Double-layer nested adaptive sliding mode control method for single-phase inverter

Abstract

Double-layer nested adaptive sliding mode control method for single-phase inverter, however, these parameter information is often not easy to obtain. And parameter mismatch during system operation will deteriorate the control performance of the system and increase the risk of system instability. To solve this problem, this patent discloses a double-layer nested adaptive sliding mode control algorithm for single-phase inverter. The algorithm does not need to use the information of filter inductance and filter capacitance, which reduces the sensitivity of the controller to parameter changes. In addition, the present invention uses a double-layer nested adaptive structure to ensure that the designed sliding mode controller gain will change with the change of disturbance, thereby improving the anti-interference ability of the system. Compared with the existing sliding mode controller, the lower sliding mode controller gain of the present invention reduces the jitter phenomenon caused by high gain, while ensuring the strong robustness of the controller, optimizing the performance of the system.

Description

Technical Field

[0001] The invention belongs to the field of single-phase inverter control, in particular to a double-layer nested adaptive sliding mode control method for a single-phase inverter. Background Art

[0002] Single-phase inverters are widely used in distributed power generation, energy storage systems, and uninterruptible power supplies. For power electronic systems including single-phase inverters, it is necessary to ensure that the output voltage can effectively track the given reference when there are uncertainties in the load and system parameters, which requires the designed controller to have strong robustness.

[0003] Sliding mode control can effectively reduce the system's sensitivity to parameter mismatch and disturbances through its high gain characteristics. However, since the upper bound of the system disturbance is often unknown, a larger controller gain is required to ensure the stability of the system. This will cause obvious jittering in the system and reduce the control performance of the system. In addition, when the disturbance of the system changes, the gain of the traditional sliding mode controller cannot adapt to its changes, but always remains a constant value. This will cause the controller gain to be either designed too large, resulting in redundant system performance; or designed too small, resulting in system instability. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a double-layer nested adaptive sliding mode control method for a single-phase inverter. It does not need to use the information of the filter inductor and the filter capacitor, which reduces the sensitivity of the controller to parameter changes. In addition, the present invention uses a double-layer nested adaptive structure to ensure that the designed sliding mode controller gain will change with the change of disturbance, thereby improving the anti-interference ability of the system. Compared with the existing sliding mode controller, the lower sliding mode controller gain of the present invention reduces the jitter phenomenon caused by high gain, while ensuring the strong robustness of the controller, optimizing the performance of the system.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] The double-layer nested adaptive sliding mode control method for a single-phase inverter comprises the following steps:

[0007] S1, based on Kirchhoff's law, the system model of single-phase inverter and the system model of output voltage tracking error were established;

[0008] S2, defining the sliding surface of the system according to the control target, and establishing the dynamic equation of the sliding surface in combination with step S1 while considering parameter mismatch and load disturbance;

[0009] S3, based on the concept of sliding mode equivalent control, a tracking error model of the sliding mode controller gain is established;

[0010] S4, based on step S3, constructs an adaptive law of the adaptive sliding mode controller gain, which can ensure that the designed sliding mode controller gain changes with the change of disturbance, thereby reducing the jitter phenomenon caused by high gain.

[0011] As a further improvement of the present invention, in step S1, a single-phase inverter system model and a system model of output voltage tracking error are established based on Kirchhoff's law. The specific process is as follows:

[0012] According to Kirchhoff's law, the system model of the single-phase inverter is expressed as:

[0013]

[0014] Where L, C and R represent the filter inductor, filter capacitor and load resistance in the single-phase inverter system, v o and i L They represent the output voltage and inductor current respectively, E represents the DC side voltage, and μ represents the control input;

[0015] To facilitate controller design, the output voltage tracking error is defined as:

[0016] e=v r -v o (2)

[0017] where v r It is represented as the reference voltage of the inverter;

[0018] Substituting (1) into (2), the dynamic equation of the output voltage tracking error is:

[0019]

[0020] in represents the first derivative of the reference voltage of the inverter;

[0021] The second-order derivative of the output voltage tracking error is:

[0022]

[0023] As a further improvement of the present invention, in step S2, the sliding surface of the system is defined according to the control target, and the dynamic equation of the sliding surface is established in combination with S1 while considering parameter mismatch and load disturbance. The specific process is as follows:

[0024] Since the control goal of the system is to ensure that the output voltage can effectively track the reference voltage of the inverter, the sliding surface of the system is selected as:

[0025]

[0026] Where λ>0 is a positive constant to be designed, σ(t) is the sliding surface of the system. When the sliding surface is equal to 0, the tracking error e of the system output voltage will also be equal to 0, indicating that the output voltage has tracked the reference voltage of the inverter.

[0027] By differentiating (5) with respect to time along the trajectories of (3) and (4), we can obtain the dynamic equation of the sliding surface:

[0028]

[0029] When there is uncertainty in the inverter's filter inductor L, filter capacitor C, and load resistance R, (6) can be rewritten as:

[0030]

[0031] Where D(t) represents the lumped disturbance in the system, which can be expressed as:

[0032]

[0033] where ξ 1 represents the system disturbance caused by load change, ξ 2 represents the system disturbance caused by parameter mismatch.

