A fuzzy switching auto-disturbance rejection control method for a starter-generator system with a continuous dwell time

Abstract

The present invention belongs to the technical field of control of starting-generating systems, and discloses a fuzzy switching anti-disturbance control method for starting-generating systems under continuous residence time. The present invention considers the multi-modal working conditions caused by load switching in the starting-generating system, and proposes a design method for a fuzzy switching anti-disturbance controller for disturbance suppression control analysis of the switching system. Based on the analysis of the disturbance suppression capability of the starting-generating system, the present invention further ensures the ability of the starting-generating system to actively suppress disturbances under load switching by designing a fuzzy switching anti-disturbance controller, effectively improving the robustness of the starting-generating system, and having certain engineering value.

Description

Technical Field

[0001] The invention belongs to the technical field of starting-generating system control, and relates to a fuzzy switching self-disturbance rejection control method of a starting-generating system under a continuous dwell time. Background Art

[0002] The starter-generator system is widely used in the fields of more-electric aircraft engines, new energy vehicles, etc., and plays a vital role in the working process of aircraft and electric vehicles. Taking more-electric aircraft engines as an example, in order to prevent the injection-ignition from burning the combustion chamber at zero rotor speed, a starter motor is required to drag the compressor of the aircraft engine to the ignition speed. In addition, when the engine reaches the idle speed, the generator extracts the shaft power and is driven by the engine rotor to power the onboard electrical equipment to ensure sufficient aircraft power. Since the load of the starter-generator will switch during the starting process and the power generation process, the starter-generator system has the characteristics of multi-mode and strong nonlinearity, and can be regarded as a type of switching nonlinear system. Therefore, in the control research of the starter-generator system, the traditional controller design method has a certain degree of conservatism. The control performance of the switching system not only depends on the performance of each subsystem, but is also seriously affected by the switching process. In the control research of the switching system, the stability of the switching process and the interference suppression ability are two key research contents. As a type of robust controller with the ability to actively suppress disturbances, the active disturbance rejection controller is widely used in many control occasions with frequent noise. The core idea of ​​the ADRC is to expand the system disturbance into a new system state, design a type of disturbance observer, and actively compensate for the system disturbance in the feedback control law. Compared with the traditional robust controller, the ADRC has the characteristics of small model dependence and strong applicability. The TS fuzzy method can realize the linearization of nonlinear systems. By reasonably defining fuzzy sets and designing fuzzy rules, the TS fuzzy method is a key auxiliary means for complex system analysis and improving the effectiveness of controller design. For typical switching nonlinear systems such as starting-generating systems, considering the switching characteristics, studying the design of the fuzzy switching ADRC is of great significance to ensure the robustness of the starting-generating system.

[0003] Most of the existing control analysis of starter-generator systems focuses on the system's ability to suppress disturbances, while ignoring the impact of the load switching process on system performance (X.Lang, T.Yang, G.Bai, S.Bozhko and P.Wheeler, "Active Disturbance Rejection Control of DC-Bus Voltages Within aHigh-SpeedAircraft Electric Starter / Generator System," in IEEE Transactions onTransportation Electrification, vol.8, no.4, pp.4229-4241, Dec.2022, doi:10.1109 / TTE.2022.3164351.), and the designed disturbance rejection controller is conservative. In addition, most of the research results on robust control of switching systems consider the ability of the system output to suppress disturbances. For example, by establishing the norm relationship between the state and the disturbance, it is obtained that the system has H ∞ Performance (L.Long and J.Zhao, "H∞Control of Switched NonlinearSystems in p-Normal Form Using Multiple Lyapunov Functions," in IEEETransactions on Automatic Control, vol.57, no.5, pp.1285-1291, May 2012, doi:10.1109 / TAC.2012.2191835.) or L ∞Performance (M.Naghnaeian and PGVoulgaris,"Characterization and Optimization of L∞Gains of Linear Switched Systems,"inIEEE Transactions on Automatic Control,vol.61,no.8,pp.2203-2218,Aug.2016,doi:10.1109 / TAC.2015.2494369.) etc. However, in actual engineering applications, simply ensuring that the state is affected by disturbances is far from enough to meet the system's robustness requirements. A system with the ability to actively suppress disturbances will have stronger robustness and faster response speed in actual engineering. Existing results have almost no research content on switching analysis and fuzzy switching anti-disturbance control of the starting-generating system. How to ensure the active disturbance suppression capability of the starting-generating system under load switching is the advantage of fuzzy switching anti-disturbance control, and is also a problem of concern to the present invention. Summary of the invention

[0004] In order to ensure the active disturbance suppression capability of the starting-generating system under load switching conditions and improve the robustness of the system, the present invention proposes a fuzzy switching self-disturbance rejection control method under a continuous residence time of the starting-generating system, and applies it to the speed and DC voltage control of the starting-generating system.

