Adaptive robust sliding mode compound control method based on nonlinear disturbance observer

Abstract

The invention discloses an adaptive robust sliding mode compound control method based on a non-linear disturbance observer. The method comprises the following steps: step 1, designing the non-linear disturbance observer; and 2, carrying out self-adaptive robust sliding mode compound control. According to the method, an adaptive law is designed based on the action characteristics and numerical boundary of a nonlinear disturbance observer on HPA output voltage disturbance, and controller parameters are dynamically adjusted according to the uncertainty of system parameters and the variation range of external disturbance, so that the stability and robustness of the system are ensured. By estimating uncertain parameters and nonlinear disturbance in the system in real time and dynamically adjusting parameters of the controller, the problem that the THD of the output current of the system is increased due to nonlinear disturbance of the output voltage caused by strong nonlinear characteristic interference of a magnetic element under the resistive and inductive load of the HPA is solved; and the system can still realize high-precision and high-efficiency current output under a complex dynamic condition.

Description

Technical Field

[0001] The present invention belongs to the fields of power supply and motor drive, and relates to a composite current control method for a hybrid power amplifier (HPA), specifically to an adaptive robust sliding mode composite control method based on a nonlinear disturbance observer. Background Art

[0002] The HPA plays a key role in the fields of high-precision power supply and motor drive. It combines the advantages of traditional switched power amplifiers and linear power amplifiers. By reducing the total harmonic distortion (THD) of the output current in the switching link while stabilizing the output voltage of the linear link, the linear link compensates for the output current harmonics of the switching link, achieving high linearity and high-efficiency output of the current. Figure 1 For the HPA circuit topology. However, when the HPA faces a resistive-inductive load, due to the strong nonlinear characteristics of magnetic components, it will cause nonlinear disturbances in the output voltage, thereby increasing the THD of the system output current and affecting the stability and accuracy of the system.

[0003] Although existing research has proposed to control the linear link by minimizing the output current of the linear link, this method does not consider the influence of disturbances on the output current when establishing the system model. In addition, the feedforward control strategy can suppress the influence of voltage disturbances in the HPA, but the transfer function of the feedforward channel in this method is a fixed value and cannot achieve automatic compensation according to the range of disturbance changes, which has certain limitations. Therefore, a control method that can achieve disturbance compensation according to the disturbance range and has strong robustness is needed. Summary of the Invention

[0004] In order to suppress the nonlinear disturbances of the HPA output voltage and thus reduce the THD of the system output current, the present invention provides a composite current control method for a hybrid power amplifier. Based on the action characteristics and numerical boundaries of the nonlinear disturbance observer on the HPA output voltage disturbance, an adaptive law is designed, and the controller parameters are dynamically adjusted according to the uncertainty of system parameters and the change range of external disturbances to ensure the stability and robustness of the system.

[0005] The object of the present invention is achieved by the following technical solutions:

[0006] An adaptive robust sliding mode composite control method based on a nonlinear disturbance observer, comprising the following steps:

[0007] Step 1: Design a nonlinear disturbance observer:

[0008] The nonlinear disturbance observer estimates the unknown disturbance through internal state variables and nonlinear functions, and its expression is as follows:

[0009]

[0010]

[0011] Where z is the internal state of the nonlinear disturbance observer, λ is the gain coefficient, and u o is the control input voltage, L km is the inductance value of the observer, x is the system state variable, and L is the load inductance. represents the estimated value of the disturbance, and L ref is the reference inductance value, L Δ is the inductance fluctuation range, w is the frequency, and t is the time. is the phase;

[0012] Step 2: Adaptive robust sliding mode composite control:

[0013] Step 2-1: Design the sliding mode function:

[0014]

[0015] Where s is the sliding mode function, c is a constant coefficient, e represents the error between the output and the standard value, and x 2 is the system output current, and x d is the integral of the reference input;

[0016] Step 2-2: Design the Lyapunov function:

[0017]

[0018] Where L is the inductance and γ is a constant. is the inductance error;

[0019] Step 2-3: Take as the estimated value of the inductance L, then the inductance error is expressed as Substitute it into the Lyapunov function and take the derivative of it to get:

[0020]

[0021] Where u Δ represents the sum of the disturbances;

[0022] Step 2-4: To ensure the stability of Lyapunov, design the corresponding reaching law:

[0023]

[0024] Where k g is the sliding mode control gain and η is the gain coefficient of the disturbance estimation error;

[0025] Step 25. Design an adaptive law according to the reaching law:

