CN110456645B - A Discrete Repetitive Control Method for Inverters - Google Patents

Abstract

The invention discloses a discrete repetitive control method for an inverter. Constructing an attraction law with interference suppression effect by adopting an equivalent interference second-order difference compensation technology; according to the attraction law, an e/v signal conversion module is constructed, and an output signal of the e/v signal conversion module is used for repeating the correction quantity of the controller. The specific controller parameter setting can be based on a specific expression representing the maximum number of steps required by an absolute attraction layer, a steady-state error band and a tracking error in the convergence process of the system to enter the steady-state error band for the first time. The invention is a discrete repetitive controller which can completely eliminate the homogeneous harmonic and the even harmonic, effectively restrain the fractional harmonic and improve the control precision.

Description

A Discrete Repetitive Control Method for Inverters

technical field

The invention relates to a discrete repetitive control method for an inverter, which is suitable for an inverter power supply and also for a periodic operation process in industrial control.

Background technique

The repetitive controller is a control technique with a "cycle learning" feature. This control technology uses the positive feedback form 1/(1-e- ^Ts ) of the delay link with delay time T to construct a periodic signal internal model with a period of T, and embed it into a stable closed-loop system, the internal model output is It will form a control effect on the cycle-by-cycle accumulation of the input signal, and solve the problem of periodic tracking of the reference signal or suppression of periodic interference signals. At present, it has been widely used in motor servo systems, power electronic inverters, hard disk/optical disk servo systems and other repetitive operation processes.

Computer control technology is used in practical engineering, and the control system is mostly realized in discrete time mode. There are two main ways to design discrete repetitive controllers: one is obtained by discretizing continuous repetitive controllers; the other is to design controllers directly for discrete time systems. The sampling period T _s is taken so that the reference signal period is an integer multiple of the sampling period, and the number of sampling points in each period is denoted as N, that is, T=NT _s . In this way, the internal modulus of the discrete periodic signal is 1/(1-Z- ^N ). The discrete repetitive controller frequency domain design uses this discrete internal model.

In practice, the inverter control technology under the periodic reference signal is used, and the system is mostly implemented in a discrete manner, which has the problem of chattering and cannot completely suppress the periodic interference signal. For the chattering problem caused by discontinuous characteristics, the commonly used method is continuous processing methods, such as saturation function, hyperbolic tangent function and unit vector continuous function instead of symbolic function, but such processing will reduce the convergence speed and robustness of the system. Awesome. In addition, while eliminating periodic interference, further suppressing signals such as aperiodic interference or fractional interharmonics, and effectively reducing the steady-state error bound is an urgent problem to be solved.

SUMMARY OF THE INVENTION

The present invention provides a discrete repetitive control method for an inverter. In order to suppress the influence of inverter homogeneous/even harmonics and fractional harmonics on system performance and improve the tracking control accuracy, the equivalent interference second-order differential compensation technology is used to embed it into the new hyperbolic tangent attraction law. The discrete repetitive controller is designed to make the closed-loop system have the characteristics described by the hyperbolic tangent attraction law, thereby suppressing the inverter homogeneous/even harmonics and fractional harmonics. The invention specifically provides the specific expressions of three indexes, such as the absolute attraction layer, the steady-state error band, and the maximum number of steps required for the tracking error to enter the steady-state error band for the first time, which is used to guide the parameter setting of the controller.