[0005] The technical solution of the present invention:

[0006] A fuzzy switching auto-disturbance rejection control method for a starting-generating system with a continuous dwell time, the specific steps are as follows:

[0007] Step 1: Consider the working process of load switching and obtain the form of the starting-generation switching system;

[0008] Step 2: Design TS fuzzy rules, perform fuzzy linearization on the nonlinear system of starting-generation switching, and obtain the mathematical model of the fuzzy starting-generation switching system;

[0009] Step 3: Considering the influence of disturbance on the system, the fuzzy switching anti-disturbance controller is designed, including the fuzzy switching extended state observer and the fuzzy switching feedback control law design;

[0010] Step 4: Establish a dynamic error system. By designing multiple Lyapunov functions, consider the impact of the switching process on the performance of the starting-generating system. Under the switching signal design scheme with a continuous dwell time, study the stability of the error system and the L ∞ Performance conditions;

[0011] Step 5: Propose solvable optimization conditions and optimize the parameters of the fuzzy switching ADRC to ensure the stability of the starting-generating system, L ∞ performance and controller effectiveness;

[0012] Step 6: Carry out fuzzy switching anti-disturbance control simulation experiments for the speed and DC voltage loops respectively, and analyze the control performance.

[0013] Beneficial effects of the present invention: The present invention considers the multi-modal working conditions caused by load switching in the starting-generating system, analyzes the disturbance suppression control of the switching system, and proposes a design method for a fuzzy switching auto-disturbance rejection controller. Based on the analysis of the disturbance suppression capability of the starting-generating system, the present invention further ensures the ability of the starting-generating system to actively suppress disturbances under load switching by designing a fuzzy switching auto-disturbance rejection controller, effectively improving the robustness of the starting-generating system and having certain engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a permanent magnet starting-generating system structure;

[0015] Figure 2 is the continuous residence time structure of stage κ;

[0016] Figure 3 Switching signals for the designed system;

[0017] Figure 4 is the motor mechanical angular velocity control curve;

[0018] Figure 5 It is the mechanical angular velocity tracking error and observation error in the starting experiment.

[0019] Figure 6 is the DC bus voltage control curve;

[0020] Figure 7 are the voltage tracking error and observation error in the power generation experiment. DETAILED DESCRIPTION

[0021] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0022] Specific implementation steps:

[0023] 1) Modeling of the starting-generation switching system

[0024] The specific structure of the starting-generating system is as follows: Figure 1As shown, it mainly includes a starter-generator, a drive device with an inverter / rectifier function, and a load device, wherein the load is manifested as a load torque dragged on the motor shaft under the starting condition, and the load is manifested as a power consumption device on the DC voltage side under the power generation condition, which is represented in the form of a resistor in the figure.

[0025] The switching of loads will directly cause the speed and DC voltage control loops of the starter-generator system to exhibit the characteristics of a switching system. Under starting conditions, considering different loads connected to the shaft, the speed control loop can be expressed as a switching system as shown below:

[0026]

[0027] in, ω m is the mechanical angular velocity of the motor, T e is the electromagnetic torque, T 2Li is the switchable load torque, i∈S represents the system mode, S is the set of all system modes, B is the viscous friction coefficient, J is the moment of inertia, and K is a given constant.

[0028] For power generation conditions, considering the switching of load resistance value, the DC voltage control loop can also be expressed as a switching system:

[0029]

[0030] Among them, u dc Indicates DC voltage, i dc Represents DC current, R i is the switchable load resistor, C is the DC side voltage stabilizing capacitor, Δ R Used to describe fluctuations in resistance value.

