CN106374765A - An inverter control system without back electromotive force sensor and its control method - Google Patents

Abstract

The invention discloses an inverter control system of a sensor without back electromotive force and a control method thereof. The inverter control system of the sensor without back electromotive force is constructed by using a single-phase bridge-type inverter, a current sensor, a driver, an observer as well as electric wires and signal wires, the signal of the back electromotive force is taken as an unknown periodic function, a time-varying state-space model of the inverter is constructed, a time-varying Lebesgue observer is designed based on the time-varying state-space model, output current information is obtained in combination with the current sensor, the back electromotive force is reconstructed, the reconstructed back electromotive force is introduced into the current model predictive control algorithm of an inverter controller, so that accurate tracking of an output current signal when the inverter is free of the back electromotive force is realized.

Description

An inverter control system without back electromotive force sensor and its control method

technical field

The invention relates to an inverter control system without a reverse electromotive force sensor and a control method thereof.

Background technique

The inverter realizes energy conversion from DC to AC by controlling the output current of the AC terminal. It is the core device for photovoltaic grid-connected and AC motor control. The current control method of the inverter is the premise to ensure the normal operation of the inverter. Traditional control methods require sensors to measure the current and back EMF at the output. Depending on the application, the reverse electromotive force can be the grid voltage or the induced electromotive force of the AC motor. High-precision sensors increase the cost of the system; and sensor failure can lead to system failure. Therefore, a controller with fewer sensors makes sense.

Contents of the invention

The purpose of the present invention is to propose an inverter control system without a back electromotive force sensor and its control method, which can realize high-precision control of the inverter current without using a voltage sensor, which can not only reduce the use of sensors, The cost of the inverter controller can be reduced, and the reliability of the inverter controller can also be improved.

An inverter control system without a back electromotive force sensor of the present invention includes an inverter, a current sensor, a back electromotive force, an observer, a controller and a driver, wherein one end of the inverter inputs direct current, and the other end outputs an inverter A current sensor is connected in series on the AC line, and the current sensor samples the current signal at a certain sampling frequency and sends it to the observer; the observer uses the sampled current signal to reconstruct the back electromotive force based on the time-varying state-space model Voltage value: send the voltage value to the controller, the controller generates a control signal based on the current model predictive control algorithm, and sends the control signal to the driver to generate the corresponding high and low levels, and sends it to the inverter through the wire.

A control method for an inverter control system without a back electromotive force sensor, comprising the steps of:

Step 1. The current sensor samples the current signal at a certain sampling frequency, and sends the sampled current signal to the observer for observation;

Step 2. The observer takes the sampled current signal and the back electromotive force to be reconstructed as new state quantities, and establishes an augmented state space model:

The sampled current signal is denoted as i _l (t), the back electromotive force signal to be reconstructed is denoted as U _s (t), and the differential equation of the dynamic process of the inverter control system is

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Where i _l (t)′ is the time derivative of the sampled current signal i _l (t), U _dc is the DC power supply voltage, L and R are the system integrated inductance and resistance, S represents the control signal, and its value range is {-1,0,1}, S=1 means direct input of DC voltage, S=0 means no output of DC voltage, S=-1 means reverse output of DC voltage;

Considering that the back electromotive force signal is a sinusoidal function under steady-state conditions, and its frequency is the grid voltage of 50 Hz, U _s (t) can be decomposed into the sum of the standard sine and cosine functions whose amplitudes are A and B respectively:

U _s (t)＝Asin(ωt)+Bcos(ωt) (2)

Among them, the angular frequency ω=2πf, f=50Hz, A and B are constants, the values of parameters A and B can be observed by the observer, and U _s (t) can be calculated, and the back electromotive force U _s ( t) reconstruction, substituting parameters A and B into formula (1), a new state-space model in the form of an augmented matrix of the inverter control system can be obtained, and the state-space model is a linear time-varying model, that is, i _l ( t) is defined as x ₁ , A and B are used as new variables x ₂ and x ₃ , and the state space model that expands formula (1) into an augmented matrix form is as follows:

$\left\{\begin{array}{c}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}& \frac{\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}& \frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; S</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\mathrm{<span\; class="notranslate">\; x</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

in, Indicates the derivative of the vector x, y is the output current;

Step 3. Design a time-varying Lebesgue observer for formula (3), and prove the validity of the Lebesgue observer, and realize the online observation of parameters A and B in step 2, thereby reconstructing the reverse Electromotive force U _s (t), the design of the Lebesgue observer is based on the Lyapunov function, and the Russell invariant set principle is used to ensure the convergence of the Lebesgue observer;

Step 4. Send the back electromotive force U _s (t) obtained in step 3 to the controller, combine the sampled current signal i _l (t) into formula (8) to solve the following optimal problem, generate a control signal S, and control the The signal S is sent to the driver to generate the corresponding high and low levels, and sent to the inverter through the wire, so that the load current i _l (t) tracks the sinusoidal expected current set above:

$\begin{array}{cc}\underset{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}& <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; RT</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span>\end{array}$

s.t.S ∈ {-1,0,1} (8).