The technical scheme adopted by the present invention to solve the above-mentioned technical problems is:

A discrete repetitive control method for an inverter, in order to suppress the homogeneous/even harmonics and fractional inter-harmonics of the inverter, so that the system output can approach a given reference signal in a limited time, the present invention constructs The following discrete new hyperbolic tangent law of attraction:

e_k+1,e_k分为k+1，k时刻的跟踪误差，且e_k＝r_k-y_k；Among them, 0<ρ<1, ε≥0, δ>0 are the parameters used to adjust the suction speed;

e _k+1 , e _k is divided into k+1, the tracking error at time k, and e _k =r _k -y _k ;

且ε＞0时，跟踪误差将严格单调收敛，无抖振、无正负交替地收敛于

的邻域内；2)当

且ε＞0时，跟踪误差将严格绝对收敛，正负交替的收敛于原点；3)当e_k≠0且ε＝0时，跟踪误差将严格单调收敛，无抖振、无正负交替的收敛于原点；4)当e_k≠0且ε＞0时，跟踪误差从任意初始值e₀开始经过

步首次穿越原点；其中，

为不小于·的最小整数；In the law of attraction (1), the dynamic behavior of the tracking error _ek is as follows: 1) When

And when ε > 0, the tracking error will converge strictly monotonically, with no chattering and no positive and negative alternation.

within the neighborhood of ; 2) when

And when ε>0, the tracking error will be strictly and absolutely convergent, and the positive and negative alternately will converge to the origin; 3) When e _k ≠ 0 and ε=0, the tracking error will be strictly monotonic convergence, no chattering, no positive and negative alternating Convergence to the origin; 4) When e _k ≠ 0 and ε > 0, the tracking error starts to pass from an arbitrary initial value e ₀

step crosses the origin for the first time; where,

is the smallest integer not less than ·;

In order to improve the system's ability to suppress align-order, even-order and fractional harmonic interference, the second-order differential compensation technology of equivalent interference is used, and the discrete attraction law (1) is modified as

用于补偿逆变器的间(分数次)谐波和其他非周期干扰；Among them, d _k+1 =w _k+1 -w _k+1-N represents the equivalent interference at time k+1, which can realize the suppression of homogeneous harmonics and even harmonics;

For compensating inverter inter (fractional) harmonics and other aperiodic disturbances;

According to the law of attraction (4), the discrete repetitive controller is designed as

Among them, u _k , u _k-1 , u _kN , u _k-1-N are the control input signals at the kth, k-1, kN, k-1-N times respectively; y _k , y _k-1 , y _k-1-N , y _kN , y _k+1-N are the output signals at the kth, k-1, k-1-N, kN, k+1-N times respectively; r _k+1 is k+1 The given reference signal at the moment; N is the period of the given reference signal; a ₁ , a ₂ , b ₁ , b ₂ in the formula (5) are the system parameters of the inverter, and the mathematical model of the inverter is as follows:

y _k+1 +a ₁ y _k +a ₂ y _k-1 =b ₁ u _k +b ₂ u _k-1 +w _k+1 (6)

Among them, y _k+1 , y _k , y _k-1 are the output signals of the inverter k+1, k, k-1 time, u _k , u _k-1 represent the inverter k, k-1 time Control input signal, a ₁ , a ₂ , b ₁ , b ₂ are system parameters; w _k+1 is the system interference signal at time k+1, including homogeneous harmonics, even harmonics and other interharmonics and parameters Perturbed;

Taking u _k as the control input signal of the inverter, the output signal y _k of the inverter system can be measured and obtained, which changes with the reference signal r _k , and the dynamic behavior of the system tracking error is represented by equation (4);

Further, in order to characterize the attraction process of the law of attraction, the present invention provides the specific expressions of the absolute attraction layer, the steady-state error band, and the maximum number of steps required for the tracking error to enter the steady-state error band for the first time; these three indices can be used. It is used to guide the parameter tuning of the controller, where the absolute attraction layer and the steady-state error band are defined as follows:

1) Absolute attraction layer Δ _AAL

|e _k+1 |<|e _k |, when |e _k |>Δ _AAL (7)

2) Steady state error band Δ _SSE

|e _k+1 |≤Δ _SSE , when |e _k |≤Δ _SSE (8)

Here, _ΔAAL is the absolute attraction layer boundary, and _ΔSSE is the steady-state error band boundary.