[0031] 2) TS fuzzy switching system modeling

[0032] For system (1), the given system parameters are as follows:

[0033] Moment of inertia: J = 10 -4 Kg·m 2 , viscous friction coefficient: B = 10 -5 , K = 10 -8 , motor speed range: ω m ∈[0,10 4 )rads / min, system mode: i∈{1,2}, switching load torque: T 2L1 =10 -5 ω m , T 2L2 =0.

[0034] Choose x = ωm , u=T e , the specific form of the speed control system can be obtained as:

[0035] When system mode i=1:

[0036]

[0037] When system mode i=2:

[0038]

[0039] In order to ensure the effectiveness of control analysis and controller design, the nonlinear terms in the system can be quantified by TS fuzzy method. -4 x 2 Perform fuzzy linearization. First, select the number of fuzzy rules as 2 and set the antecedent variable to the system state x.

[0040]

[0041] By fitting the nonlinear terms by means of upper and lower bounds, we can obtain

[0042]

[0043] From formula (3), we can calculate the membership function

[0044] h 11 (x(t)) = h 21 (x(t))=10 -4 x(t),

[0045] h 12 (x(t)) = h 22 (x(t))=1-10 -4 x(t).

[0046] Therefore, the speed fuzzy switching system can be expressed as

[0047]

[0048] Among them, a 11 =-1.2, a 12 =-0.2, a 21 =-1.1, a 22 =-0.1, b il =10 4 .

[0049] For system (2), set the system parameters as follows:

[0050] Voltage stabilizing capacitor: C = 2mF, system mode: i∈{1,2}, switchable load resistance value: R1 = 2kΩ, R2 = 1kΩ, resistance floating: Δ R =0.4sin(u dc ).

[0051] Choose x=u dc , u=i dc , the DC voltage switching system can be expressed as:

[0052] When system mode i=1:

[0053]

[0054] ●When system mode i=2:

[0055]

[0056] Select the number of fuzzy rules as 2, and set the antecedent variable as the system state x. By using the TS fuzzy method, the nonlinear terms contained in the system under mode 1 and mode 2 are fuzzy linearized, and we can get

[0057]

[0058] Based on formula (4), the membership function can be calculated

[0059] h 11 (x(t)) = h 21 (x(t))=0.5+0.5sin(x(t)),

[0060] h 12 (x(t)) = h 22 (x(t))=1-(0.5+0.5sin(x(t)))=0.5-0.5sin(x(t)).

[0061] Therefore, the DC voltage fuzzy switching system can be expressed as:

[0062]

[0063] Among them, a 11 =-0.35, a 12 =-0.15, a 21 =-0.7, a 22 =-0.3, b il =500.

[0064] 3) Design of fuzzy switching auto-disturbance rejection controller

[0065] Based on the fuzzy modeling of the starter-generator switching system, the starter-generator system has the following general form when load switching is considered, after TS fuzzy linearization, and system disturbance is considered:

[0066]

[0067] Here, ω represents the system disturbance.

[0068] In order to ensure that the starting-generating system has the ability to actively suppress disturbances, a fuzzy switching anti-disturbance controller is designed for system (5). The specific form of the controller is as follows:

[0069] Fuzzy switching extended state observer:

[0070]

[0071] Fuzzy switching feedback control law:

[0072]

[0073] Where r is the reference signal, and denote the observed values ​​of x and ω respectively, and g il are the observer gain and controller gain to be optimized, respectively. il >0 and b il is a given constant.

[0074] 4) System stability analysis

[0075] In order to analyze the stability of the control system, the error system model is established. The tracking error and observation error are defined as e s = rx and The specific form of the tracking error and observation error system is

[0076]

[0077]

[0078] in,

[0079] The tracking error system (8) and the observation error system (9) can be organized into state space form:

[0080]

[0081] Where, e=[e s e c ] T ,

[0082] The structure of the continuous dwell time is shown as follows Figure 2 As shown. Taking the κth stage as an example, the continuous residence time includes two components, which require that the system switching must have a duration of no less than τ p The dwell time of the system is also allowed to Multiple switching occurs within the interval, and the interval between two adjacent switching times must be less than τ p .

[0083] Given parameters α>0 and μ>1, if there exists γ>0 and the system modally dependent Lyapunov function V σ (e(t)): in is a field of positive real numbers, such that S represents the set of system modes, and i≠j, the following conditions are All are established:

[0084]

[0085] V i (e(t s ))≤μV j (e(t s )), (12)

[0086] Then you can get

[0087]

[0088] in, and denote the starting time of the κth and κ+1th stages respectively, and Respectively Moment and The system mode at time, represent The total number of system mode changes in the interval.

