A control strategy consisting of an extended dual-state observer and a corresponding controller

Abstract

This invention discloses a control strategy comprised of an extended dual-state observer and a corresponding controller. The extended dual-state observer treats the total disturbance (load torque and internal disturbance of the permanent magnet synchronous motor speed model) and the control input gain (consisting of the pole pair number, permanent magnet flux linkage, and rotor and load rotational inertia of the permanent magnet synchronous motor speed model) as two extended states. The observer estimates the speed based on readily available controller output signals and the permanent magnet synchronous motor speed signal. The speed control scheme based on this observer does not require prior knowledge of the speed model parameters and permanent magnet flux linkage, and can identify time-varying control input gain even when disturbances exist in the speed model, improving the adaptability of the permanent magnet synchronous motor control system under complex operating conditions. Furthermore, a speed control scheme adaptable to time-varying rotational inertia, permanent magnet flux linkage, and disturbance torque is designed based on the extended dual-state observer.

Description

Technical Field

[0001] This invention belongs to the field of motor control, specifically relating to a control strategy consisting of an extended dual-state observer and a corresponding controller. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in various fields, such as industrial robotic arms, electric vehicles, CNC machine tools, and robots, due to their simple structure, high efficiency, high power density, high torque-to-inertia ratio, low noise, and maintenance-free operation. However, in some applications, the load's moment of inertia is difficult to measure or exhibits time-varying behavior (e.g., winding machines, robotic arms with two or more degrees of freedom). Simultaneously, the permanent magnet flux linkage changes with temperature. This mismatch between the actual system parameters and the system parameters in the controller design leads to a reduction in the control performance of the PMSM. Unknown load torque exists in PMSM control systems in industrial settings. Therefore, identifying the control input gain of the PMSM speed model under unknown load torque conditions is of great significance.

[0003] This invention proposes a control strategy consisting of an extended two-state observer (ETSO) and a corresponding controller. Compared with existing extended state observers, this observer can estimate not only the total disturbance (load torque and internal disturbance) of the permanent magnet synchronous motor speed model, but also the control input gain (composed of rotor and load rotational inertia, pole pair number, and permanent magnet flux linkage). Compared with methods that use multiple extended state observers or multiple sliding mode observers to estimate load torque and rotational inertia, this invention uses only one observer and can estimate the control input gain under time-varying load torque conditions, thus improving the adaptability of the permanent magnet synchronous motor control system under complex operating conditions. Summary of the Invention

[0004] The purpose of this invention is to promote the development of the relevant technical field, and to propose a control strategy consisting of an extended dual-state observer and a corresponding controller, as well as a permanent magnet synchronous motor equipped with the algorithm.

[0005] In this statement The time derivative dx(t) / dt of x(t) can be expressed as follows based on the dq coordinate system of the permanent magnet synchronous motor model:

[0006]

[0007]

[0008]

[0009]

[0010] Where i d (t), i q (t), ω(t), L d L q R s ψ f J(t), n p T e (t), d(t), u d (t), u q d(t) represents the d-axis current, q-axis current, rotor speed, d-axis inductance, q-axis inductance, stator resistance, stator flux linkage, moment of inertia, number of pole pairs, electromagnetic torque, disturbance torque, d-axis voltage, and q-axis voltage, respectively. The disturbance torque d(t) includes various torques that affect the motor speed other than electromagnetic torque, such as load torque, frictional torque, cogging effect, and unmodeled motor dynamics.

[0011] The focus of this invention is the identification of the input gain of the speed model control for a permanent magnet synchronous motor under unknown disturbance conditions. Therefore, the dq-axis current controller will employ a PI current controller based on feedback decoupling, and the overall control framework will adopt field-oriented control (FOC), such as... Figure 1 As shown. Let the reference value for the motor speed be ω. * (t). Let the d-axis current tracking error be... q-axis current tracking error in This is the reference value for the d-axis current. This is the q-axis current reference value. Under the action of the current controller, e... d (t) and e q (t) is a smaller value. Let the q-axis current reference value be... For u(t), equation (4) can be rewritten as

[0012]

[0013] Let the speed model control input gain of the permanent magnet synchronous motor be a(t): = 3n p ψ f / 2J(t), total disturbance Then equation (3) can be rewritten as

[0014]

[0015] Considering the characteristics of the actual control system, assume that there exist positive constants D1, D2, D3, D4, and D5 such that |f(t)| ≤ D1, D2 ≤ a(t) ≤ D3. This assumption allows for time-varying control input gain a(t) and total disturbance f(t).

