EAST fast control power supply current tracking control method based on disturbance suppression

Abstract

The application discloses an EAST fast control power current tracking control method based on disturbance suppression, and the method comprises the following steps: predicting single-step output current according to an EAST fast control power output current sampling value, and obtaining optimal control law of a current moment based on the single-step output current and applying the optimal control law to the EAST fast control system; for the extended state observation, separating low-frequency external disturbance from high-frequency disturbance current in lumped disturbance, wherein the lumped disturbance comprises external disturbance and load inductance mismatch; observing low-frequency disturbance by the extended disturbance state, and reducing observation error caused by high-frequency disturbance based on an adaptive input gain term; compared with a conventional control strategy, ILESO has lower observation error under similar bandwidth gain.

Description

Technical Field

[0001] This invention relates to the field of EAST fast control power supply operation technology, specifically to an EAST fast control power supply current tracking control method based on disturbance suppression. Background Technology

[0002] Energy is the driving force of economic development and the material foundation of modern civilization. Nuclear fusion energy is the most ideal new energy source for mankind's future, with advantages such as readily available raw materials and pollution-free products. The Experimental Advanced Superconducting Tokamak (EAST) is an important component of nuclear fusion power generation.

[0003] The EAST device's plasma vertical displacement active feedback controller detects the vertical displacement of the plasma and calculates the given signal from the Fast Control Power Supply (FCPS). The FCPS then excites the active feedback coil, generating a rapidly changing magnetic field to maintain the plasma's vertical stability. If plasma displacement occurs, the Plasma Control System (PCS) accurately and quickly issues a command, and the power supply rapidly outputs current to establish the necessary magnetic field to pull the plasma back to its equilibrium position.

[0004] To adjust the magnetic field in a timely manner, a power supply system capable of providing high voltage and high current is required. Cascaded H-bridge inverters, as a new type of high-voltage, high-power inverter, are widely used in the design of EAST fast-control power supplies due to their advantages such as high equivalent switching frequency, DC-side floating isolation, and high output current. Each branch of the fast-control power supply system consists of three cascaded H-bridge inverter circuits. Therefore, with a given voltage of ±10V, the output voltage of one branch is between ±1620V, and the output current is between ±1500A. The entire fast-control system consists of six branches connected in parallel. Therefore, for the fast-control power supply system, a given voltage of ±10V corresponds to an output voltage of ±1620V and an output current of ±9000A.

[0005] Load-side lumped disturbances, a common occurrence in EAST fast control systems, significantly degrade the power supply's output current tracking performance, thus requiring suppression. PI control with integrators can suppress slow-varying disturbances, but the large time delay of the integral stage reduces the power supply's tracking speed, making it less than optimal for EAST fast control power supplies with high speed requirements. Model predictive control (MPC) is a viable optimization strategy for EAST fast control systems due to its fast dynamic response and flexible constraints; however, MPC relies heavily on the accuracy of the object's parameter model, and its performance degrades significantly when the predictive model mismatches. Extended state observers (ESOs), requiring only the object's relative order and no further prior information about disturbances, have gained widespread application. Numerous studies have shown that this method outperforms conventional PI control in suppressing load-side disturbances in EAST fast control power supplies.

[0006] Linear ESO (LESO) has gained attention in the design of EAST fast control power supplies due to its simplicity of analysis and ease of design and implementation. The lumped disturbance in the load circuit of the EAST fast control power supply, consisting of external disturbances and inductor mismatch, is observed using LESO. However, the actual equivalent switching frequency of the power supply is above 10kHz, with the specific value depending on the number of cascaded H-bridges. At this point, the parameter mismatch in the lumped disturbance contains high-frequency components in the control input portion. High-gain bandwidth LESO introduces stability issues, while low-bandwidth LESO generates observation errors and degrades tracking performance, which significantly reduces the tracking performance of the EAST fast control system for lumped disturbances.

[0007] Among related technologies, the photovoltaic microgrid energy storage control strategy based on active disturbance rejection control proposed in patent application CN115528665A has relatively difficult parameter selection and is not accurate enough in observing the lumped disturbance composed of load-side external disturbances and inductor mismatch. The article "Fast Control Power Supply Current Control of a Fully Superconducting Tokamak Nuclear Fusion Power Generation Device Based on Improved Grey Prediction Single Neuron PI, Journal of Electrical Engineering" proposes to adaptively adjust the output gain of the single neuron proportional-integral (PI) control according to the error between the predicted current and the reference current to achieve fast and accurate control of the output current, but it does not consider the lumped disturbance composed of load-side external disturbances and inductor mismatch. Summary of the Invention

[0008] The present invention aims to solve the problems of high observation error and poor tracking performance of the existing EAST fast control power supply output current control method when dealing with external disturbances and changes in load inductance.