[0026]

[0027] Step 26. Use the mapping adaptive algorithm to perform amplitude limiting correction on the adaptive law. When is too large or too small, the mapping adaptive algorithm adjusts it, and the corrected adaptive law is as follows:

[0028]

[0029]

[0030] In the formula, is a projection operator used to ensure that the inductance value L changes within the physically allowed range. θ is a variable used by the projection operator to determine the direction of inductance change. Specifically: when L ≥ L ref + L Δ and θ > 0, the inductance change rate is 0, that is, the inductance value no longer increases; when L ≤ L ref - L Δ and θ < 0, the inductance change rate is also 0, that is, the inductance value no longer decreases; in other cases, the inductance change rate is determined by θ, indicating that the inductance value will be adjusted according to the value of θ;

[0031] Step 27. The corrected adaptive law is used to dynamically adjust the inductance estimate value Calculate the control input u according to the sliding mode control law 0 Compensate for the disturbance and apply it to the system to achieve precise control of the output current of the HPA.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] 1. By real-time estimating the uncertain parameters and nonlinear disturbances in the system and dynamically adjusting the controller parameters, the present invention solves the problem that the output voltage of the HPA under an inductive load is nonlinearly disturbed due to the strong nonlinear characteristics of magnetic components, increasing the THD of the system output current, and ensures that the system can still achieve high-precision and high-efficiency current output under complex dynamic conditions.

[0034] 2. The control method of the present invention has been verified to be effective through simulation, can significantly reduce the THD of the output current, improve the performance of the HPA, and is applicable to occasions requiring high-precision current control. Description of the Drawings

[0035] Figure 1 is the circuit topology structure of the HPA;

[0036] Figure 2 is the structure of the nonlinear disturbance observer;

[0037] Figure 3 is the structure of the adaptive robust sliding mode controller;

[0038] Figure 4 is the comparison result of the output current error without inductance fluctuation;

[0039] Figure 5 is the comparison result of the output current error when the inductance fluctuates by 2.5%;

[0040] Figure 6 is the comparison result of the output current error when the inductance fluctuates by 5%;

[0041] Figure 7 is the comparison result of the output current error when the inductance fluctuates by 10%;

[0042] Figure 8 is the comparison schematic diagram of the total THD of the output current in two ways. Specific implementation manner

[0043] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0044] The present invention provides an adaptive robust sliding mode composite control method based on a nonlinear disturbance observer. The method adjusts the controller by designing an adaptive law and according to the uncertainty of system parameters and the variation range of external disturbances to ensure the stability and robustness of the system. However, the prerequisite for the method to hold is to ensure that the parameter fluctuations and disturbances are bounded, and it is necessary to establish a relatively accurate evaluation model for the error of the system. For a system where an accurate disturbance model cannot be established or the disturbance numerical boundary and action characteristics are not clear, the system disturbance can be estimated through known quantities by designing a nonlinear disturbance observer. Therefore, the method of the present invention can be divided into two parts: designing a nonlinear disturbance observer and adaptive robust sliding mode composite control.

[0045] (1) Design a nonlinear disturbance observer

[0046] The nonlinear disturbance observer of the present invention estimates unknown disturbances through internal state variables and nonlinear functions. Its design allows the observer to accurately estimate the disturbance boundary of the HPA output voltage even when the system parameters change, enabling the control system to adjust the control strategy accordingly, thereby effectively suppressing the influence of these disturbances on the system performance.

[0047] Figure 2 is the structure of the nonlinear disturbance observer, I out is the output current of the HPA, Ukm is the control input voltage of the observer, L km is the inductance value of the observer, d represents the estimated value of the disturbance, z represents the internal state of the observer, p(x) is a nonlinear function related to the disturbance form, and l(x) is the nonlinear disturbance observer gain.

[0048] Due to the optimization of the inductance value in the observer, the nonlinear disturbance observer can still estimate the disturbance boundary of the HPA output voltage under parameter variations. When the inductance fluctuation range is L Δ the inductance value in the observer is as shown in Equation (1), and the final expression of the nonlinear disturbance observer is as shown in Equation (2).

[0049]

[0050]

[0051] (2) Adaptive robust sliding mode composite control

[0052] The adaptive robust sliding mode composite control method based on the nonlinear disturbance observer establishes a sliding mode function according to the estimated value provided by the nonlinear disturbance observer and the current state of the system, designs an adaptation law, and can dynamically adjust the controller parameters according to the uncertainty of the system parameters and the variation range of external disturbances to adapt to the changes of the system and optimize the control performance. The structure of the adaptive robust sliding mode controller is as Figure 3 shown.