[0034] As a further improvement of the present invention, in step S3, a tracking error model of the sliding mode controller gain is established based on the concept of sliding mode equivalent control, and the specific process is as follows:

[0035] Assume that the lumped disturbance defined in step S2 satisfies:

[0036]

[0037] where a 0 is the upper bound of the lumped perturbation, an unknown constant, and a 1 represents the upper bound of the lumped perturbation derivative and is a known constant;

[0038] According to the dynamic equation (7) of the sliding surface, the controller of the system is designed as:

[0039]

[0040] where k 1 >0 indicates a positive definite controller gain, η is a very small positive constant, k(t) is the adaptive sliding mode controller gain, and sgn(·) represents the sign function;

[0041] According to the definition of sliding mode equivalent control, when the sliding surface converges to 0, by solving the algebraic equation We can get:

[0042] u eq (t)=-D(t) (11)

[0043] where u eq (t) represents the designed sliding mode equivalent control law, and its approximate value is obtained by low-pass filtering the high-frequency switching signal -[k(t)+η]sgn(σ)

[0044]

[0045] Where τ>0 is a very small time constant. If τ is selected to be small enough, then It will also be very small;

[0046] Assume that there exists a constant 1>∈ 1 >0 and∈ 0 >0 makes u eq (t) and satisfy:

[0047]

[0048] Inequality (13) is the eq (t) the assumption of the estimation accuracy, which depends on the bandwidth of the filter 1 / τ;

[0049] In the control process, in order to always ensure that the variable slides on the sliding surface, k(t) needs to satisfy:

[0050]

[0051] Among them, 0<α<1,∈>0 are variables designed to ensure the controller margin.

[0052] The tracking error of the adaptive sliding mode control gain is defined as:

[0053]

[0054] As long as δ(t) converges to 0, the sliding mode gain k(t) will be able to ensure that the sliding mode surface converges to 0.

[0055] As a further improvement of the present invention, an adaptive law of the adaptive sliding mode controller gain is constructed in step S4, and the specific process is as follows:

[0056] By selecting the adaptive sliding mode control gain as:

[0057]

[0058] Where γ>0 represents the positive parameter to be designed, q>1 is the parameter to ensure the controller margin, and r 0 >0 is a fixed positive scalar;

[0059] Under the designed adaptive sliding mode controller gain (16), it can ensure that the tracking error δ(t) of the adaptive sliding mode control gain converges to 0, thereby ensuring that the designed sliding mode surface can eventually converge to 0. Beneficial effects:

[0060] The present invention provides a double-layer nested adaptive sliding mode control algorithm for a single-phase inverter, which does not need to use information about the filter inductor and the filter capacitor, thereby reducing the sensitivity of the controller to parameter changes. In addition, the present invention uses a double-layer nested adaptive structure to ensure that the designed sliding mode controller gain changes with changes in disturbances, thereby improving the anti-interference ability of the system. Compared with the existing sliding mode controller, the lower sliding mode controller gain of the present invention reduces the jitter phenomenon caused by high gain, while ensuring the strong robustness of the controller, optimizing the performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 Schematic diagram of a single-phase inverter according to an embodiment of the present invention;

[0062] Figure 2 Experimental results of the double-layer nested adaptive sliding mode control algorithm for single-phase inverters under linear load according to the embodiment of the present invention;

[0063] Figure 3 Experimental results of the double-layer nested adaptive sliding mode control algorithm for a single-phase inverter according to an embodiment of the present invention under a reference voltage step. DETAILED DESCRIPTION

[0064] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0065] The present invention provides a double-layer nested adaptive sliding mode control algorithm for a single-phase inverter, which does not need to use information about the filter inductor and the filter capacitor, thereby reducing the sensitivity of the controller to parameter changes. In addition, the present invention uses a double-layer nested adaptive structure to ensure that the designed sliding mode controller gain changes with changes in disturbances, thereby improving the anti-interference ability of the system. Compared with the existing sliding mode controller, the lower sliding mode controller gain of the present invention reduces the jitter phenomenon caused by high gain, while ensuring the strong robustness of the controller, optimizing the performance of the system.

[0066] like Figure 1 As shown in the figure, the schematic diagram of the single-phase inverter is shown. It consists of three parts, namely the full-bridge inverter part, the LC filter part and the load resistance part. The double-layer nested adaptive sliding mode control algorithm of the single-phase inverter is specifically implemented as follows:

[0067] By collecting the output voltage information v o , and define the reference value of the output voltage υ r, the output voltage tracking error can be obtained:

[0068] e=v r -v o (33)

[0069] According to the designed sliding surface dynamic equation, the controller of the system can be designed as:

[0070]

[0071] According to the definition of sliding mode equivalent control, the approximate value of the sliding mode equivalent control law can be obtained:

[0072]

[0073] According to the approximate sliding mode equivalent control law, the tracking error of the adaptive sliding mode control gain can be obtained as:

[0074]

[0075] Using the tracking error of the adaptive sliding mode control gain, the update law of the adaptive sliding mode control gain can be designed as:

[0076]

[0077] Substituting (37) into (34) we obtain the final double-layer nested adaptive sliding mode control law.