[0089] If the residence time τ in each stage p Satisfy τ p >1 / f s , further, we can get

[0090]

[0091] Among them, T s and f s They represent the maximum operating time and the maximum mode switching frequency of the T stage respectively, and t0 represents the initial time.

[0092] Based on formula (13), we can conclude that:

[0093] If the residence time in each stage meets the following conditions:

[0094]

[0095] Then, when time t is large enough, the error system (10) is uniformly asymptotically stable under the disturbance f≡0.

[0096] In addition, if the system disturbance f≠0, if the Lyapunov function is selected as the following standard quadratic form:

[0097] V i (e) = e T P i e,

[0098] in, is the positive definite symmetric matrix to be solved.

[0099] From equations (13) and (14), it can be concluded that the dynamic error system (10) has L ∞ Disturbance suppression capability, in the form of:

[0100] ||e(t)|| ∞ ≤γ1||f(t)|| ∞ ,

[0101] in, λ min (P i ) represents the matrix P i The minimum eigenvalue of .

[0102] 5) Controller parameter optimization

[0103] By choosing Among them, P i =diag{p 1i p 2i}, it is easy to obtain the following inequality is a sufficient condition for equation (11) and equation (12):

[0104]

[0105] p 1i ≤μp 1j , p 2i ≤μp 2j , (16)

[0106] in,

[0107] Y=-γ 2 I, I = diag{1 1}.

[0108] Therefore, given the parameters α>0 and μ>1, if there exists p 1i >0, p 2i >0,z 1ik , z 2ik and γ>0, so that equations (15) and (16) hold, then the dynamic fuzzy error system (10) is uniformly asymptotically stable and has L not exceeding γ1 ∞ Performance gain. In addition, the optimized fuzzy switching ADRC parameters can be expressed as:

[0109]

[0110] 6) Speed ​​control and DC voltage control experiments

[0111] Switching signal design: For the speed control experiment, we select α = 0.8, μ = 1.1, T = 2, and f = 10. According to the dwell time condition (14), the switching signal design under the continuous dwell time should satisfy:

[0112]

[0113] In the DC voltage control experiment, α=0.4,μ=1.05,T=2,f=10 are selected. At this time, the dwell time should satisfy:

[0114]

[0115] Therefore, in both the speed control experiment and the DC voltage control experiment, the switching signal can be designed as follows: Figure 3 As shown, the dwell time is set to 0.6s.

[0116] In the speed control experiment, γ = 1.8 is selected. By solving inequalities (15) and (16), the fuzzy switching anti-disturbance rejection parameters of the speed loop can be obtained as:

[0117] g 11 =g 12 =7.0820,

[0118] g 21 =g 22 =2.3909,

[0119]

[0120]

[0121] Given speed expected signal ω m =9000rads / min and system disturbance ω = 0.1sin(t). The speed control simulation experiment results are as follows Figure 4 and Figure 5As shown in the figure, due to the load torque switching, the system presents a multi-mode state, and in the case of external disturbances, the designed fuzzy switching anti-disturbance controller can still ensure that the system state can quickly track the set target speed value. Figure 5 The tracking error and observation error values ​​are shown, indicating that the dynamic error system has good stability. The experimental results show that the designed fuzzy switching anti-disturbance controller can actively suppress system disturbances, and the speed switching control system has strong robustness within the proposed method, verifying the effectiveness of the controller design.

[0122] In the DC voltage control experiment, γ = 1.8 is selected. By solving inequalities (15) and (16), the parameters of the fuzzy switching anti-disturbance controller of the DC voltage loop can be obtained as follows:

[0123] g 11 =g 12 =8.1872,

[0124] g 21 =g 22 =1.9621,

[0125]

[0126]

[0127] The voltage reference signal is selected as 270V, and the disturbance ω(t) is set to 0.5sin(t). The detailed experimental results are shown in Figure 6 and Figure 7 shown. Figure 6 It shows that the designed fuzzy switching anti-disturbance controller can ensure that the system state tracks the voltage given signal well, the actual DC voltage value can be stabilized at the expected 270V, and is not affected by the switching process and system disturbances. The voltage control system has strong robustness. Figure 7 The tracking error curve and observation error curve are shown respectively, where the tracking error can converge to 0 and the observation error fluctuates in a small range. The designed fuzzy switching auto-disturbance rejection controller and fuzzy extended state observer have good control and disturbance observation effects.