Under the action of the discrete repetitive controller (5), and the equivalent disturbance second-order differential compensation error satisfies

, the expressions of each indicator are as follows:

1) The absolute attraction layer _ΔAAL is expressed as:

Δ _AAL = max{Δ _AAL1 ,Δ _AAL2 } (10)

In the formula, Δ _AAL1 and Δ _AAL2 are positive real numbers and satisfy

Among them, Δ is the supremum of the equivalent interference compensation error;

2) The steady-state error band Δ _SSE is expressed as:

Δ _SSE =max{Δ _SSE1 ,Δ _SSE2 ,Δ}

(12)

In the formula, Δ _SSE1 and Δ _SSE2 are positive real numbers, which are determined by the following formula

In the formula, ξ is a positive real number, which is determined by the following formula

where sech( ) is the hyperbolic secant function,

3) Convergence steps |k ^** |

Among them, e ₀ is the initial value of the tracking error, e _i is the tracking error at the ith moment; ψ satisfies

The technical idea of the present invention is to propose a discrete repetitive controller for inverters, which is a time domain design method, which is different from the commonly used frequency domain method. The time-domain design of the controller is easy to incorporate with existing interference suppression methods. The invention embeds the second-order differential compensation term of equivalent interference into the law of attraction, and at the same time achieves effective suppression of the interference of aligned harmonics, even harmonics and fractional harmonics, and makes the steady-state error bound of the system tracking error smaller.

The control effects of the present invention are mainly manifested in: equivalent interference second-order difference compensation, complete elimination of homogeneous harmonics and even-order harmonics, effective suppression of fractional harmonics, fast convergence performance and high tracking accuracy.

Description of drawings

Fig. 1 is the control system design flow chart based on the law of attraction method.

FIG. 2 is a comparison diagram of the error convergence speed of the law of attraction proposed by the present invention, the law of exponential attraction and the conventional law of attraction of hyperbolic tangent.

Figure 3 is a block diagram of a discrete repetitive controller.

Figure 4 is an internal model block diagram of the discrete repetitive control system.

FIG. 5 is a block diagram of an inverter control system in an embodiment of the present invention.

作用下的给定参考信号、输出信号和跟踪误差信号；Fig. 6 is in the controller (9) (there are only homogeneous/even harmonics, and the interference compensation term is considered

The given reference signal, output signal and tracking error signal under the action;

)作用下的给定参考信号、输出信号和跟踪误差信号；Fig. 7 is in the controller (9) (there are only homogeneous/even harmonics, and the interference compensation term is considered

) under the action of the given reference signal, output signal and tracking error signal;

)作用下的给定参考信号、输出信号和跟踪误差信号；Fig. 8 is in the controller (9) (there are only homogeneous/even harmonics, and the interference compensation term is considered

) under the action of the given reference signal, output signal and tracking error signal;

)作用下的给定参考信号、输出信号和跟踪误差信号；Fig. 9 is in the controller (9) (the existence of homogeneous/even/fractional harmonics, and considering the interference compensation term

) under the action of the given reference signal, output signal and tracking error signal;

)作用下的给定参考信号、输出信号和跟踪误差信号；Fig. 10 is in the controller (9) (there are only homogeneous/even/fractional harmonics, and the interference compensation term is considered

) under the action of the given reference signal, output signal and tracking error signal;

)作用下的给定参考信号、输出信号和跟踪误差信号；Fig. 11 is in the controller (9) (only homogeneous/even/fractional harmonics exist, and the disturbance compensation term is considered

) under the action of the given reference signal, output signal and tracking error signal;

Detailed ways

The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

Referring to Figure 1-11, a discrete repetitive control method for an inverter, the control system design flowchart is shown in Figure 1, and the mathematical model of the inverter control system is:

y _k+1 +a ₁ y _k +a ₂ y _k-1 =b ₁ u _k +b ₂ u _k-1 +w _k+1 (1)