The invention utilizes single-phase bridge inverter, current sensor, driver, observer, electric wires and signal lines to build an inverter control system without back electromotive force sensor, takes the back electromotive force signal as an unknown periodic function, and constructs an inverter Based on the time-varying state-space model of the detector, a time-varying Lebesgue observer is designed based on the time-varying state-space model, and combined with the current sensor to obtain the output current information, the back electromotive force is reconstructed, and the reconstructed back electromotive force The current model predictive control algorithm of the inverter controller is introduced to realize the accurate tracking of the output current signal of the inverter when there is no back electromotive force sensor.

Description of drawings

Fig. 1 is the schematic diagram of the inverter control system without back electromotive force sensor of the present invention;

Fig. 2 is a work flow chart of the present invention;

Fig. 3 is the experimental result that the observed value of A and B of the present invention reconstructs back electromotive force;

Fig. 4 is the experimental result of the back electromotive force of the present invention reconstruction and true value error;

Fig. 5 is the result of the current tracking experiment reconstructed based on the back electromotive force observation of the present invention.

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

detailed description

The present invention utilizes a single-phase bridge inverter, a current sensor, a driver, an observer, and electric wires and signal lines to construct an inverter control system without a back electromotive force sensor, uses a current sensor to obtain output current information, and inputs the obtained current information The Lebesgue observer reconstructs the voltage value of the back electromotive force from the observed back electromotive force signal and the current signal measured by the current sensor, and applies the voltage value to the current model predictive control algorithm of the controller to generate a control signal, The actual output current of the inverter can accurately and quickly track the expected current, and realize the accurate tracking of the inverter current when the inverter has no back electromotive force sensor.

An inverter control system without a back electromotive force sensor of the present invention, as shown in Figure 1, includes an inverter 3, a current sensor 4, a back electromotive force 5, an observer 7, a controller 8 and a driver 9, wherein, One end of the inverter 3 inputs the DC power supply 1, and the other end outputs the inverted AC power. A current sensor 4 is connected in series on the AC line. The current sensor 4 samples the current signal at a certain sampling frequency and sends it to the observer 7; Based on the time-varying state space model, the device 7 uses the sampling current signal to reconstruct the voltage value of the back electromotive force 5; the voltage value is sent to the controller 8, and the controller 8 generates a control signal based on the current model predictive control algorithm, and the control signal Send it to the driver 9 to generate corresponding high and low levels, and send it to the inverter 3 through wires, so that the actual current can accurately and quickly track the expected current, and realize the accurate tracking of the current signal when the inverter has no back electromotive force sensor.

As shown in Figure 2, a control method of an inverter control system without a back electromotive force sensor in the present invention, especially focuses on the reconstruction of the back electromotive force, and specifically includes the following steps:

Step 1, constructing an inverter control system without a back electromotive force sensor including a single-phase bridge inverter 3, a current sensor 4, a back electromotive force 5, an observer 7, a controller 8 and a driver 9, wherein the single-phase One end of the bridge inverter 3 inputs a DC power supply, the other end outputs an inverted AC power, and a current sensor 4 is connected in series. The current sensor 4 samples the current signal at a certain sampling frequency, and after integral amplification and filtering processing, the The sampled current signal is sent to the observer 7 for observation;

Step 2. The observer 7 takes the sampled current signal and the back electromotive force to be reconstructed as new state quantities, and establishes an augmented state space model:

The sampled current signal is recorded as i _l (t), and the back electromotive force signal to be reconstructed is recorded as U _s (t). The dynamic process of the inverter control system can be described as:

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, i _l (t) is the sampled current signal, U _s (t) is the back electromotive force, U _dc is the DC power supply voltage, L and R are the system integrated inductance and resistance, i _l (t)′ is i _l (t) The derivative with respect to time, S represents the control signal, and its value range is {-1,0,1}, S=1 represents direct input of DC voltage, S=0 represents no output of DC voltage, S=-1 represents DC voltage reverse output;

Considering that the back electromotive force signal is a sinusoidal function under steady-state conditions, and its frequency is the grid voltage of 50 Hz, U _s (t) can be decomposed into the sum of the standard sine and cosine functions whose amplitudes are A and B respectively:

U _s (t)＝Asin(ωt)+Bcos(ωt) (2)

