A finite-time output feedback control method based on voltage constraint of buck converter

Abstract

The application discloses a finite time output feedback control method based on voltage constraint of a Buck converter, establishes a mathematical model of the Buck converter working in an inductor current continuous mode, and obtains an error dynamic equation; for the output voltage error, an asymmetric barrier Lyapunov function is constructed and derivation is carried out to design a finite time state feedback controller under output limitation; current information is reconstructed by using voltage information of the Buck converter to design a reduced-order observer; an estimated value of the reduced-order observer is transmitted to the finite time state feedback controller to obtain a finite time output feedback controller under output limitation; the output voltage error generates a control signal through the finite time output feedback controller, and a PWM signal is generated by comparing the control signal with a triangular wave signal to control on-off of a controllable switching device. The method saves cost, avoids circuit overheating and hardware damage, and improves system anti-interference capability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of DC-DC converters of pure electric vehicles, and particularly relates to a finite-time output feedback control method based on voltage constraint of a Buck converter. BACKGROUND

[0002] The Buck converter is widely used in electric vehicle systems, photovoltaic systems, fuel cell systems, direct current transmission and the like due to its high efficiency conversion and low cost. Since the converter is a non-smooth, nonlinear time-varying system, on the one hand, it is easily affected by external factors such as voltage perturbation and load jump, and on the other hand, internal factors such as modeling error, parasitic inductance and parasitic capacitance can also cause system instability and performance deficiency, so how to quickly stabilize the voltage in the presence of interference has important practical significance.

[0003] Compared with the asymptotically stable control method, the finite-time control method can reach stability in a limited time in the ideal case where external interference does not exist, and has higher tracking accuracy and stronger anti-interference performance. In actual situations, external interference is inevitable, but due to the existence of fractional power terms, the method can still achieve satisfactory results, so it has attracted the attention of many domestic and foreign researchers.

[0004] Generally speaking, most of the nonlinear control results including the finite-time control method are based on full-state feedback. The design of the state feedback controller requires voltage and current information, which is measured by voltage and current sensors, and the measurement of current generally uses a current sensor based on the Hall effect. However, such current sensor has the following problems: (1) although a low-pass filter can be used, the current measurement result is not accurate due to the high sensitivity of the sensor to measurement noise; (2) the additional circuit using the current sensor causes power loss; (3) the high cost of the current sensor greatly increases the design cost of the controller; (4) when the current sensor is in a high-temperature and high-current environment, it is prone to overheating, which eventually leads to its failure.

[0005] In addition, the requirement for the response speed of the converter to voltage is getting higher and higher, and if there is no limit, the circuit hardware is easy to be damaged. The traditional method of protecting the circuit is to add a current limiter in the hardware circuit, which increases the cost and reduces the conversion efficiency. In addition, in a complex converter system, the traditional PID control method is used for circuit protection, and the parameter adjustment is often too complex, which hinders the optimization of performance. SUMMARY

[0006] In view of the deficiencies in the prior art, the application provides a finite-time output feedback control method based on voltage constraint of a Buck converter.

[0007] The application achieves the above technical objective through the following technical means.

[0008] A finite time output feedback control method based on Buck converter voltage constraint:

[0009] S1, for the Buck converter working in the inductor current continuous mode, a mathematical model is established by using the state space average method, and the output voltage error e=x1=V o -V r is obtained, and the error dynamic equation of the Buck converter system is obtained; wherein, V o represents the output voltage, V r represents the reference output voltage;

[0010] S2, for the output voltage error, an asymmetric barrier Lyapunov function is constructed;

[0011] S3, the result of derivation of the asymmetric barrier Lyapunov function is used to design a finite time state feedback controller under output constraint by using the backstepping method;

[0012] S4, the current information is reconstructed by using the voltage information of the Buck converter working in the inductor current continuous mode, and a reduced-order state observer is designed;

[0013] S5, the estimated value obtained in S4 is transmitted to the finite time state feedback controller to obtain a finite time output feedback controller under output constraint;

[0014] S6, the difference x1 between the output voltage V o and the reference output voltage V r in the circuit is amplified by an error amplifier, and then a control signal is generated by the finite time output feedback controller, and then the PWM signal is generated by comparing the control signal with the triangular wave signal through the PWM generator, and the on-off of the controllable switching device S in the Buck converter system is controlled.