Among them, y _k+1 , y _k , y _k-1 are the output signals of the inverter k+1, k, k-1 time, u _k , u _k-1 represent the inverter k, k-1 time Control input signal, a ₁ , a ₂ , b ₁ , b ₂ are system parameters; w _k+1 is the system interference signal at time k+1, including homogeneous harmonics, even harmonics and other inter (fractional) Harmonics and parametric perturbations;

The given reference signal r _k is a sinusoidal signal with a period of N, which satisfies

r _k =Asin(2πk/N), r _k =r _kN (2)

Among them, r _k , r _kN are the given reference signals at time k, kN respectively, and A is the amplitude of the given reference signal r _k ;

The present invention constructs the following discrete new hyperbolic tangent attraction law:

e_k+1,e_k分为k+1，k时刻的跟踪误差，且e_k＝r_k-y_k；图2为本发明所提出的吸引律(实线)、常规双曲正切吸引律

(点划线)和指数吸引律e_k+1＝(1-ρ)e_k-εsgn(e_k)(虚线)的比较图；由图2可知本发明所提出的吸引律在减少了系统颤振的同时，实现了更快速误差收敛；Among them, 0<ρ<1, ε≥0, δ>0 are the parameters used to adjust the suction speed;

e _k+1 , e _k is divided into k+1, the tracking error at time k, and e _k =r _k -y _k ; Fig. 2 is the law of attraction (solid line) proposed by the present invention, the law of attraction of conventional hyperbolic tangent

(dotted line) and exponential attraction law e _k+1 =(1-ρ)e _k -εsgn(e _k ) (dotted line) comparison diagram; it can be seen from FIG. 2 that the attraction law proposed by the present invention reduces the system vibration At the same time of vibration, faster error convergence is achieved;

且ε＞0时，跟踪误差将严格单调收敛，无抖振、无正负交替地收敛于

的邻域内；2)当

且ε＞0时，跟踪误差将严格绝对收敛，正负交替地收敛于原点地邻域内；3)当e_k≠0且ε＝0时，跟踪误差将严格单调收敛，无抖振、无正负交替地收敛于原点；4)当e_k≠0且ε＞0时，跟踪误差从任意初始值e₀开始经过

步首次穿越原点；其中，

为不小于·的最小整数；In the law of attraction (1), the dynamic behavior of the tracking error _ek is as follows: 1) When

And when ε > 0, the tracking error will converge strictly monotonically, with no chattering and no positive and negative alternation.

within the neighborhood of ; 2) when

And when ε>0, the tracking error will converge strictly and absolutely, and the positive and negative will converge in the neighborhood of the origin alternately; 3) When e _k ≠ 0 and ε=0, the tracking error will converge strictly monotonically, no chattering, no positive Negative alternately converge to the origin; 4) When e _k ≠ 0 and ε > 0, the tracking error starts to pass from an arbitrary initial value e ₀

step crosses the origin for the first time; where,

is the smallest integer not less than ·;

In order to improve the suppression ability of the system for align-order, even-order and fractional harmonic interference, the discrete attraction law (3) can be modified as

用于补偿逆变器的间(分数次)谐波和其他非周期干扰；Among them, d _k+1 =w _k+1 -w _k+1-N represents the equivalent interference at time k+1, which can realize the suppression of homogeneous harmonics and even harmonics;

For compensating inverter inter (fractional) harmonics and other aperiodic disturbances;

According to the tracking error e _k =r _k -y _k and the system (1),

Express d _k+1 =w _k+1 -w _k+1-N as

Substituting Equation (8) into Equation (6), the expression of the discrete repetitive controller (see Figure 3) is

As shown in Figure 4, the repetition controller (9) can also be expressed as

u _k = u _kN +v _k (10)

in,

Taking u _k as the control input signal of the inverter, the output signal y _k of the inverter system can be measured and obtained, which changes with the reference signal r _k , and the dynamic behavior of the system tracking error is represented by equation (6);

Further, in order to characterize the attraction process of the law of attraction, the present invention provides the specific expressions of the absolute attraction layer, the steady-state error band, and the maximum number of steps required for the tracking error to enter the steady-state error band for the first time; these three indices can be used. It is used to guide the parameter tuning of the controller, where the absolute attraction layer and the steady-state error band are defined as follows:

1) Absolute attraction layer Δ _AAL

|e _k+1 |<|e _k |, when |e _k |>Δ _AAL (12)

2) Steady state error band Δ _SSE

|e _k+1 |≤Δ _SSE , when |e _k |≤Δ _SSE (13)

Here, _ΔAAL is the absolute attraction layer boundary, and _ΔSSE is the steady-state error band boundary.