Wherein, the angular frequency ω=2πf, f=50Hz, A and B are constants, and the values of the parameters A and B are observed by the observer 7, and U _s (t) can be calculated, and the back electromotive force U _s can be realized Reconstruction of (t), by substituting parameters A and B into formula (1), a new state-space model in the form of an augmented matrix of the inverter control system can be obtained, and the state-space model is a linear time-varying model, namely i _l (t) is defined as x ₁ , A and B are used as new variables x ₂ and x ₃ , and the original state-space model (that is, formula (1)) is expanded into a state-space model in the form of an augmented matrix as follows:

$\left\{\begin{array}{c}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}& \frac{\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}& \frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; S</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\mathrm{<span\; class="notranslate">\; x</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

in, Indicates the derivative of the vector x, y is the output current;

Step 3. Design a time-varying Lebesgue observer 7 for formula (3), and prove the effectiveness of the Lebesgue observer 7, and realize the online observation of parameters A and B in step 2, thereby reconstructing Back electromotive force, the specific method is as follows:

Step 31. Construct an observer model based on the inverter model, such as formula (4), initialize each state quantity, and at k=0, the state quantity Set the parameter l ₀ , the calculation period is Ts, and its state estimation value It can be directly measured that this man-made system is a state observer, through the output error to correct the estimated model of the state, so that the estimated value of the state Tend to the real state of the system:

$\left\{\begin{array}{c}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}& \frac{\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}& \frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; +</span>\left[\begin{array}{c}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ \frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}\\ \frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}\end{array}\right]<span\; class="notranslate">\; \&times;</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

where the error signal is defined as Then the dynamic system of the error signal is:

$\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& \frac{\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}& \frac{\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}\\ \frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

If it is proved that when t→∞, the state quantity will converge to x, that is, approaching 0, it can be proved that the Lebesgue observer 7 can observe the parameters A and B, which proves that the back electromotive force reconstruction method proposed by the present invention is effective. The present invention utilizes the designed Lyapunov function and Russell invariant set principle to prove its validity;

Proposition 1 (Designing Lyapunov Functions): Definition D=I is a diagonal matrix, then V is a Lyapunov function;

Proof 1: Since D is a positive definite diagonal matrix, at the same time

$\begin{array}{cc}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; V</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; )</span>& {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

where V is continuously differentiable and satisfies:

(1) V(0)=0, and for all

(2) In R ²⁽ⁿ⁺¹⁾ ,

Therefore, V is a Lyapunov function, Proposition 1 is proved;

Proposition 2 (Observer convergence analysis): The state quantity of the observer Converge on the state quantity x;

Proof 2: Since the error system is a time-varying system, the validity of the observer 7 is proved by the Russell invariant set principle as follows:

define set It can be seen that it is a consistent positive invariant set of the error system;

definition is the largest invariant set in the set S(R);

According to Russell's invariant set principle, when t→∞, every point starting from S(R) converges to E, that is, for any Satisfied

At the same time, for satisfy

Since the set {cos(ωt)sin(ωt)} is linearly independent, the solution to the above equation exists and is unique, the largest invariant set is a single-element set, whose element is the origin, Proposition 2 is proved;

Step 4. Discrete implementation of observer 7

From the observer equation we know:

$<span\; class="notranslate">\; \{</span>\begin{array}{c}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 1</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

At time k, x ₁ (k) is obtained after integrating the collected current signal, and the continuous observer is written in a discrete form, and the estimated value of each state at time k+1 is:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&lsqb;</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

Calculation error When the relative error approaches 5%, it can be considered that the error has converged and meets the requirements, and the state estimation value has tended to the real state of the system, and the parameter Therefore, each frequency component at time k can be calculated, and the amplitude and phase of the fundamental wave and each harmonic can be further calculated; if the relative error does not meet the requirements, the observer 7 enters the next iteration, using the output current i _l ( The error of the measured value of t) and the observed value is used to correct parameters A and B; the parameters A and B obtained above are substituted into (2) formula to obtain the back electromotive force U _s (t);

Record the expected current as i _l *(t), the value at the kth sampling time is recorded as i _l *(k), from U _s (k) and the actual measured output current i _l (k), solve the following optimal question:

$\begin{array}{cc}\underset{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}& <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; RT</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span>\end{array}$

s.t.S ∈ {-1,0,1} (8)

That is, the high-precision tracking of the current is realized, as shown in Figure 5;

Step 5, the back electromotive force U _s (t) is sent to the controller 8, the controller 8 generates the control signal S based on the formula (8) (ie, the current model predictive control algorithm), and sends the control signal S to the driver 9 to generate The corresponding high and low levels are sent to the inverter 3 through wires, so that the actual current can accurately and quickly track the expected current.