[0015] Further, the Buck converter mathematical model is:

[0016]

[0017] Let the output voltage error e=x1=V o -V r , and the error dynamic equation of the Buck converter system is obtained:

[0018]

[0019] Wherein, V o , i L , C, L, R, Vin Vout, iL, C, L, RL and Vin are output voltage, inductor current, capacitor, inductor, load resistance and input voltage in Buck converter topology respectively, u is the input of Buck converter system, representing duty cycle signal.

[0020] Further, the asymmetric barrier Lyapunov function is specifically:

[0021]

[0022] Wherein, θ1 and θ2 are lower constraint and upper constraint respectively, and the intermediate quantity Satisfies the following relationship:

[0023]

[0024] Further, the derivative of the asymmetric barrier Lyapunov function is:

[0025]

[0026] The intermediate quantity

[0027] Further, the finite time state feedback controller is specifically:

[0028]

[0029] Wherein, α2(x1) is a positive function, δ is a normal number, and the intermediate quantity ε2 satisfies the following relationship:

[0030]

[0031] Wherein, α1(x1) is a positive function, Is a virtual controller.

[0032] Further, when x1 changes in the constraint domain (-θ1, θ2), And timely adjustment, generates sufficient control effect, pulls x1 back from the boundary, and converges to the equilibrium point, so that x1 is always limited in the constraint domain (-θ1, θ2).

[0033] Further, the reduced order state observer is:

[0034]

[0035] Wherein, Is the estimated value of x2, z is an auxiliary variable, and M(x1) satisfies G(x1) represents a gain function.

[0036] Further, the finite time output feedback controller has an output as follows:

[0037]

[0038] The present application has the beneficial effects as follows:

[0039] (1) In the present application, when the system state x1 approaches the constraint boundary, the barrier Lyapunov function will approach infinity, at this time, under the action of the finite time state feedback controller, x1 is always limited within the constraint boundary. Therefore, the output constraint problem can be solved by using the barrier Lyapunov function, and good control effect can be achieved without increasing the calculation burden.

[0040] (2) In the present application, the finite time state feedback controller under the output constraint is designed by constructing the asymmetric barrier Lyapunov function and the finite time state feedback controller under the output constraint, and the finite time output feedback controller with output constraint is designed, the effective constraint of the output voltage is realized, the circuit is protected, and the circuit hardware is prevented from being damaged; compared with the state feedback, the finite time output feedback controller of the present application does not use the current observer, but uses the voltage information to reconstruct the current information, saves the cost, avoids the power loss and the overheating phenomenon, and improves the anti-interference ability of the system. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 The figure is a Buck converter topology structure diagram of the present application;

[0042] Figure 2 The figure is a Buck converter control block diagram of the present application;

[0043] Figure 3 The figure is a Buck converter starting stage response waveform diagram of the present application;

[0044] Figure 4 The figure is a Buck converter variable input voltage stage response waveform diagram of the present application;

[0045] Figure 5 The figure is a Buck converter variable load stage response waveform diagram of the present application. DETAILED DESCRIPTION

[0046] The present application provides a finite time output feedback control method based on Buck converter voltage constraint. In order to make the purpose, technical scheme and effect of the present application more clear and definite, the technical scheme in the embodiment of the present application will be described clearly and completely in combination with the drawings in the embodiment of the present application. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0047] The Buck converter topology diagram of the application is shown in Figure 1 The control block diagram is shown in Figure 2 The topology contains a DC voltage source, a controllable switching device S, a diode D, an inductor L, a capacitor C and a load R. The specific parameters are as follows: input voltage V in = 24V, output voltage V o = 12V, load R = 30Ω, capacitor parameter C = 1mF, inductor parameter L = 1.2mH, system frequency f = 1000kHz.

