the dynamic equation of the electromechanical system:

[0009]

[0010] in is the location of the electromechanical system, is the speed of the electromechanical system, is the parameter vector The estimated value of , , , ; is the dynamic vector of the electromechanical system, Input current to the motor; is the parameter estimation error; is the equivalent unknown disturbance of the electromechanical system; is the elastic stiffness of the electromechanical system, is the electromechanical system damping, is the friction force of the electromechanical system, is the unknown disturbance force of the electromechanical system, The quality of electromechanical system; for The transpose of for The transpose of

[0011] Step 2: Design an extended state observer that takes system parameters into consideration: Based on the mathematical model of the electromechanical system established in step 1, the unknown disturbance of the system is regarded as an extended system state, and an extended state observer that takes system parameters into consideration is designed to estimate the unknown system dynamics and parameter estimation errors;

[0012]

[0013] It is the status The estimate, is the extended state observer gain, is the extended state observer error, For unknown disturbance The equivalent system state, is a parameter An estimated value of

[0014] Step 3: Design an adaptive parameter estimation law based on the extended state observer: Based on the extended state observer designed in step 2, design an adaptive parameter estimation law to accurately estimate the unknown parameters of the electromechanical system:

[0015]

[0016] is the parameter estimation gain, is the estimated value of the system dynamic vector, yes The second norm of .

[0017] Compared with the prior art, the present invention has the following significant advantages:

[0018] (1) An extended state observer that takes into account model parameters is used to estimate the state and disturbance. The extended state observer has the advantages of small estimation error and fast convergence speed for state estimation.

[0019] (2) An adaptive parameter estimation method is designed based on the extended state observer. This parameter estimation method has no requirements for the selection of the controller and does not require additional sensors. It can accurately estimate the unknown parameters of the system using only the information of the control variable and the system response.

[0020] The method proposed in the present invention has a high convergence speed and high convergence accuracy, and has broad application prospects in the fields of high-precision control, state monitoring, aerospace, etc., and also provides a method for parameter estimation.

[0021] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a block diagram of the data-driven electromechanical system parameter and state simultaneous estimation method of the present invention.

[0023] Figure 2 It is the motion trajectory diagram of the electromechanical system in the simulation.

[0024] Figure 3 It is the speed estimation error diagram of the present invention.

[0025] Figure 4 It is the disturbance estimation error diagram of the present invention.

[0026] Figure 5 is the parameter in the simulation of the present invention Estimation result graph.

[0027] Figure 6 is the parameter in the simulation of the present invention Estimation result graph.

[0028] Figure 7 is the parameter in the simulation of the present invention Estimation result graph.

[0029] Figure 8 is the parameter in the simulation of the present invention Estimation result graph. DETAILED DESCRIPTION

[0030] The present invention provides a data-driven method for simultaneously estimating the parameters and states of an electromechanical system. First, a dynamic model of the electromechanical system is established based on the mechanism. Then, an extended state observer is designed based on the dynamic model to achieve simultaneous and accurate estimation of the system state and disturbance. Then, an adaptive parameter estimation law is designed based on the state and disturbance estimation values ​​obtained above to achieve accurate estimation of the parameters of the electromechanical system. Figure 1 , the implementation process of the present invention is described in detail below, the steps are as follows:

[0031] Step 1: Establish a mathematical model of the electromechanical system: Establish a mathematical model of the electromechanical system based on the dynamics equation of the electromechanical system.

[0032] The electromechanical system is driven by a motor, in which the motor adopts FOC drive mode, so the motor torque equation can be expressed as follows:

[0033] (1)

[0034] in, is the motor torque, is the motor torque constant, Input current to the motor.

[0035] When considering the elastic load, the dynamic equation of the electromechanical system is as follows:

[0036] (2)

[0037] in is the quality of the electromechanical system, is the location of the electromechanical system, is the transmission ratio, is the elastic stiffness of the electromechanical system, is the electromechanical system damping, is the friction force of the electromechanical system, is the unknown disturbance force of the electromechanical system. Therefore, according to the motor torque equation (1) and the dynamic equation (2), the system state is selected as , we can get the state space equation of a certain electromechanical system as follows:

[0038] (3)

[0039] In the formula, is the speed of the electromechanical system; for The differential of for The differential of , , , are different electromechanical system parameters, where , , , ; is the equivalent unknown disturbance of the electromechanical system.

[0040] Step 2: Design an extended state observer that takes into account system parameters: Assume that the unknown disturbance is differentiable and its derivative is bounded, that is, there is a positive constant satisfy Condition. Equivalent unknown disturbance to the unknown electromechanical system Equivalent to system status And its derivative is ,Right now , Therefore, the new system state can be modified to The following nonlinear extended state observer is used to estimate the system state and equivalent disturbance:

[0041] (4)

[0042] Where: Respectively, the status The estimate of They are The estimated value of yes The differential of is the extended state observer error, is a parameter An estimated value of is the gain of the extended state observer. A larger gain can be selected to ensure the convergence of the extended state observer. Since the extended state observer takes the model parameters into account, the estimated values ​​of the state and disturbance of the extended state observer are more accurate under the premise of accurate parameters.