[0009] The present invention solves the above-mentioned technical problems through the following technical means:

[0010] A current tracking control method for EAST fast control power supply based on disturbance suppression is proposed. The method includes the following steps:

[0011] The single-step output current is predicted based on the sampled value of the EAST fast control power supply output current, and the optimal control law at the current moment is obtained based on the single-step output current and applied to the EAST fast control system.

[0012] For extended state observation, the low-frequency external disturbance and high-frequency disturbance current in the lumped disturbance are separated, wherein the lumped disturbance includes external disturbance and load inductance mismatch;

[0013] Low-frequency disturbances are observed by the expanded disturbance state, and an adaptive input gain term is used to reduce the observation error caused by high-frequency disturbances.

[0014] Furthermore, the step of predicting the single-step output current based on the sampled value of the EAST fast control power supply output current, and obtaining the optimal control law for the current moment based on the single-step output current and applying it to the EAST fast control system, includes:

[0015] The output current sampling value of the EAST fast control power supply is predicted based on the discretized output current prediction model to obtain the single-step output current. The discretized output current prediction model is expressed as follows:

[0016]

[0017] In the formula, i H (k+1) is the output current value at time k+1, i H (k) is the output current value at time k, R H It is the equivalent resistance, L H It is the self-inductance of the fast control coil, T s It is the sampling period, u H (k) is the output voltage at time k, u H (k)=u H (k-1)+Δu H (k), u H (k-1) is the output voltage at time k-1, Δu H (k) is the increment of the control quantity at time k;

[0018] The formula for the single-step output current is expressed as follows:

[0019]

[0020] In the formula, i Hpre (k+1) is the single-step output current at time k+1, i Hpre (k) is the single-step output current at time k, and μ is the prediction error feedback gain;

[0021] The optimal control law for the current moment is obtained based on the single-step output current and applied to the EAST fast control system.

[0022] Furthermore, the formula for the optimal control law at the current moment obtained based on the single-step output current is expressed as follows:

[0023]

[0024] In the formula, It is the optimal control law at time k, r * It is a reference signal.

[0025] Furthermore, for the observation of the extended state, the low-frequency external disturbance and high-frequency disturbance current in the lumped disturbance are separated, wherein the lumped disturbance includes external disturbance and load inductance mismatch, including:

[0026] Based on the lumped disturbance, the equivalent lumped disturbance current f of the power supply is... d Represented as:

[0027]

[0028] Low-frequency external disturbance f in lumped disturbance separation d_lf With high-frequency disturbance current f d_hf for:

[0029]

[0030] Where: ΔL H It is a load inductance mismatch, i H d is the output current, d is the external disturbance, and u is the output current. H It is the output voltage, R H It is the equivalent resistance, L H It is the self-inductance of the fast control coil

[0031] Furthermore, the observation of low-frequency disturbances by the expanded disturbance state, and the reduction of observation errors caused by high-frequency disturbances based on an adaptive input gain term, includes...

[0032] Based on an improved linear extended state observer, the low-frequency external disturbance on the load side of the EAST fast control power supply is observed by the extended disturbance state. The formula for the improved linear extended state observer is expressed as follows:

[0033]

[0034] In the formula, ε1 and ε2 are the observation errors of the extended state space, i H It is the output current. It is a current state observation, f d_lf It is a low-frequency external disturbance. It is the extended perturbation observation state, θ is the adaptive input gain term, and uH It is the output voltage, R H β1 and β2 are the equivalent resistances, and β1 and β2 are the LESO observation gains.

[0035] The augmented error state space of the improved linear extended state observer and the EAST fast control system is:

[0036]

[0037] In the formula, It is the first derivative of the observation error, ΔL H It is a load inductance mismatch, L H It is the self-inductance of the fast control coil, A e Here, ε is the Hurwitz matrix, ε is the observation error matrix of the extended state space, and δ... t It is the error between the input gain and the adaptive term, f d_hf It is the high-frequency disturbance current, U is the disturbance input vector, ε0 is the augmentation error, and C e It is the state transition matrix.

[0038] Furthermore, after observing low-frequency disturbances by the expanded disturbance state and reducing observation errors caused by high-frequency disturbances based on an adaptive input gain term, the method further includes:

[0039] The adaptive law for the adaptive input gain term is designed based on the Lyapunov function, and the formula is expressed as:

[0040]

[0041] In the formula, It is the first derivative of the adaptive input gain term. It is the first derivative of the error between the input gain and the adaptive term, ε0 is the augmented error, and u H It is the output voltage, λ t It is any positive number, δ t It is the error between the input gain and the adaptive term.