[0048] The implementation process of a finite time output feedback control method based on Buck converter output constraint is as follows:

[0049] Step 1: for Buck converter working in inductor current continuous mode, the state space average method is used to establish its mathematical model, and then the error dynamic equation is obtained;

[0050] Based on the topology diagram Figure 1 , the Buck converter mathematical model established by the state space average method is as follows:

[0051]

[0052] Wherein, V o , i L are output voltage and inductor current respectively, C and L are capacitor parameter and inductor parameter respectively, R and V in are load resistance and input voltage respectively; u is the input of Buck converter system, representing duty cycle signal, u = 1 represents that switching element is on, and u = 0 represents that switching element is off;

[0053] From the Buck converter mathematical model, let the output voltage error e = x1 = V o -V r , the error dynamic equation of Buck type converter system is obtained:

[0054]

[0055] Wherein, V r represents reference output voltage.

[0056] Step 2: for output voltage error, an asymmetric barrier Lyapunov function is constructed, which is as follows:

[0057]

[0058] Wherein, θ1 and θ2 are lower constraint and upper constraint respectively, which are empirical values; the intermediate quantity satisfies the following relationship:

[0059]

[0060] The derivative of V1(x1) is:

[0061]

[0062] Intermediate variable

[0063] According to the properties of the secant function, when x1∈(-θ1,θ2), there is Therefore, in the design of the finite-time state feedback controller, the is explicitly contained in the controller. When x1 changes within the constraint domain (-θ1,θ2), the will also be adjusted in time, so as to generate sufficient control action to pull x1 back from the boundary and converge at the equilibrium point, so that x1 is always limited within the constraint domain (-θ1,θ2).

[0064] Step 3: Derive the result from the asymmetric barrier Lyapunov function, and design the finite-time state feedback controller under output constraint using backstepping method, which is:

[0065]

[0066] where α2(x1) is a positive function, δ is a normal number, and the intermediate variable ε2 satisfies the following relationship:

[0067]

[0068] where α1(x1) is a positive function, is a virtual controller.

[0069] Step 4: Use the voltage information of the Buck converter operating in continuous inductor current mode to reconstruct the current information, and design a reduced-order state observer; Specifically:

[0070]

[0071] where is the estimated value of x2, z is an auxiliary variable, and M(x1) satisfies G(x1) represents the gain function.

[0072] Step 5: Pass the estimated value from step 4 to the finite-time state feedback controller designed in step 3 to obtain the finite-time output feedback controller under output constraint, and its output is:

[0073]

[0074] Step 6: The output voltage V o in the sensor sensor detection circuit is amplified by the difference x1 of the reference output voltage V r , then a control signal u is generated by the finite time output feedback controller, and the control signal is compared with a triangular wave signal by the PWM generator to generate a PWM signal, which controls the on-off of the controllable switching device S of the Buck converter system to realize the function of maintaining the stability of the output voltage.

[0075] Embodiment: The design of the application is verified by the following simulation results:

[0076] The following gives a comparison of three cases: the system startup time (i.e. the system starts to respond to the system steady state), the output waveforms of the finite time output feedback controller and the PI controller are compared; the system suddenly changes the input voltage, the output waveforms of the finite time constrained output feedback controller, the finite time unconstrained output feedback controller and the PI controller are compared; the system suddenly changes the load, the output waveforms of the finite time constrained output feedback controller, the finite time unconstrained output feedback controller and the PI controller are compared.

[0077] Case 1: Response waveform of Buck converter at startup time

[0078] As shown in Figure 3 , under the given reference output voltage 12V, the finite time constrained output feedback controller of the application and the PI controller are compared from startup to stable state; from the simulation results, it can be concluded that the PI controller has a larger overshoot, takes longer time to reach steady state, and exceeds the constraint boundary.

[0079] Case 2: Response waveform of Buck converter when input voltage suddenly changes

[0080] As shown in Figure 4 , at t=0.6s, the input voltage suddenly changes from 24V to 34V, and at t=0.63s, the input voltage suddenly changes from 34V to 24V, and the voltage response waveforms under the three controllers are observed; from the simulation graph, the voltage fluctuation of the finite time constrained output feedback controller of the application is smaller than that of the finite time unconstrained output feedback controller and the PI controller, the convergence speed is faster, and the finite time unconstrained output feedback controller and the PI controller both exceed the constraint boundary, which shows that the finite time constrained output feedback controller of the application has stronger anti-input voltage change ability.