Under the action of the discrete repetitive controller (9), and the equivalent disturbance second-order differential compensation error satisfies

, the expressions of each indicator are as follows:

1) The absolute attraction layer _ΔAAL is expressed as:

Δ _AAL = max{Δ _AAL1 ,Δ _AAL2 } (15)

In the formula, Δ _AAL1 and Δ _AAL2 are positive real numbers and satisfy

Among them, Δ is the supremum of the second-order differential compensation error of equivalent interference;

2) The steady-state error band Δ _SSE is expressed as:

Δ _SSE =max{Δ _SSE1 ,Δ _SSE2 ,Δ}

(17)

In the formula, Δ _SSE1 and Δ _SSE2 are positive real numbers, which are determined by the following formula

In the formula, ξ is a positive real number, which is determined by the following formula

where sech( ) is the hyperbolic secant function,

3) Convergence steps |k ^** |

Among them, e ₀ is the initial value of the tracking error, e _i is the tracking error at the ith moment; ψ satisfies

Further, after the discrete repetitive controller design is completed, the controller parameters need to be tuned. Adjustable parameters ρ, ε, δ can be adjusted according to the three indicators that characterize the attraction process of the law of attraction.

The following descriptions are made for the above repetitive controller design:

1) The law of attraction proposed by the present invention adopts the hyperbolic tangent function to design a new law of attraction; compared with the law of attraction of the exponential and the conventional law of attraction of the hyperbolic tangent, the law of attraction proposed by the present invention is in terms of convergence speed and reduction of system chattering. There are significant advantages (see Figure 2);

为d_k+1的补偿值，用于补偿分数谐波和其他非周期干扰。干扰补偿方法常用的有两种：(1)一种简单的补偿值确定方法是一步延迟方法，即

(2)一种d_k+1界已知时的补偿值确定方法。设等效干扰d_k+1的上、下界分别为d_u、d_l，则d_k+1满足不等式d_l≤d_k+1≤d_u；记

则

可取

2) The introduction of d _k+1 into the law of attraction reflects the suppression measures for periodic interference signals with known periods, such as homogeneous and even harmonic interference in inverters;

is the compensation value of d _k+1 , which is used to compensate fractional harmonics and other aperiodic disturbances. There are two commonly used interference compensation methods: (1) A simple compensation value determination method is a one-step delay method, namely

(2) A compensation value determination method when the d _k+1 bound is known. Let the upper and lower bounds of the equivalent disturbance d _k+1 be d _u and d _l respectively, then d _k+1 satisfies the inequality d _l ≤d _k+1 ≤d _u ;

but

desirable

用于补偿逆变器的间(分数次)谐波和其他非周期干扰，可得使得使得系统跟踪误差的稳态误差界达到d_k+1-2d_k+d_k-1＝O(T³)，获得更小稳态误差界。The invention adopts the equivalent interference second-order differential compensation technology, and uses

For compensating the inverter's inter (fractional) harmonics and other aperiodic disturbances, it can be obtained that the steady-state error bound of the system tracking error reaches d _k+1 -2d _k +d _k-1 =O(T ³ ) to obtain a smaller steady-state error bound.

3) In formula (9), y _k-1 , y _k+1-N , y _k , y _kN , y _kN-1 can be obtained by measurement; u _kN , u _k , u _k-1 , u _{k -1-N} , which is the stored value of the control signal, which can be read from memory.