[0016] For ease of design, the rotational speed model (6) is rewritten as follows:

[0017]

[0018]

[0019]

[0020] Where x1(t):=ω(t), Additionally, a0∈[D2, D3] is the estimated value of a(t0). To estimate the error, t0 represents the initial time.

[0021] Due to physical limitations in the current controller output of actual control systems, the dq-axis current can only fall within a finite range. This is because the q-axis current loop reference value... Therefore, in the design of the speed controller, u(t) is designed to be a bounded value, that is, there exists a positive constant k1 such that for any t≥t0, |u(t)|≤k1. Thus, we can obtain |h1(t)|≤D4+k1D5, |h2(t)|≤D5.

[0022] For the rotational speed models (7)-(9), the extended dual-state observer is designed as follows:

[0023]

[0024]

[0025]

[0026] in and Let x1(t), x2(t), and x3(t) be the estimates, respectively, where α1, α2, α3, β1, β2, and ε are positive constants, and α1α2 > α3, β1 > β2. The nonlinear functions Γ1(α1, β1), Γ2(α2, β2), and ε are also given. Defined respectively

[0027]

[0028]

[0029]

[0030] There are four excitation conditions mentioned above, referred to as excitation A, excitation B, excitation C, and excitation D. If all excitation conditions are met, the observer error model can be obtained based on the rotational speed model (7)-(9) and the extended two-state observer (10)-(12).

[0031]

[0032]

[0033]

[0034] in This represents the state estimation error.

[0035] If not all excitation conditions are met, the observer error model can be obtained based on the rotational speed model (7)-(9) and the extended dual-state observer (10)-(12).

[0036]

[0037]

[0038] in

[0039] Based on the parameter definitions and state estimation error definitions in the speed model (7)-(9), we can obtain

[0040] a(t): = x3(t) + a0 (18)

[0041] f(t):=x2(t)-x3(t)u(t) (19)

[0042] make For the estimate of a(t), For the estimate of f(t), we can obtain

[0043]

[0044]

[0045] in Estimate the error for a(t). The error is estimated for f(t).

[0046] make and When all the incentive conditions are met, equations (13)-(15) can be rewritten as follows:

[0047]

[0048] Where η(t):=[η1(t) η2(t) η3(t)] T A1(t) and B1(t) are defined as follows:

[0049]

[0050] If A1(t) is a Hurwib matrix, then there exists a symmetric positive definite matrix P1(t) such that the Lyapunov equation A1 T (t)P1(t)+P1(t)A1(t)+I=0 holds true, where

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Let the incentive A be |u * (t)|<k1, the incentive B is Where u * Let B(t) be an intermediate variable of the controller, and σ1 and σ2 be positive adjustable coefficients, where σ1 ≤ σ2. According to the definitions of B1(t) and P1(t), if the excitation B satisfies the condition, then there exists a positive constant D6 such that...

[0058] ||B1 T (t)P1(t)||≤D6 (23)

[0059] If the excitation B satisfies the condition, then A1(t) is a Hurwib matrix, and consequently P1(t) is a symmetric positive definite matrix. Let and Let Λ be the maximum and minimum eigenvalues ​​of P1(t) under the condition that excitation B is satisfied. max For λ max1 The maximum value of (t), Λ min For λ min1 The minimum value of (t).

[0060] P1(t) is differentiable when stimuli A and B are valid. We take the time derivative of P1(t) when stimuli A and B are valid.

