An adaptive robust sliding mode compound control method based on nonlinear disturbance observer

Abstract

The application discloses a kind of adaptive robust sliding mode compound control methods based on nonlinear disturbance observer, the method includes the following steps: step one, design nonlinear disturbance observer;Step two, adaptive robust sliding mode compound control.This method is based on the action characteristics and numerical boundary of nonlinear disturbance observer to HPA output voltage disturbance, design adaptive law, and according to the uncertainty of system parameters and the variation range of external disturbance, dynamically adjust the controller parameters, to ensure the stability and robustness of system.The application estimates the uncertain parameters and nonlinear disturbance in the system in real time, dynamically adjusts the controller parameters, solves the problem that the output voltage of HPA under resistive-inductive load is disturbed due to the strong nonlinear characteristics of magnetic element, increases the THD of system output current, ensures that the system can still achieve high-precision, high-efficiency current output under complex dynamic conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of power supply and motor drive, and relates to a hybrid power amplifier (HPA) composite current control method, in particular to an adaptive robust sliding mode composite control method based on a nonlinear disturbance observer. BACKGROUND

[0002] The HPA plays a key role in the field of high-precision power supply and motor drive, and combines the advantages of traditional switching power amplifiers and linear power amplifiers, so that the linear part compensates for the output current harmonics of the switching part by stabilizing the output voltage of the linear part while reducing the total harmonic distortion (THD) of the output current of the switching part, realizing high linearity and high efficiency of the output current, Figure 1 The HPA circuit topology is shown in the figure. However, when the HPA faces a resistive-inductive load, due to the strong nonlinear characteristics of the magnetic element, nonlinear disturbance of the output voltage is caused, which in turn increases the THD of the output current of the system and affects the stability and precision of the system.

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

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

[0005] The purpose of the application 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 one, design a nonlinear disturbance observer:

[0008] The nonlinear disturbance observer estimates 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, u o is the control input voltage, L km is the inductance value of the observer, x is the system state variable, L is the load inductance, represents the estimated value of the disturbance, L ref is the reference inductance value, L Δ is the inductance fluctuation range, w is the frequency, t is the time, is the phase;

[0012] Step two, adaptive robust sliding mode composite control:

[0013] Step two one, design the sliding mode function:

[0014]

[0015] where s is the sliding mode function, c is the constant coefficient, e represents the error between the output and the standard value, x2 is the system output current, x d is the integral of the reference input;

[0016] Step two two, design the Lyapunov function:

[0017]

[0018] where L is the inductance, γ is a constant, is the inductance error;

[0019] Step two three, take as the estimated value of the inductance L, then the inductance error is represented as Bring it into the Lyapunov function and take its derivative, we get:

[0020]

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

[0022] Step two four, to ensure the stability of Lyapunov, design the corresponding reaching law:

[0023]

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

[0025] Step two five, according to the reaching law, design the adaptive law:

[0026]

[0027] Step two six, the adaptive law is corrected by using a mapping adaptive algorithm, when The mapping adaptive algorithm adjusts it when it is too large or too small, and the corrected adaptive law is as follows:

[0028]

[0029]

[0030] In the formula, It is a projection operator, which is used to ensure that the inductance value L changes within the physically allowed range, and theta is a variable used to determine the direction of inductance change by the projection operator, specifically: when L >= L ref +L Δ And theta>0, the inductance change rate is 0, that is, the inductance value no longer increases; when L <= L ref -L Δ And theta<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 theta, indicating that the inductance value will be adjusted according to the value of theta;

[0031] Step two seven, the corrected adaptive law is used to dynamically adjust the inductance estimated value According to the sliding mode control law, the control input u0 compensates for the disturbance and is applied to the system to realize accurate control of the HPA output current.

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

[0033] 1. The present application solves the problem of non-linear disturbance of output voltage caused by the strong non-linear characteristics of magnetic elements under inductive load, which increases the THD of system output current, by real-time estimation of uncertain parameters and non-linear disturbances in the system, dynamic adjustment of controller parameters, 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 application has been verified by simulation to be effective, which can significantly reduce the THD of output current and improve the performance of HPA, and is suitable for occasions requiring high-precision current control. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The HPA circuit topology is shown in Figure 1;

[0036] Figure 2 The nonlinear disturbance observer structure is shown in Figure 2;

[0037] Figure 3For adaptive robust sliding mode controller structure;

[0038] Figure 4 For the comparative results of output current error under inductance fluctuation 2.5%;

[0039] Figure 5 For the comparative results of output current error under inductance fluctuation 5%;

[0040] Figure 6 For the comparative results of output current error under inductance fluctuation 10%;

[0041] Figure 7 For the comparative results of output current error under inductance fluctuation 10%;

[0042] Figure 8 For the comparative results of output current error under inductance fluctuation 10%; DETAILED DESCRIPTION

[0043] The technical solutions of the present application are further described below in conjunction with the drawings, but are not limited thereto, and any modification or equivalent replacement of the technical solutions of the present application without departing from the spirit and scope of the technical solutions of the present application shall be covered in the protection scope of the present application.