[0081] Case 3: Response waveform of Buck converter when load suddenly changes

[0082] As shown in Figure 5As shown, at t=0.6s, the load resistance is suddenly changed from 30Ω to 20Ω, at t=0.63s, the load resistance is suddenly changed from 20Ω to 30Ω, and the voltage response waveforms under the three controllers are observed; from the simulation results, the voltage overshoots of the finite time constrained output feedback controller are less than those of the finite time unconstrained output feedback controller and the PI controller, and the time to reach the steady state is shorter, only the finite time constrained output feedback controller is always kept within the constraint boundary, which shows that the finite time constrained output feedback controller of the application has stronger anti-load change ability.

[0083] The embodiments are preferred embodiments of the application, but the application is not limited to the above embodiments, and any obvious improvements, replacements or modifications made by those skilled in the art without departing from the essential content of the application shall fall within the protection scope of the application.

Claims

1. A finite-time output feedback control method based on voltage constraint of Buck converter, characterized in that: S1, for Buck converter working in inductor current continuous mode, the mathematical model is established by state space averaging method. From the mathematical model of Buck converter, let output voltage error e=x1=V o -V r , the error dynamic equation of Buck converter system is obtained; where V o represents the output voltage, V r represents the reference output voltage; S2, for the output voltage error, an asymmetric barrier Lyapunov function is constructed; S3, the result of derivation of the asymmetric barrier Lyapunov function is used to design a finite-time state feedback controller under output constraint by using backstepping method; The asymmetric barrier Lyapunov function is specifically: where θ1, θ2 are lower and upper constraints, respectively, and the intermediate quantity satisfies the following relationship: S4, the current information is reconstructed by using the voltage information of the Buck converter working in the continuous mode of inductor current, and a reduced-order state observer is designed; S5, the estimated value obtained in S4 is transmitted to the finite-time state feedback controller to obtain a finite-time output feedback controller under output constraint; S6, the output voltage V o the difference x1 between the reference output voltage V r amplified by the error amplifier, and then a control signal is generated by the finite-time output feedback controller. The control signal is compared with the triangular wave signal by the PWM generator to produce a PWM signal, which controls the on-off of the controllable switching device S in the Buck converter system.

2. The finite-time output feedback control method based on Buck converter voltage constraint according to claim 1, wherein, The mathematical model of the Buck converter is: Let the output voltage error e = x1 = V o -V r The error dynamic equation of the Buck converter system is obtained as follows: where V o , i L , C, L, R, V in are the output voltage, inductor current, capacitance, inductance, load resistance and input voltage in the Buck converter topology, respectively, and u is the Buck converter system input, representing the duty cycle signal.

3. The finite-time output feedback control method based on Buck converter voltage constraint according to claim 1, wherein, The result of derivation of the asymmetric barrier Lyapunov function is: intermediate amount 4. The finite-time output feedback control method based on Buck converter voltage constraint according to claim 3, characterized in that, The finite-time state feedback controller is specifically: Wherein, α2(x1) is a positive function, δ is a normal number, and the intermediate quantity ε2 satisfies the following relationship: wherein a1(x1) is a positive function, is a virtual controller.

5. The finite-time output feedback control method based on Buck converter voltage constraint according to claim 4, wherein, When x1 varies within the constraint domain (-θ1, θ2), And timely adjustment, produce control effect, pull x1 from the boundary back, and converge to the equilibrium point, so that x1 is always limited within the constraint domain (-θ1, θ2).

6. The finite-time output feedback control method based on Buck converter voltage constraint according to claim 4, wherein, The reduced-order state observer is: wherein is an estimate of x2, z is an auxiliary variable, and M(x1) satisfies G(x1) denotes a gain function.

7. The finite-time output feedback control method based on Buck converter voltage constraint according to claim 6, wherein, The output of the finite-time output feedback controller is:

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