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] If incentives A and B are true, let incentive C be... Where σ3 is a positive adjustable coefficient. Let Where σ∈(0,1). Since r(t) is a symmetric matrix, if all the principal minors of r(t) are greater than zero, that is...

[0068] σ-εn1(t)>0 (25)

[0069]

[0070]

[0071] Then r(t) is a positive definite matrix. According to equations (25)-(27) and According to the definition, if the stimuli A, B and C satisfy the condition, then r(t) can be made a symmetric positive definite matrix by reducing σ3.

[0072] Since a(t) ∈ [D2, D3] in equation (6), the estimated value of a(t) is... It should belong to the interval [D2, D3] in all cases. Let the excitation D satisfy one of the following three conditions: 1) 2) and 3) and According to equation (12), if the excitation D satisfies, then

[0073] Based on the above explanation, when all excitation conditions are satisfied, A1(t) is a Hurwitz matrix and the modulus of B1(t) is bounded, the stability of equation (22) can be proved by the Lyapunov method.

[0074] make When not all incentive conditions are met, equations (16)-(17) can be rewritten as follows:

[0075]

[0076] in A2 and B2 are defined as follows:

[0077]

[0078] According to (12), when not all incentive conditions are met... Right now It remains unchanged. Because when all the incentive conditions are met... If it is bounded, then It is bounded for any t ≥ t0. Also, since the control input gain a(t) is bounded, the control input gain estimation error... Bounded. In speed controller design It is a bounded value, meaning there exists a positive constant D7 such that because Therefore, h3(t) is bounded when not all the excitation conditions are met, that is, there exists a positive constant D8 such that |h3(t)|≤D8.

[0079] Based on the above explanation, if the excitation conditions are not all satisfied, A2(t) is a Hurwitz matrix and h1(t) and h3(t) are bounded, then the stability of equation (28) can be proved by the Lyapunov method.

[0080] To satisfy the convergence condition of the extended two-state observer, the speed controller output u(t) should be bounded and its time derivative should be bounded. First, the speed controller is designed as follows:

[0081]

[0082] Where k1 and k2 are positive constants, and e(t) = x r (t)-x1(t) is the speed tracking error, x r (t):=ω * (t) is the reference velocity, and the function...

[0083]

[0084] According to (29), we can obtain |u * (t)|≤k1. Since the controller output u(t) should be bounded and the time derivative is bounded, the following first-order low-pass filter is designed to process (29).

[0085]

[0086] k3 and k4 are positive constants.

[0087] Based on the characteristics of a first-order low-pass filter, Because of |u * Since |u(t)|≤k1, then |u(t)|≤k1.

[0088] Beneficial effects of this invention:

[0089] (1) The extended dual-state observer provided by the present invention has a small computational load and can be operated on a small digital processor or microcontroller.

[0090] (2) The extended dual-state observer provided by the present invention does not require injecting high-frequency signals or inputting specific reference signals into the permanent magnet synchronous motor. It can estimate the control input gain and total disturbance of the speed model online when the permanent magnet synchronous motor is running normally.

[0091] (3) The extended dual-state observer provided by the present invention can estimate the time-varying control input gain when the load torque exists and the load torque is time-varying, thereby improving the control performance of permanent magnet synchronous motor under complex working conditions. Attached Figure Description

[0092] Figure 1 Control block diagram of an embodiment of the present invention

[0093] Figure 2 Motor speed waveform

[0094] Figure 3 Speed ​​tracking error waveform

[0095] Figure 4 Control input gain estimation waveform

[0096] Figure 5 Waveform of total disturbance estimate Detailed Implementation

[0097] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0098] To provide a clearer understanding of the technical features, objectives, and effects of this invention, specific embodiments are described in detail with reference to the accompanying drawings. This invention relates to a speed control scheme for a permanent magnet synchronous motor based on field-oriented control. Therefore, this embodiment assumes that the coordinate transformation program, phase current sampling, speed calculation algorithm based on encoder data, and current PI controller in the field-oriented control have been completed and are functioning correctly in a microcontroller or digital signal processor.

