CN107370402B - A switching control method based on discrete Lyapunov function - Google Patents

Abstract

The invention discloses a switching control method based on a discrete Lyapunov function, which belongs to the fields of power electronic converter technology and intelligent control. According to the discrete mathematical model of the converter, the invention defines the discrete Lyapunov function based on the error term of the controlled variable and the reference variable, obtains the control law from the second Lyapunov stability theorem, and selects different definition variables α in the dynamic response stage and the steady state stage , and then output the switch signal through PWM modulation; the method includes the feedback item of the controlled quantity, the error value compensation item of the controlled quantity and the reference quantity, and the feedforward compensation item of the future reference input. The control method of the invention is simple in principle, easy to realize digitally, combines the advantages of deadbeat control and the "feedforward-feedback" feature of model predictive control, and has the advantages of fast dynamic response, good control performance and strong robustness.

Description

A switching control method based on discrete Lyapunov function

technical field

The invention relates to a single-phase voltage type PWM rectification technology, in particular to a switching control method based on a discrete Lyapunov function, and belongs to the technical field of power electronic converters.

Background technique

With the development of the economy, the demand for high-power DC power supply is increasing year by year. The input current of traditional uncontrolled and phase-controlled power supply has large harmonics, low power factor has a great impact on the power grid, and the current response is slow and cannot meet the needs of production and life; Voltage-type PWM rectifiers can eliminate the input current harmonics from the source, and have unity power factor, so they are the focus of the current power electronics field.

The control method based on the discrete lyapunov function, when the defined variable α is zero, that is, the traditional deadbeat control, and the deadbeat control depends on the mathematical model of the controlled object, so the accuracy of the controlled object parameters affects the control The influence of performance is great. In the application of single-phase PWM rectifier, the drift of inductance parameters and inaccurate sampling may make the current unstable and distort, so the robustness is poor; when the defined variable α is not zero, the stability of the system is not zero. The dynamic control performance is good and the robustness is strong, but there is a problem of slow dynamic response.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the existing control strategies, the present invention aims to provide a switching control method based on discrete Lyapunov functions. This method obtains the control law based on the second Lyapunov stability theorem, combines the advantages of deadbeat control and the "feedforward-feedback" characteristics of model predictive control, and has the advantages of fast dynamic response, good control performance, and strong robustness.

The object of the present invention can be achieved through the following technical solutions.

A switching control method based on discrete Lyapunov function, the control method selects different defined variables α in the dynamic response stage and the steady state stage, and then modulates the output switching signal through PWM; specifically includes: (1) sampling to obtain the grid voltage e, input Current i, voltage Vdc across the DC side capacitor C; (2) The voltage outer loop is controlled by PI to obtain the reference current i*; (3) The discrete Lyapunov function is defined to obtain the control law of the AC side of the rectifier, which is selected according to the state of the converter Different α parameters; (4) output the switch signal S(k) through the PWM modulation unit and act on the switch tube.

Further, in step (1), the phase-locked circuit is used to obtain the zero-crossing point of the grid voltage, and the DSP calculates the grid period in real time according to the zero-crossing point of the grid voltage, and changes the control period accordingly, and simultaneously calculates the grid voltage according to the zero-crossing point of the grid voltage. The value e is converted into a digital signal; the input current value i is sampled by the current Hall sensor, and the DC voltage value Vdc across the DC side capacitor C of the rectifier module is sampled by the voltage division method, and converted into a digital signal.

Further, in step (2), the difference between the sampled DC side output voltage Vdc and the command DC voltage Vdc_ref is adjusted by PI, and the difference between the output DC voltage Vdc and the command DC voltage Vdc_ref is used as the input of the voltage outer loop, The voltage outer loop adopts PI control, the output of the PI regulator obtains the amplitude of the reference current, and the reference current i* is obtained by multiplying the reference current amplitude and the grid voltage phase information.

Further, in step (3), according to the second theorem of lyapunov stability, the discrete Lyapunov function is defined as According to this, the control law of the AC side of the rectifier at time k+1 is obtained as Select a steady-state error value △H, when |Vdc-Vdc_ref|>△H, let α be 0, hope the dynamic response speed is fast, when |Vdc-Vdc_ref|<△H, let α be greater than 0, the selection range of α is α∈[0.1, 0.75], the purpose is to reduce the steady-state error and enhance the robustness of the system.