[0128] This paper considers the load switching of the starter-generator system and proposes a fuzzy switching anti-disturbance control method based on continuous dwell time. The results show that the proposed fuzzy switching anti-disturbance controller can effectively improve the active suppression capability of the starter-generator system for disturbances under load switching conditions and enhance the robustness of the system.

Claims

1. A fuzzy switching auto-disturbance rejection control method for a starting-generating system with a continuous dwell time, characterized in that: Here are the steps: 1) Modeling of the starting-generation switching system The starter-generator system includes a starter-generator, a drive device with an inverter / rectifier function, and a load, wherein the load is manifested as the load torque dragged on the motor shaft under the starting condition, and the load is manifested as a power consumption device on the DC voltage side under the generating condition; the switching of the load will directly cause the speed and DC voltage control loop of the starter-generator system to present the characteristics of a switching system; Under starting conditions, considering different shaft loads, the speed control loop is expressed as a switching system as shown below: in, ω m is the mechanical angular velocity of the motor, T e is the electromagnetic torque, T 2Li is the switchable load torque, i∈S represents the system mode, S is the set of all system modes, B is the viscous friction coefficient, J is the moment of inertia, and K is a given constant; Under power generation conditions, considering the switching of load resistance value, the DC voltage control loop is also expressed in the form of a switching system: Among them, u dc represents the DC voltage, i dc Represents DC current, R i is the switchable load resistor, C is the DC side voltage stabilizing capacitor, Δ R Used to describe fluctuations in resistance values; 2) TS fuzzy switching system modeling For the switching system of formula (1), the given system parameters are as follows: Moment of inertia J = 10 -4 Kg·m 2 , viscous friction coefficient B = 10 -5 , K = 10 -8 , the motor's mechanical angular velocity range ω m ∈[0,10 4 )rads / min, system mode i∈{1,2}, switchable load torque T 2L1 =10 -5 ω m , T 2L2 =0; Choose x = ω m , u=T e , the specific form of the speed control system is: ●When system mode i=1: ●When system mode i=2: In order to ensure the effectiveness of control analysis and controller design, the nonlinear term -10 in the switching system of formula (1) is calculated by TS fuzzy method. -4 x 2 Perform fuzzy linearization; first, select the number of fuzzy rules as 2 and set the antecedent variable to the system state x; By fitting the nonlinear terms by means of upper and lower bounds, we can obtain According to formula (3), the membership function is calculated h 11 (x(t))=h 21 (x(t))=10 -4 x(t) h 12 (x(t))=h 22 (x(t))=1-10 -4 x(t) Therefore, the speed fuzzy switching system is expressed as Among them, a 11 = -1.2, a 12 = -0.2, a 21 = -1.1, a 22 = -0.1, b il = 10 4 ; For the switching system of formula (2), the system parameters are set as: The voltage stabilizing capacitor C = 2mF, the system mode i∈{1,2}, the switchable load resistance value R1 = 2kΩ, R2 = 1kΩ, the resistance floating Δ R =0.4sin(u dc ); Choose x=u dc , u=i dc , the DC voltage switching system is expressed as: ●When system mode i=1: ●When system mode i=2: The number of fuzzy rules is selected as 2, and the antecedent variable is set as the system state x. Through the TS fuzzy method, the nonlinear terms contained in the system under mode 1 and mode 2 are fuzzy linearized, and the obtained Based on formula (4), the membership function is calculated h 11 (x(t))=h 21 (x(t))=0.5+0.5sin(x(t)) h 12 (x(t))=h 22 (x(t))=1-(0.5+0.5sin(x(t)))=0.5-0.5sin(x(t)) Therefore, the DC voltage fuzzy switching system is expressed as: Among them, a 11 = -0.35, a 12 = -0.15, a 21 = -0.7, a 22 = -0.3, b il = 500; 3) Design of fuzzy switching auto-disturbance rejection controller Based on the fuzzy modeling of the starter-generator switching system, the starter-generator system has the following general form when load switching is considered, after TS fuzzy linearization, and system disturbance is considered: Where ω represents the system disturbance; In order to ensure that the starting-generating switching system has the ability to actively suppress disturbances, a fuzzy switching anti-disturbance controller is designed for the starting-generating system in formula (5), as follows: Fuzzy switching extended state observer: Fuzzy switching feedback control law: Where r is the reference signal, and denote the observed values ​​of x and ω respectively, and g il are the observer gain and controller gain to be optimized, respectively. il >0 and b il is a given constant; 4) Establish a dynamic error system, and consider the influence of the switching process on the performance of the starting-generating system through the design of multiple Lyapunov functions. Under the switching signal design scheme with continuous dwell time, the stability of the error system and the L ∞ Performance conditions; 5) Propose solvable optimization conditions and optimize the parameters of the fuzzy switching anti-disturbance controller to ensure the stability of the starting-generation system, L ∞ performance and controller effectiveness; 6) Carry out fuzzy switching anti-disturbance control simulation experiments on the speed and DC voltage loops respectively, and analyze the control performance.