[0099] Example 1: This invention relates to... Figure 1 The design steps for the control strategy consisting of the extended dual-state observer and the corresponding speed controller, as shown in the dashed box section, are as follows:

[0100] Step 1: Design the parameters σ1 and σ2 in excitation B. Parameters σ1 and σ2 should satisfy 0 < σ1 ≤ σ2.

[0101] Step 2: Design the parameter σ3 in excitation C. The parameter σ3 should be chosen to be a small value so that r(t) is a symmetric positive definite matrix. After excitations A and B are satisfied, determine whether excitation C is satisfied.

[0102] Step 3: Design parameter a0 in excitation D. a0 is a preset value for a(t0). a0 only needs to satisfy a0∈(D2, D3), not a0=a(t0). In actual operating conditions, the load's rotational inertia and permanent magnet flux linkage are within a certain range; therefore, the speed model control input gain is bounded. When designing D2 and D3, ensure that the control input gain a(t) of the permanent magnet synchronous motor speed model belongs to (D2, D3). After excitations A, B, and C are satisfied, determine whether excitation D is satisfied.

[0103] Step 4: Design the extended two-state observer parameters α1, α2, α3, β1, β2, and ε, where α1 and α2 > α3, and β1 > β2. ε should be selected according to the actual controlled object. A smaller ε can improve the observer's response speed, but too small an ε will cause system oscillation.

[0104] Step 5: The microcontroller or digital signal processor performs extended two-state observer calculations based on the controller output u(t) and the speed signal ω(t) obtained through the encoder, and obtains... and

[0105] Step 6: Design the speed controller parameters k1, k2, k3, and k4. Due to the q-axis current reference value... The parameter k1 will be determined based on the controller output u(t), therefore, the parameter k1 should be determined according to the physical constraints i q The design is based on the range of (t). Parameter k2 is related to the controller response speed; increasing k2 can improve the response speed. Parameter k3 is used to limit... The range of k4. A smaller k4 makes the controller output u(t) smoother.

[0106] Step 7: The microcontroller or digital signal processor calculates the rotational speed reference signal ω. * (t), the rotational speed signal ω(t) obtained through the encoder, and the signal obtained through the extended two-state observer. and Perform controller operations and obtain the result u(t).

[0107] Step 8: The microcontroller or digital signal processor calculates the q-axis current reference value based on the controller output u(t).

[0108] Step 9: The microcontroller or digital signal processor... and Perform current controller calculations.

[0109] Extended two-state observer updates control input gain estimate The condition is that incentives A, B, C, and D are all true. If none of the four incentive conditions are true, then... No update. Excitations B and C are related to the first and second time derivatives of the controller output u(t), i.e. and ü(t). The excitation D is used to... Restricted to (D2, D3).

[0110] To further illustrate the working principle of the proposed control strategy, simulation tests were conducted in Matlab / Simulink. First, the parameters of the permanent magnet synchronous motor system are: n p =5, L d =0.00295H, L q =0.00295H, R s =0.59Ω, ψ f =0.09145Wb、J(t)={0.02Kg·m 2 , t < 50; 0.03 kg·m 2 The parameters of the speed controller are: k1 = 30, k2 = 1, k3 = 30, k4 = 200. The parameters of the extended dual-state observer are: α1 = 3, α2 = 3, α3 = 1, β1 = 2, β2 = 1, ε = 0.08. The initial state of the extended dual-state observer is... and All parameters are set to zero. The excitation parameters are: σ1 = 1, σ2 = 30, σ3 = 0.3. The upper and lower bounds of the control input gain are: D2 = 1, D3 = 100. The initial value of the control input gain estimate is set to: a0 = 100. To test the tracking performance of the proposed control strategy under unknown disturbances and unknown control input gain, the rotational speed reference signal is set to: ω * (t)=15sin(2t)+20. Figures 2 to 5 This is the result of the simulation test.