Compared with the prior art, the beneficial effects of the present invention are:

1. The input current ripple on the AC side of the single-phase voltage PWM rectifier is low, and the system can achieve unity power factor operation;

2. The system has fast dynamic response;

3. The system has good robustness.

Description of drawings

Fig. 1 is a kind of novel control method schematic diagram of the single-phase PWM rectifier based on discrete Lyapunov function of the present invention;

Fig. 2 is the Bode diagram of the current inner-loop closed-loop transfer function G(z) of the present invention as a function of α;

FIG. 3 is a graph showing the relationship between the control convergence speed ρ and α according to the present invention.

Fig. 4 is the simulation waveform of AC side voltage and current of switching control based on Lyapunov discrete function applying the present invention

FIG. 5 is the simulation waveform of the output voltage of the DC side of the switching control based on the Lyapunov discrete function applying the present invention.

Detailed ways

The embodiments of the present invention will be further described below in conjunction with the accompanying drawings and specific examples, but the implementation and protection of the present invention are not limited to this. Persons can implement or understand with reference to the prior art.

A switching control method based on discrete Lyapunov function in this example, the main steps are as follows:

(S1) The zero-crossing point of the grid voltage is obtained by using the phase-locked circuit. The DSP calculates the grid period in real time according to the zero-crossing point of the grid voltage, and changes the control period accordingly. At the same time, the grid voltage value e is calculated according to the zero-crossing point of the grid voltage and converted into a digital Signal;

(S2) using the current Hall sensor to sample the input current value i, using the voltage division method to sample the DC voltage value Vdc at both ends of the DC side capacitor C of the single-phase voltage type PWM rectifier module, and converting it into a digital signal;

(S3) The difference between the output DC voltage Vdc and the command DC voltage Vdc_ref is used as the input of the voltage outer loop, the voltage outer loop adopts PI control, and the output of the PI regulator obtains the amplitude of the reference current, which is related to the phase information of the grid voltage. Multiply to get the reference current i*;

(S4) Define the discrete Lyapunov function, obtain the control law of the AC side of the rectifier, and select different α parameters according to the state of the converter; the details are as follows:

A) e is the single-phase AC voltage; Ls and R are the AC side inductance and its equivalent resistance respectively; Vr is the AC side voltage of the rectifier; i is the AC side current of the rectifier; C is the DC side capacitance; Vdc is the DC side output voltage; _RL is a purely resistive load.

The mathematical model of single-phase PWM rectifier AC measurement can be expressed as:

Assuming that the sampling frequency of the system is T, rewrite equation (1) into discrete form:

i(k) represents the sampled value of the current at the k sampling time; e(k) represents the sampled value of the AC voltage at the k sampling time; i(k+1) represents the predicted current at k+1 time at the k sampling time; Vr(k+ 1) Indicates the voltage on the AC side of the rectifier at the sampling time of k+1.

B) Define the variable x(k) as the error between the current sampling value and the reference value at the k sampling time as follows:

x(k)=i(k)-i ^* (k) (3)

According to the second theorem of Lyapunov stability, and based on the error value of the current sampling value of the single-phase PWM rectifier and the current reference value, the discrete Lyapunov function L(x(k)) is defined as follows:

The Lyapunov functions of the system at k sampling time and k+1 sampling time are:

The increment ΔL(x(k)) of the Lyapunov function at adjacent moments is:

C) In order to ensure the stability of the system, according to the second theorem of Lyapunov stability, in order to ensure that ΔL(x(k))<=0:

i(k+1)-i ^* (k+1)=α[i(k)-i ^* (k)] (7)

Figure 2 shows the Bode diagram of the current inner-loop closed-loop transfer function G(z) changing with α, and Figure 3 shows the relationship between the control convergence speed ρ and α. It can be seen from Fig. 2 and Fig. 3 that the larger the α, the smaller the steady-state error, the smaller the overshoot of the unit step response, and the slower the control convergence speed. Therefore, a steady-state error value △H is selected. When |Vdc-Vdc_ref|>△H, let α be 0, and the dynamic response speed is expected to be fast. When |Vdc-Vdc_ref|<△H, let α be greater than 0, according to the Bode diagram It is suggested that the selection range of α is α∈[0.1, 0.75], the purpose is to reduce the steady-state error and enhance the robustness of the system.

Combining equations (2) and (7), the control law Vr(k+1) on the AC side of the rectifier at the sampling time of k+1 can be obtained as follows:

(S5) The switch signal S(k) is output through the PWM modulation unit and acts as a switch tube.

In step (S2), the output DC voltage (Vdc) is sampled by using resistor divider, isolated by HCPL-7840, and then adjusted by the operational amplifier to make the sampled voltage adapt to the voltage range of the DSP sampling port.