4) The law of attraction method given in the present invention is also suitable for feedback control under the constant value reference signal. The equivalent disturbance is d _k+1 =w _k+1 -w _k ; its controller is as follows:

Example

Closed-loop control of the inverter output waveform. As shown in Figure 5, the adopted inverter system consists of a given sinusoidal signal part, a repetitive controller, a PWM modulation part, an inverter main control circuit and a sampling circuit. The given sinusoidal signal, repetitive controller and PWM modulation module are all realized by the DSP control board, and the rest are realized by the inverter hardware circuit. The entire inverter control system is given the desired output signal by the DSP, and after PWM modulation, the high and low pulse signals of the power switch tube of the inverter are driven to realize on and off. The output signal of the inverter is restored to a sinusoidal signal through the LC filter, and the required voltage and current signal data are sampled by the voltage sensor and the current sensor and returned to the DSP, and then the input signal is corrected after repeating the action of the controller to realize the inverter. The inverter waveform tracking control reduces the THD value of the inverter output waveform.

The design process of the inverter discrete repetitive controller is given below.

Firstly, the mathematical model of the system is established. The main control circuit, LC filter circuit and sampling circuit of the inverter are modeled as objects, and the following second-order differential equation model is obtained

y _k+1 +a ₁ y _k +a ₂ y _k-1 =b ₁ u _k +b ₂ u _k-1 +w _k+1 (23)

Among them, y _k+1 , y _k , y _k-1 represent the inverter output voltages at times k+1, k, k-1, respectively, and u _k , u _k-1 represent the inverters at times k and k-1 The control quantity of , w _k+1 is the uncertain characteristic of the inverter system, which is composed of external disturbances and unmodeled characteristics. The system parameters a ₁ , a ₂ , b ₁ , and b ₂ in the model are obtained through mechanism modeling, and their specific values are as follows:

a ₁ =-0.5775,a ₂ =0.2804,b ₁ =0.4102,b ₂ =0.2589 (24)

In the embodiment, the inverter's given reference signal r _k+1 =220sin( _2πfkTs ), the unit is V, the signal frequency is 50Hz, the sampling period is _Ts =0.0001s, and the reference signal period is 0.02s. The disturbance signal of the inverter system is

Among them, the first term is used to simulate the homogeneous harmonic interference signal of the inverter, the second term is used to simulate the even harmonic interference signal of the inverter, and the third term is used to simulate the inter-inverter (fractional) harmonics The interference signal, the fourth term is the random disturbance signal.

Numerical simulation is carried out with the above system parameters to verify the implementation results of discrete repetitive controller on the inverter system.

仿真时，逆变器系统干扰只考虑齐次谐波和偶次谐波干扰，则h₁＝10,h₂＝5,h₃＝0,h₄＝0；控制器参数选取为ρ＝0.5,ε＝0.2,δ＝0.5，仿真结果见图6。1) Using the controller (9) and considering the interference compensation term

During the simulation, the inverter system interference only considers the homogeneous harmonic and even harmonic interference, then h ₁ =10,h ₂ =5,h ₃ =0,h ₄ =0; the controller parameters are selected as ρ=0.5 , ε = 0.2, δ = 0.5, the simulation results are shown in Figure 6.

仿真时，逆变器系统干扰只考虑齐次谐波和偶次谐波干扰，则h₁＝10,h₂＝5,h₃＝0,h₄＝0；控制器参数选取为ρ＝0.5,ε＝0.2,δ＝0.5，仿真结果见图7。2) Adopt the controller (9) and consider the interference compensation term

During the simulation, the inverter system interference only considers the homogeneous harmonic and even harmonic interference, then h ₁ =10,h ₂ =5,h ₃ =0,h ₄ =0; the controller parameters are selected as ρ=0.5 , ε=0.2, δ=0.5, the simulation results are shown in Figure 7.