[0044] The present application provides an adaptive robust sliding mode composite control method based on a nonlinear disturbance observer, which adjusts the controller according to the system parameter uncertainty and the variation range of external disturbance to ensure the stability and robustness of the system by designing an adaptive law, but the precondition for the method to be established is to ensure that the parameter fluctuation and the disturbance are bounded, which requires a relatively accurate evaluation model to be established for the error of the system. For systems that cannot establish an accurate disturbance model or the disturbance numerical boundary and action characteristics are not clear, a nonlinear disturbance observer can be designed to estimate the system disturbance by known quantities. Therefore, the method of the present application can be divided into two parts: designing a nonlinear disturbance observer and an adaptive robust sliding mode composite control.

[0045] (1) Designing a nonlinear disturbance observer

[0046] The nonlinear disturbance observer of the present application estimates unknown disturbance through internal state variables and nonlinear functions, and its design allows the observer to accurately estimate the disturbance boundary of the HPA output voltage even if the system parameters vary, so that the control system can adjust the control strategy accordingly, thereby effectively suppressing the influence of these disturbances on the system performance.

[0047] Figure 2 The nonlinear disturbance observer structure is I out is the output current of the HPA, U km is the control input voltage of the observer, L kmis 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 form of the disturbance, and l(x) is a 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 variation. When the inductance fluctuation value range is L Δ , the inductance value in the observer is shown as formula (1), and the final expression of the nonlinear disturbance observer is shown as formula (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 film function according to the estimated value provided by the nonlinear disturbance observer and the current state of the system, designs an adaptive law, and can dynamically adjust the controller parameters according to the uncertainty of the system parameters and the change range of the external disturbance, so as to adapt to the changes of the system and optimize the control performance. The structure of the adaptive robust sliding mode controller is shown as formula (3). Figure 3

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

[0054]

[0055]

[0056] Taking the estimated value of the inductance L, the inductance error can be represented as Taking it into the Lyapunov function and taking its derivative, formula (5) is obtained:

[0057]

[0058] In order to ensure the stability of the Lyapunov function, the corresponding approaching law can be designed as follows:

[0059]

[0060] According to the approaching law, the adaptive law is designed as shown in formula (7):

[0061]

[0062] ​The designed adaptive law is brought into the Lyapunov function, and it can be seen that the sliding mode function s tends to 0 when t tends to infinity. The adaptive law is corrected by using the mapping adaptive algorithm, and when When the adaptive law 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 inductance estimation value According to the sliding mode control rate, the control input u0 compensating for the disturbance is calculated and applied to the system, so as to realize accurate control of the output current of the HPA.

[0065] Figure 4 The comparative results of the output current error under the condition of no inductance fluctuation are shown. It can be seen that the system itself has current error under the condition of no fluctuation, and the voltage error of the system using the standard voltage feed-in linear link and the proposed control method is similar. Figures 5-7 The comparative results of the output current error under the conditions of inductance fluctuation of 2.5%, 5% and 10% are shown. It can be seen that as the inductance fluctuation range increases, the output current error of the control group using the standard voltage feed-in method increases continuously, while the output current error of the system using the proposed control method is less than that of the control group using the standard voltage feed-in method. Figure 8 The comparative 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 proposed control method is less than that of the standard voltage direct feed method, which further verifies the effectiveness of the proposed control method.

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

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, is the internal state of the nonlinear disturbance observer, is the gain coefficient, is the control input voltage, is the inductance of the observer, is the system state variable, is the load inductance, represents the estimated value of the disturbance; Step 2: Adaptive robust sliding mode composite control: Step 2.1: Design the 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, is the load inductance, is a constant, is the inductance error; Step 2 and 3: Take is the estimated value of inductance L, then the inductance error is expressed as , bring it into the Lyapunov function and take its derivative, we get: Where, represents the sum of the interferences; Step 24: To ensure the stability of Lyapunov, design the corresponding reaching law: Where, is the sliding mode control gain, 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 perform limit correction on the adaptive law. If it is too large or too small, the mapping adaptive algorithm adjusts it. The modified adaptive law is as follows: Where, It is a projection operator used to ensure that the inductance value L varies within the physically allowed range. is a variable used in the projection operator to determine the direction of inductance change. is the reference inductance value, is the inductance fluctuation range; Step 27: The modified adaptive law is used to dynamically adjust the inductance estimate , according to the sliding mode control law The control input voltage u0 is calculated to compensate for the disturbance 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, , is the reference inductance value, is the inductance fluctuation range, is the frequency, t is the time, It's the phase.

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