As a preference, the DSP processor of Texas Instruments 2000 series can be used for algorithm calculation.

In step (S3), the difference between the output DC voltage (Vdc) and the command DC voltage (Vdc_ref) is used as the input of the voltage outer loop, the voltage outer loop is controlled by PI, and the output of the PI regulator obtains the amplitude of the reference current, the reference current The amplitude is multiplied by the grid voltage phase information to obtain the reference current i*.

As shown in Figure 4, the AC grid side voltage e and AC current i are in the same phase, and the input power factor is high, which is approximately 1; the robustness is good. It can be seen from Figure 5 that the dynamic response of the system is fast.

Those skilled in the art can make various modifications or supplements to the specific embodiments or substitute in similar manners without departing from the principle and essence of the present invention, but these modifications all fall within the protection scope of the present invention. Therefore, the technical scope of the present invention is not limited to the above-mentioned embodiments.

Claims (2)

1. a kind of switching control method based on discrete Lyapunov function, it is characterized in that, choose different definition variable α in dynamic response stage and steady-state stage, then output switching signal by PWM modulation; Concretely comprise: (1) sampling obtains grid voltage , input current, DC voltage Vdc at both ends of the DC side capacitor C; specifically, the zero-crossing point of the grid voltage is obtained by using a phase-locked circuit, and the DSP calculates the grid cycle in real time according to the zero-crossing point of the grid voltage, and changes the control cycle accordingly. At the same time, according to the grid voltage The grid voltage is calculated at the zero-crossing point of the rectifier and converted into a digital signal; the input current is sampled by the current Hall sensor, and the DC voltage Vdc across the DC side capacitor C of the rectifier is sampled by the voltage division method, and converted into a digital signal; (2) The voltage outer loop Using PI control, the reference current i* is obtained; (3) the discrete Lyapunov function is defined to obtain the control law of the AC side of the rectifier, and different α is selected according to the state of the rectifier: According to the second theorem of lyapunov stability, the discrete Lyapunov function is defined as

According to this, the control law of the AC side of the rectifier at the sampling time of k+1 is obtained as

Select a steady-state error value △H, when |Vdc-Vdc_ref|>△H, Vdc_ref is the command DC voltage, let α be 0, hope the dynamic response speed is fast, when |Vdc-Vdc_ref|<△H, let α be greater than 0, the selection range of α is α∈[0.1, 0.75], the purpose is to reduce the steady-state error and enhance the robustness of the system; Let e be the grid voltage; Ls and R are the AC side inductance and its equivalent resistance, respectively; Vr is the control law of the AC side voltage of the rectifier; i is the input current; C is the DC side capacitance; R _L is the pure resistive load; The mathematical model of the AC side of the single-phase PWM rectifier can be expressed as:

Assuming that the sampling frequency of the system is T, rewrite equation (1) into discrete form: i(k) represents the sampling value of current at sampling time k; e(k) represents the sampling value of grid voltage at sampling time k; i(k+1) represents the predicted current at the k+1 sampling time at the k sampling time; Vr(k+1) represents the control law of the AC side of the rectifier at the k+1 sampling time; The variable x(k) is defined as the error between the current sampling value and the reference value at the k sampling time as follows: x(k)=i(k)-i ^* (k) (3) According to the second theorem of Lyapunov stability, and based on the error value of the current sampling value of the single-phase PWM rectifier and the current reference value, the discrete Lyapunov function L(x(k)) is defined as follows:

The Lyapunov functions of the system at k sampling time and k+1 sampling time are: The increment ΔL(x(k)) of the Lyapunov function at adjacent moments is:

In order to ensure the stability of the system, according to the second theorem of Lyapunov stability, in order to ensure ΔL(x(k))<=0, let: i(k+1)-i ^* (k+1)=α[i(k)-i ^* (k)] (7) Combining equations (2) and (7), the control law Vr(k+1) on the AC side of the rectifier at the sampling time of k+1 is obtained as follows:

(4) Based on the control law of the AC side of the rectifier, the PWM modulation unit outputs the switch signal S(k) and acts as a switch tube. 2. a kind of switching control method based on discrete Lyapunov function according to claim 1, is characterized in that: in step (2), is to adjust the difference of the direct current voltage Vdc that is sampled and command direct current voltage Vdc_ref by PI, The difference between the DC voltage Vdc and the command DC voltage Vdc_ref is used as the input of the voltage outer loop, the voltage outer loop is controlled by PI, and the output of the PI regulator obtains the amplitude of the reference current, which is multiplied by the grid voltage phase information to obtain the reference current. i*.

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