[0078] Figure 2 The experimental results of the double-layer nested adaptive sliding mode control algorithm for single-phase inverter under linear load are shown in Figure 2. From the experimental results, it can be seen that under linear load, the output voltage waveform is sinusoidal and has no distortion.

[0079] Figure 3 The experimental results of the double-layer nested adaptive sliding mode control algorithm for a single-phase inverter under a reference voltage step are shown in the figure. From the experimental results, it can be seen that when the output voltage reference undergoes a step change, the output voltage can respond quickly and track the change of the upper reference. During the whole process, the output voltage always remains sinusoidal without obvious jitter.

[0080] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A double-layer nested adaptive sliding mode control method for a single-phase inverter, characterized in that: The following steps are involved: S1, based on Kirchhoff's law, the system model of single-phase inverter and the system model of output voltage tracking error were established; In step S1, based on Kirchhoff's law, a single-phase inverter system model and an output voltage tracking error system model are established. The specific process is as follows: According to Kirchhoff's law, the system model of the single-phase inverter is expressed as: Where L, C and R represent the filter inductor, filter capacitor and load resistance in the single-phase inverter system, v o and i L They represent the output voltage and inductor current respectively, E represents the DC side voltage, and μ represents the control input; To facilitate controller design, the output voltage tracking error is defined as: e=υ r -u o (2) where υ r It is represented as the reference voltage of the inverter; Substituting (1) into (2), the dynamic equation of the output voltage tracking error is: in represents the first derivative of the reference voltage of the inverter; The second-order derivative of the output voltage tracking error is: S2, defining the sliding surface of the system according to the control target, and establishing the dynamic equation of the sliding surface in combination with step S1 while considering parameter mismatch and load disturbance; In step S2, the sliding surface of the system is defined according to the control target. In the case of considering parameter mismatch and load disturbance at the same time, the dynamic equation of the sliding surface is established in combination with S1. The specific process is as follows: Since the control goal of the system is to ensure that the output voltage can effectively track the reference voltage of the inverter, the sliding surface of the system is selected as: Where λ>0 is a positive constant to be designed, σ(t) is the sliding surface of the system. When the sliding surface is equal to 0, the tracking error e of the system output voltage will also be equal to 0, indicating that the output voltage has tracked the reference voltage of the inverter. By differentiating (5) with respect to time along the trajectories of (3) and (4), we can obtain the dynamic equation of the sliding surface: When there is uncertainty in the inverter's filter inductor L, filter capacitor C, and load resistance R, (6) can be rewritten as: Where D(t) represents the lumped disturbance in the system, which can be expressed as: Where ξ1 represents the system disturbance caused by load change, and ξ2 represents the system disturbance caused by parameter mismatch; S3, based on the concept of sliding mode equivalent control, a tracking error model of the sliding mode controller gain is established; In step S3, based on the concept of sliding mode equivalent control, a tracking error model of the sliding mode controller gain is established. The specific process is as follows: Assume that the lumped disturbance defined in step S2 satisfies: Where a0 is the upper bound of the lumped disturbance, which is an unknown constant, and a1 represents the upper bound of the derivative of the lumped disturbance, which is a known constant; According to the dynamic equation (7) of the sliding surface, the controller of the system is designed as: where k1>0 indicates a positive definite controller gain, η is a very small positive constant, k(t) is the adaptive sliding mode controller gain, and sgn(·) represents the sign function; According to the definition of sliding mode equivalent control, when the sliding surface converges to 0, by solving the algebraic equation We can get: u eq (t)=-D(t) (11) where u eq (t) represents the designed sliding mode equivalent control law, and its approximate value is obtained by low-pass filtering the high-frequency switching signal -[k(t)+η]sgn(σ) Where τ>0 is a very small time constant. If τ is selected to be small enough, then It will also be very small; Assume that there exist constants 1>∈1>0 and ∈0>0 such that u eq (t) and satisfy: Inequality (13) is the eq (t) the assumption of the estimation accuracy, which depends on the bandwidth of the filter 1 / τ; In the control process, in order to always ensure that the variable slides on the sliding surface, k(t) needs to satisfy: Among them, 0<α<1,∈>0 is a variable designed to ensure the controller margin; The tracking error of the adaptive sliding mode control gain is defined as: As long as δ(t) converges to 0, the sliding mode gain k(t) will be able to ensure that the sliding surface converges to 0; S4, based on step S3, constructing an adaptive law of the adaptive sliding mode controller gain, which can ensure that the designed sliding mode controller gain changes with the change of disturbance, thereby reducing the chattering phenomenon caused by high gain; In step S4, an adaptive law of the adaptive sliding mode controller gain is constructed, and the specific process is as follows: By selecting the adaptive sliding mode control gain as: Where γ>0 represents the positive definite parameter to be designed, q>1 is the parameter to ensure the controller margin, and r0>0 is a fixed positive scalar; Under the designed adaptive sliding mode controller gain (16), it can ensure that the tracking error δ(t) of the adaptive sliding mode control gain converges to 0, thereby ensuring that the designed sliding mode surface can eventually converge to 0.

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