仿真时，逆变器系统干扰只考虑齐次谐波和偶次谐波干扰，则h₁＝10,h₂＝5,h₃＝0,h₄＝0；控制器参数选取为ρ＝0.5,ε＝0.2,δ＝0.5，仿真结果见图8。3) Using the controller (9) and considering the interference compensation term

During the simulation, the inverter system interference only considers the homogeneous harmonic and even harmonic interference, then h ₁ =10,h ₂ =5,h ₃ =0,h ₄ =0; the controller parameters are selected as ρ=0.5 , ε=0.2, δ=0.5, and the simulation results are shown in Figure 8.

仿真时，逆变器系统干扰考虑齐次谐波、偶次谐波干扰、分数谐波干扰以及随机干扰，则h₁＝10,h₂＝5,h₃＝2,h₄＝0.05，可获得Δ＝2.6341；控制器参数选取为ρ＝0.5,ε＝0.2,δ＝0.5，可得Δ_AAL＝Δ_SSE＝3.6483；仿真结果见图9。4) Using the controller (9) and considering the interference compensation term

During simulation, the inverter system interference considers homogeneous harmonics, even-order harmonics, fractional harmonics and random interference, then h ₁ =10, h ₂ =5, h ₃ =2,h ₄ =0.05, which can be Obtain Δ = 2.6341; the controller parameters are selected as ρ = 0.5, ε = 0.2, δ = 0.5, Δ _AAL = Δ _SSE = 3.6483; the simulation results are shown in Figure 9.

仿真时，逆变器系统干扰考虑齐次谐波、偶次谐波干扰、分数谐波干扰以及随机干扰，则h₁＝10,h₂＝5,h₃＝2,h₄＝0.05，可获得Δ＝0.762；控制器参数选取为ρ＝0.5,ε＝0.2,δ＝0.5，可得Δ_AAL＝Δ_SSE＝0.7929；仿真结果见图10。5) Adopt the controller (9) and consider the interference compensation term

During simulation, the inverter system interference considers homogeneous harmonics, even-order harmonics, fractional harmonics and random interference, then h ₁ =10, h ₂ =5, h ₃ =2,h ₄ =0.05, which can be Δ=0.762 is obtained; the controller parameters are selected as ρ=0.5, ε=0.2, δ=0.5, and _ΔAAL = _ΔSSE =0.7929 can be obtained; the simulation results are shown in Figure 10.

仿真时，逆变器系统干扰考虑齐次谐波、偶次谐波干扰、分数谐波干扰以及随机干扰，则h₁＝10,h₂＝5,h₃＝2,h₄＝0.05，可获得Δ＝0.2989；控制器参数选取为ρ＝0.5,ε＝0.2,δ＝0.5，可得Δ_AAL＝0.331，Δ_SSE＝0.3327；仿真结果见图11。6) Adopt the controller (9) and consider the interference compensation term

During simulation, the inverter system interference considers homogeneous harmonics, even-order harmonics, fractional harmonics and random interference, then h ₁ =10, h ₂ =5, h ₃ =2,h ₄ =0.05, which can be Δ=0.2989 is obtained; the controller parameters are selected as ρ=0.5, ε=0.2, δ=0.5, _ΔAAL =0.331, _ΔSSE =0.3327; the simulation results are shown in Figure 11.

The above numerical simulation results verify that the discrete repetitive controller given by the patent of the present invention works in 0.02s. As shown in Figure 6-8, the repetitive control can well eliminate periodic interference (homogeneous harmonic and even harmonic interference). ). As shown in Figure 9-11, the repetitive controller using the equivalent interference second-order differential compensation technology has a greater advantage in suppressing fractional harmonic signals, and the steady-state error bound is smaller.