In order to verify the effectiveness of the control without back electromotive force sensor of the present invention, an experimental platform without back electromotive force sensor is set up. Figure 3 and Figure 4 reflect the identification process of the back electromotive force, the back electromotive force jumps from 3V to 1.6V, and the observer identifies the new value within five cycles, as shown in Figure 3. And under the two different reverse electromotive forces, the error between the identification value and the real value is kept within 0:2V, as shown in Figure 4. Figure 5 shows that the tracking current is basically not affected by the jump and can accurately track the upper expected current. Therefore, the control without the reverse electromotive force sensor of the present invention will not reduce the reliability of the system; meanwhile, the use of sensors can be reduced, and the cost of the inverter controller can be reduced.

The above are only preferred embodiments of the present invention, and do not limit the technical scope of the present invention in any way, so any minor modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention still belong to within the scope of the technical solutions of the present invention.

Claims (2)

1. An inverter control system without a reverse electromotive force sensor is characterized by comprising an inverter, a current sensor, a reverse electromotive force sensor, an observer, a controller and a driver, wherein one end of the inverter inputs direct current, the other end of the inverter outputs inverted alternating current, a current sensor is connected in series on an alternating current circuit, and the current sensor samples a current signal at a certain sampling frequency and sends the current signal to the observer; the observer reconstructs a voltage value of the back electromotive force by utilizing the sampling current signal based on a time-varying state space model; and the voltage value is sent to a controller, the controller generates a control signal based on a current model predictive control algorithm, and the control signal is sent to a driver to generate a corresponding high level and a corresponding low level and is sent to the inverter through a lead.

2. The control method of the inverter control system without the back electromotive force sensor according to claim 1, comprising the steps of:

step 1, a current sensor samples a current signal at a certain sampling frequency, and sends the sampled current signal to an observer for observation;

step 2, the observer takes the sampled current signal and the back electromotive force to be reconstructed as a new state quantity, and an augmented state space model is established:

the sampled current signal is denoted as i_l(t) the back EMF signal to be reconstructed is denoted as U_s(t), the differential equation of the dynamics of the inverter control system is

$i_l{\left(t\right)}^{\&prime;}=\frac{-R}{L}{i}_l\left(t\right)+(U_{dc}\&times;S-U_s(t\left)\right)---\left(1\right)$

Wherein i_l(t)' is the sampled current signal i_l(t) timeDerivative of, U_dcThe direct current power supply voltage is L, R, the inductor and the resistor are integrated in a system, S represents a control signal and has a value range of { -1,0,1}, S ═ 1 represents direct input of the direct current voltage, S ═ 0 represents no output of the direct current voltage, and S ═ 1 represents reverse output of the direct current voltage;

considering that the back electromotive force signal under the steady state working condition is a sine function, and the frequency of the back electromotive force signal is 50Hz and U of the power grid voltage_s(t) can be decomposed as the sum of the standard sine and cosine functions with amplitudes a and B, respectively:

U_s(t)＝Asin(ωt)+Bcos(ωt) (2)

where the angular frequency ω is 2 pi f, f is 50Hz, and a and B are constants, U can be calculated by observing the values of parameters a and B by an observer_s(t), namely, the counter electromotive force U can be realized_s(t) reconstructing, and substituting the parameters A and B into the formula (1), so as to obtain a new state space model in the form of an augmentation matrix of the inverter control system, wherein the state space model is a linear time-varying model, i.e. i_l(t) is defined as x₁A and B as new variables x₂、x₃The state space model expanding the formula (1) into the form of an augmented matrix is as follows:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\left[\begin{array}{ccc}\frac{-R}{L}& \frac{cos\left(\mathrm{\&omega;}t\right)}{L}& \frac{sin\left(\mathrm{\&omega;}t\right)}{L}\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]x+U_{dc}\&times;S\\ y=\&lsqb;\begin{array}{ccc}1& 0& 0\end{array}\&rsqb;x\end{array}\right.---\left(3\right)$

wherein,represents the derivative of the vector x, y being the output current;

step 3, designing a time-varying Leeberg observer aiming at the formula (3), proving the effectiveness of the Leeberg observer, and realizing the online observation of the parameters A and B in the step 2 so as to reconstruct the back electromotive force U_s(t), the design of the Leiberg observer is based on the Lyapunov function, and the convergence of the Leiberg observer is ensured by adopting the Lassel invariant set principle;

step 4, the back electromotive force U obtained in the step 3 is used_s(t) to a controller, combining the sampled current signal i_l(t) substituting the formula (8) to solve the following optimal problem, generating a control signal S, sending the control signal S to a driver to generate corresponding high and low levels, and sending the control signal S to an inverter through a lead so as to enable a load current i_l(t) tracking the set sinusoidal desired current:

$\begin{array}{cc}\underset{S}{\min }& |i_l^{*}(k+1)-(1-\frac{{\mathrm{RT}}_s}{L})\&times;i_l(k+1)+U_s\left(k\right)-U_{dc}\&times;S|\\ s.t.& S\&Element;\{-1,0,1\}\end{array}---\left(8\right).$