[0053] The present invention designs a sliding mode function as shown in Equation (3) according to the characteristics of the system model, and designs a Lyapunov function as shown in Equation (4):

[0054]

[0055]

[0056] Take as the estimated value of the inductance L, then the inductance error quantity can be expressed as Substitute it into the Lyapunov function and take the derivative of it to obtain Equation (5):

[0057]

[0058] To ensure the stability of Lyapunov, the corresponding reaching law can be designed as follows:

[0059]

[0060] Design an adaptation law according to the reaching law as shown in Equation (7):

[0061]

[0062] Substituting the designed adaptive law into the Lyapunov function, it can be seen that when \(t\) approaches infinity, the sliding mode function \(s\) approaches 0. The mapping adaptive algorithm is used to limit and correct the adaptive law. When it is too large or too small, the mapping adaptive algorithm can adjust it. The finally corrected adaptive law is shown in Equation (8):

[0063]

[0064] The corrected adaptive law is used to dynamically adjust the inductor estimation value Calculate the control input \(u\) according to the sliding mode control law 0 Compensate for the disturbance and apply it to the system to achieve precise control of the output current of the HPA.

[0065] Figure 4 The comparison results of the output current error without inductor fluctuation are shown. It can be seen that there is an inherent current error in the system without fluctuation, and the voltage errors of the standard voltage feeding linear link and the proposed control method are similar. Figures 5 - 7 The comparison results of the output current error with inductor fluctuations of 2.5%, 5%, and 10% are shown. It can be seen that as the inductor fluctuation range increases, the output current error of the control group using the standard voltage feeding method continuously increases, while the output current error of the system using the control method proposed in the present invention is less than that of the control group using the standard voltage feeding method. Figure 8 The comparison diagram of the total THD of the output current of the two methods is shown. The THD of the output current obtained by using the control method proposed in the present invention is less than that of the standard voltage direct feeding method, further verifying the effectiveness of the control method proposed in the present invention.

[0066] It can be seen from the simulation results that the method proposed in the present invention has a significant effect on reducing the THD of the output current of the HPA. This method can effectively compensate the output current harmonics of the switching link, improve the linearity and purity of the output current, and can maintain high-precision and high-efficiency current output even under complex working conditions such as inductor fluctuations. This verifies the effectiveness and feasibility of the method proposed in the present invention.

Claims

1. An adaptive robust sliding mode composite control method based on nonlinear disturbance observer, characterized in that The method comprises the following steps: Step 1: Design a nonlinear disturbance observer: The nonlinear disturbance observer estimates the unknown disturbance through internal state variables and nonlinear functions, and its expression is as follows: Where z is the internal state of the nonlinear disturbance observer, λ is the gain coefficient, and u o is the control input voltage, L km is the inductance of the observer, x is the system state variable, L is the load inductance, represents the estimated value of the disturbance; Step 2: Adaptive robust sliding mode composite control: Step 21: Design sliding mode function: Where s is the sliding film function, c is the constant coefficient, e is the error between the output and the standard value, x2 is the system output current, and x d is the integral of the reference input; Step 22: Design the Lyapunov function: Where L is the inductance, γ is a constant, is the inductance error; Step 23: Take is the estimated value of inductance L, then the inductance error is expressed as Substitute it into the Lyapunov function and take its derivative, and we get: In the formula, u Δ represents the sum of interferences; Step 24: To ensure the stability of Lyapunov, design the corresponding reaching law: In the formula, k g is the sliding mode control gain, η is the gain coefficient of the disturbance estimation error; Step 25: Design an adaptive law based on the convergence law: Step 26: Use the mapping adaptive algorithm to correct the limit of the adaptive law. If it is too large or too small, the mapping adaptive algorithm adjusts it. The modified adaptive law is as follows: In the formula, is a projection operator used to ensure that the inductance value L changes within the physically allowed range, and θ is a variable used by the projection operator to determine the direction of inductance change; Step 27: The modified adaptive law is used to dynamically adjust the estimated inductance value The control input u0 compensation disturbance is calculated according to the sliding mode control law and applied to the system to achieve precise control of the HPA output current.

2. The adaptive robust sliding mode composite control method based on nonlinear disturbance observer according to claim 1 is characterized in that In the step 1, L ref is the reference inductance value, L Δ is the range of inductance fluctuation, w is the frequency, t is the time, It's the phase.

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