Claims (2)

1. A discrete repetitive control method for an inverter, characterized by:

1) constructing a discrete hyperbolic tangent attraction law:

wherein rho is more than 0 and less than 1, epsilon is more than or equal to 0, and delta is more than 0 and is a parameter for adjusting the suction speed;

e_k+1,e_ktracking divided into k +1, k momentsError, and e_k＝r_k-y_k；

In the attraction law (1), tracking error e_kThe dynamic behavior of (c) is as follows: 1) when in use

When epsilon is more than 0, the tracking error will be strictly and monotonously converged, and no buffeting and no positive and negative alternation are converged at

Within a neighborhood of (c); 2) when in use

When epsilon is more than 0, the tracking error is strictly and absolutely converged, and the positive and negative alternate convergence is at the origin; 3) when e is_kWhen not equal to 0 and epsilon is 0, the tracking error is strictly and monotonously converged, and the tracking error is converged to the origin without buffeting and positive and negative alternation; 4) when e is_kNot equal to 0 and epsilon > 0, the tracking error is from an arbitrary initial value e₀Begin to pass through

The step passes through the origin for the first time; wherein,

is the smallest integer not less than;

2) in order to improve the inhibiting capability of the system on the even order, the even order and the fractional harmonic interference, an equivalent interference second order difference compensation technology is adopted to modify the discrete attraction law (1) into a discrete attraction law

Wherein d is_k+1＝w_k+1-w_k+1-NThe equivalent interference at the k +1 moment is expressed, and the suppression of the homogeneous harmonic and the even harmonic can be realized;

for compensating inter-fractional sub-harmonics and other non-periodic disturbances of the inverter;

3) the discrete repetitive controller is designed according to the attraction law (4)

Wherein u is_k，u_k-1，u_k-N，u_k-1-NRespectively are control input signals at the k, k-1, k-N, k-1-N moments; y is_k,y_k-1,y_k-1-N,y_k-N,y_k+1-NRespectively are output signals at the k, k-1, k-1-N, k-N, k +1-N moments; r is_k+1A given reference signal at time k + 1; n is the period of a given reference signal; a in formula (5)₁,a₂,b₁,b₂For the system parameters of the inverter, the mathematical model of the inverter is as follows:

y_k+1+a₁y_k+a₂y_k-1＝b₁u_k+b₂u_k-1+w_k+1 (6)

wherein, y_k+1,y_k,y_k-1Is the output signal at the moment k +1, k, k-1 of the inverter, u_k,u_k-1Control input signal representing the time of inverter k, k-1, a₁,a₂,b₁,b₂Is a system parameter; w is a_k+1System interference signals at the moment k +1 comprise homogeneous harmonics, even harmonics and other inter-harmonics and parameter perturbations;

4) will u_kAs control input signal for inverterAnd the output signal y of the inverter system can be measured and obtained_kFollows the reference signal r_kThe dynamic behavior of the system tracking error is characterized by equation (4);

5) and a repetitive controller (5) is adopted, the attraction process of the tracking error of the system is represented by an absolute attraction layer, a steady-state error band and at most 3 indexes of the steps required by the tracking error entering the steady-state error band for the first time, and the 3 indexes can be used for guiding the parameter setting of the controller.

2. A discrete repetitive control method for an inverter as set forth in claim 1, characterized in that: under the action of the repetitive controller (5), the equivalent interference second order differential compensation error meets the requirement

The expression of the 3 indices is as follows:

1) absolute attraction layer Δ_AALExpressed as:

Δ_AAL＝max{Δ_AAL1,Δ_AAL2} (8)

in the formula,. DELTA._AAL1，Δ_AAL2Is positive and real, and satisfies

Wherein, delta is the supremum of the equivalent interference second order difference compensation error;

2) steady state error band Δ_SSEExpressed as:

Δ_SSE＝max{Δ_SSE1,Δ_SSE2,Δ} (10)

in the formula,. DELTA._SSE1，Δ_SSE2Is positive and real, is determined by

Where ξ is a positive real number and is determined by the following equation

Where sech (-) is a hyperbolic secant function,

3) convergence step number | k^**|

Wherein e is₀As initial value of tracking error, e_iTracking error at the ith moment; psi satisfies

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