2. The fuzzy switching auto-disturbance rejection control method for a starting-generating system with a continuous dwell time according to claim 1, characterized in that: Step 4) is as follows: In order to analyze the stability of the control system, the error system model is established; the tracking error and observation error are defined as e s = rx and The specific forms of the tracking error system of formula (8) and the observation error system of formula (9) are: in, The tracking error system and the observation error system are organized into state space form: Among them, e=[e s e c ] T , For the κth stage, the duration of residence time includes two components, which require that the system switching must have a duration no less than τ p The dwell time of the system is also allowed to Multiple switching occurs within the interval, and the interval between two adjacent switching times must be less than τ p ; Given parameters α>0 and μ>1, if there exists γ>0 and the system modally dependent Lyapunov function in is a field of positive real numbers, such that S represents the set of system modes, and i≠j, the following conditions are All are established: V i (e(t s ))≤μV j (e(t s )) (12) Then you can get in, and denote the starting time of the κth and κ+1th stages respectively, and Respectively Moment and The system mode at time, represent The total number of system mode changes within the interval; If the residence time τ in each stage p Satisfy τ p >1 / f s , further, we get Among them, T s and f s They represent the maximum operating time and the maximum mode switching frequency of the T stage respectively, and t0 represents the initial time; Based on formula (13), we can conclude that: If the residence time in each stage meets the following conditions: Then, when the time t is large enough, the dynamic fuzzy error system of formula (10) is uniformly asymptotically stable under the disturbance f≡0; In addition, if the system disturbance f≠0, if the Lyapunov function is selected as the following standard quadratic form: V i (e)=e T P i yes in, is the positive definite symmetric matrix to be solved; From equations (13) and (14), we can conclude that the dynamic fuzzy error system of equation (10) has L ∞ Disturbance suppression capability, in the form of: ||e(t)|| ∞ ≤γ1||f(t)|| ∞ in, λ min (P i ) represents the matrix P i The minimum eigenvalue of .

3. The fuzzy switching auto-disturbance rejection control method for a starting-generating system with a continuous dwell time according to claim 1, characterized in that: Step 5) is as follows: By choosing Among them, P i =diag{p 1i p 2i }, it is easy to obtain the following inequality which is a sufficient condition for equations (11) and (12); p 1i ≤μp 1j ,p 2i ≤μp 2j , (16) in, Y=-γ 2 I, I=diag{11}; Therefore, given the parameters α>0 and μ>1, if there exists p 1i >0, p 2i >0,z 1ik , z 2ik and γ>0, so that equations (15) and (16) hold, then the dynamic fuzzy error system of equation (10) is uniformly asymptotically stable and has an L value not exceeding γ1. ∞ performance gain; in addition, the optimized fuzzy switching ADRC parameters are expressed as:

4. The fuzzy switching auto-disturbance rejection control method for a starting-generating system with a continuous dwell time according to claim 1, characterized in that: Step 6) is as follows: Switching signal design: For the speed control experiment, we select α = 0.8, μ = 1.1, T = 2, f = 10. According to the dwell time condition (14), the switching signal design under the continuous dwell time should satisfy: In the DC voltage control experiment, α=0.4,μ=1.05,T=2,f=10 are selected. At this time, the dwell time should satisfy:

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