[0043] Note that the system dynamics equation can be rewritten as:

[0044] (5)

[0045] in is the dynamic vector of the electromechanical system, is the parameter estimation error, for The transpose of for Therefore, in the case of the extended state observer estimating the state and disturbance, the following equation holds true

[0046] (6)

[0047] in is the estimated value of the system dynamic vector.

[0048] Step 3: Design an adaptive law for parameter estimation based on an extended state observer: Based on the designed extended state observer taking into account the model parameters, the adaptive parameter estimation rate can be designed as:

[0049] (7)

[0050] in is the parameter estimation gain, which is a positive definite diagonal matrix, where is the parameter estimated gain value; yes The second norm of .

[0051] Applying the extended state observer designed in step 2 and the parameter estimation law designed in step 3 to the electromechanical system, we can get the estimated value of the state and the estimated values ​​of the parameters .

[0052] The parameter estimation method proposed in the present invention only needs to know the system input And the system output No need to add additional sensors to detect unknown conditions and disturbance In addition, this method can estimate the system dynamics. The method is insensitive to continuous excitation conditions and does not require special controller design. It can be applied to any controller such as PID controller, which greatly improves the application scope of parameter estimation methods.

[0053] The effectiveness of the proposed method was verified using the MATLAB simulation tool. According to the above method, a mechatronic system simulation model was built in Simulink and simulated. The simulation results are shown in Figure 2. Figure 2-Figure 8 As shown, the electromechanical system trajectory is Figure 2 As shown in Figure 2, the speed estimation error is Figure 3 As shown, the disturbance estimation error is Figure 4 As shown, the parameters The estimated results are as follows Figure 5 As shown, the parameters The estimated results are as follows Figure 6 As shown, the parameters The estimated results are as follows Figure 7 As shown, the parameters The estimated results are as follows Figure 8 shown.

[0054] It can be seen that in terms of state estimation, compared with the traditional ESO, the parameter estimation results obtained by the extended disturbance observer considering the model parameters proposed in the present invention have a smaller speed error estimate, a very small disturbance error, and an accurate state estimation result with a fast convergence speed. In terms of parameter estimation, compared with the traditional gradient method, the parameter estimation results using the present invention can converge to their true values ​​more quickly, and there is no fluctuation after the estimated parameters converge to their true values. The estimation error of the system parameters is small, which greatly improves the accuracy of parameter estimation.

Claims

1. A data-driven method for simultaneously estimating parameters and states of an electromechanical system, characterized in that: include: Step 1: Establish the mathematical model of the electromechanical system, that is, the dynamic equation of the electromechanical system: Where x1 is the position of the electromechanical system, x2 is the velocity of the electromechanical system, is the parameter vector w = [w1, w2, w3, w4] T The estimated value of w1=ik M / m,w2=k T / m, w3=B / m, w4=F f / m; φ(x,u)=[u,-x1,-x2,-1] is the dynamic vector of the electromechanical system, and u is the motor input current; is the parameter estimation error; d = F d / m is the equivalent unknown disturbance of the electromechanical system; k T is the elastic stiffness of the electromechanical system, B is the damping of the electromechanical system, and F f is the friction force of the electromechanical system, F d is the unknown disturbance force of the electromechanical system, and m is the mass of the electromechanical system; for The transpose of T is the transpose of w; k M is the motor torque constant; i is the transmission ratio; Step 2: Design an extended state observer that takes system parameters into consideration: Based on the mathematical model of the electromechanical system established in step 1, the unknown disturbance of the system is regarded as an extended system state, and an extended state observer that takes system parameters into consideration is designed to estimate the unknown system dynamics and parameter estimation errors; z=[z1,z2,z e ] T is the state x = [x1, x2, x e ] T is the estimate of , η is the extended state observer gain, is the extended state observer error, x e is the system state equivalent to the unknown disturbance d, is the parameter w = [w1, w2, w3, w4] T An estimated value of Step 3: Design an adaptive parameter estimation law based on the extended state observer: Based on the extended state observer designed in step 2, design an adaptive parameter estimation law to accurately estimate the unknown parameters of the electromechanical system: N is the parameter estimation gain, φ(z,u)=[u,-z1,-z2,-1] is the system dynamic vector estimate, and ||φ(z,u)|| is the binary norm of φ(z,u).

2. The data-driven electromechanical system parameter and state simultaneous estimation method according to claim 1, characterized in that: The adaptive parameter estimation rate is specifically: Where n1, n2, n3, n4 are parameter estimation gains, 3. The data-driven electromechanical system parameter and state simultaneous estimation method according to claim 1, characterized in that: Estimated value of the error in the estimation of the electromechanical system parameters: in, is the parameter w = [w1, w2, w3, w4] T is the estimated value of the system dynamic vector; φ(z,u)=[u,-z1,-z2,-1] is the estimated value of the system dynamic vector.

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