[0111] At t=0, the actual control input gain a(0) = 3n p ψ f / 2J(0)=34.29375, while the estimated value of the control input gain is... This mismatch in control input gain leads to poor speed tracking performance, such as... Figure 2 and Figure 3 As shown. In practical applications, the total moment of inertia J(t) is often impossible to measure, leading to a mismatch in control input gain and consequently poor speed tracking performance. For example... Figure 4 As shown, due to the effect of the extended dual-state observer, the estimated control input gain gradually approaches the actual control input gain. Simultaneously, the speed tracking performance is improved, as... Figure 2 and Figure 3 As shown. At t=50, the control input gain undergoes a sudden change. At this time, the actual control input gain a(50)=3n p ψ f / 2J(50)=22.8625. Due to the effect of the extended dual-state observer, the estimated control input gain gradually approaches the actual control input gain again, such as Figure 4 As shown. This proves that the extended two-state observer can function normally when both the disturbance torque d(t) and the control input gain a(t) are time-varying. At t = 80, the disturbance torque d(t) increases by 2 Nm. At this time, the extended two-state observer can quickly estimate the total disturbance, as shown. Figure 5 As shown, the speed tracking error can also quickly converge to near zero, as... Figure 3 As shown. During the time intervals t∈[0, 20] and t∈[50, 60], a large internal disturbance occurs due to the control input gain mismatch. This disturbance caused by the control input gain mismatch is part of the total disturbance and can therefore be estimated by the extended two-state observer, as shown. Figure 5 As shown.

[0112] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0113] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0114] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A permanent magnet synchronous motor control method based on an extended dual-state observer, characterized in that, Includes the following steps: Step 1: Expand the dual-state observer based on the output of the speed controller. The system checks whether the excitation conditions are met in accordance with the preset control parameters. Step 2, if all excitation conditions are met, then the extended two-state observer is: in , and They are respectively , and The estimated value, , , and It is a positive number, and State variables , , ,in This refers to the motor speed. For the total disturbance, To account for the estimation error; in addition for The estimated value, Indicates the initial time; If not all excitation conditions are met, the extended two-state observer is: in and It is a positive number, and ; Step 3, because To control the input gain The estimated value, for The estimated value; Based on the extended two-state observer and and controller output Calculate and ; Step 4, based on the speed reference signal, speed signal, and Calculate controller output ; Controller output Obtain it according to the following formula; in , , and For positive integers, For speed tracking error, For reference speed, the function Step 5, output from the controller Based on this, calculate q Shaft current reference value And let d Shaft current reference value ; Step 6, d shaft and q The shaft current controller controls based on reference values. d shaft and q Axis current.

2. The permanent magnet synchronous motor control method based on an extended dual-state observer according to claim 1, characterized in that, The control input gain estimate of the permanent magnet synchronous motor speed model is obtained by extending the two-state observer. Total disturbance estimate .

3. The permanent magnet synchronous motor control method based on an extended dual-state observer according to claim 1, characterized in that, The extended two-state observer is set up by determining whether all excitation conditions are met.

4. The permanent magnet synchronous motor control method based on an extended dual-state observer according to claim 1, characterized in that, The extended two-state observer allows for total disturbance Exists, and allows total perturbation. and control input gain The time derivative varies within a certain range.

5. The permanent magnet synchronous motor control method based on an extended dual-state observer according to claim 1, characterized in that, A speed controller based on an extended two-state observer and The controller output is obtained from the speed reference signal and the speed signal. .

6. The permanent magnet synchronous motor control method based on an extended dual-state observer according to claim 1, characterized in that, To satisfy the convergence condition of the extended two-state observer, a saturation function is used. The low-pass filter causes the speed controller output to... It is a bounded value and its time derivative is bounded.

7. A permanent magnet synchronous motor, characterized in that, The method for controlling a permanent magnet synchronous motor based on an extended dual-state observer, as described in any one of claims 1-6, controls the operation of the permanent magnet synchronous motor, can estimate the control input gain in real time, compensate for the influence of total disturbance, and improve the dynamic characteristics and control accuracy of speed control.

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