[0042] Furthermore, after designing the adaptive law for the adaptive input gain term based on the Lyapunov function, the method further includes:

[0043] Analyzing the stability of the closed-loop control, the transfer function of the closed-loop reference tracking is obtained, expressed by the formula:

[0044]

[0045] In the formula, the characteristic equation of the system is Δ=s 3 +(β1+L H θ)s 2 +(2β2+β1-β2LH θ)s+β2=0,i H It is the output current, r * It is the reference signal, and s is the complex variable of the transfer function;

[0046] Based on the transfer function of closed-loop reference tracking, the closed-loop stability condition is obtained as follows:

[0047]

[0048]

[0049] In the formula, ω0 is the bandwidth, L H θ is the self-inductance of the fast control coil, and θ is the adaptive input gain term.

[0050] Furthermore, the method also includes:

[0051] Discretizing the extended state space of the EAST fast control system after separating the low-frequency external disturbance and the high-frequency disturbance current from the lumped disturbance, we obtain:

[0052]

[0053] In the formula, i H (k+1) is the output current value at time k+1, i H (k) is the output current value at time k, u H (k) is the output voltage at time k, T s It is the sampling period, ΔL H It is a load inductance mismatch, f d_hf It is a high-frequency disturbance current, f d_lf (k) is the low-frequency external disturbance at time k, f d_lf (k+1) is the low-frequency external disturbance at time k+1;

[0054] The z-domain form of the improved linearly extended state observer is as follows:

[0055]

[0056] In the formula, ε1(k) and ε2(k) are the observation errors at time k, and i H (k) is the output current at time k. The current state observation at time k, f d_lf (k) represents low-frequency external disturbance. This is the observed state of the expanding perturbation at time k. This is the observed state of the extended perturbation at time k+1, where X(k) is the additional remainder term for the auxiliary Lyapunov stabilization, β3 is the parameter to be tuned for the auxiliary remainder term, and u H (k) is the output voltage at time k. θ(k) is the adaptive gain step size, θ(k) is the adaptive input gain at time k, b0 is the initial adaptive input gain, and β1 is the adaptive input gain step size. + =T s β1, β2 + =T s β2.

[0057] Furthermore, the method also includes:

[0058] The Lyapunov function V(k) for the z-domain is constructed as follows:

[0059]

[0060] In the formula, ε(k) is the observation error matrix of the expanded state space at time k, and P e It is a positive definite matrix. It is the z-domain input gain error, and T is the transpose sign.

[0061] Furthermore, the method also includes:

[0062] In the optimal control law, the lumped disturbance is compensated through feedforward and feedback loops, as expressed by the following formula:

[0063]

[0064] The advantages of this invention are:

[0065] (1) This invention uses Model Predictive Control (MPC) to act on the EAST fast control system. For the extended state observation part, the low-frequency external disturbance and high-frequency disturbance current in the lumped disturbance are separated so that the low-frequency part can be observed through the extended state. For the high-frequency disturbance, an adaptive input gain term is established to reduce the observation error caused by it, and optimized observation performance is achieved under similar low bandwidth gain. This invention uses Improved LESO (ILESO) with adaptive input gain to divide the lumped disturbance of the load circuit into low-frequency disturbance and high-frequency disturbance. Under similar bandwidth gain, ILESO has a lower observation error. Under the same disturbance influence on the load side of the EAST fast control power supply H-bridge, and with similar observation bandwidth gain, the comparison results with the conventional LESO+MPC strategy show that the MPC control strategy of the improved LESO adopted in this invention has a lower observation error and better tracking performance for the current control of the H-bridge load side. Specifically, the overshoot caused by the mismatch of the prediction model is effectively reduced and the response adjustment time is shortened.

[0066] (2) The present invention adopts Model Predictive Control (MPC) to establish a power supply mathematical model for the EAST fast control H-bridge power supply and obtain the output current prediction model after discretization; it adopts a non-minimization description of discrete convolution and model, which has a large amount of information redundancy and is conducive to improving the robustness of the system; at the same time, it adopts a rolling optimization strategy instead of global one-time optimization, which can make up for the uncertainty caused by model mismatch, distortion, interference and other factors in a timely manner, and has good dynamic performance.

[0067] (3) Based on the transfer function and system characteristic equation of the closed-loop reference tracking, the present invention obtains the stability conditions of the closed-loop system through the Routh criterion, thereby ensuring that ILESO+MPC is closed-loop stable for any ω0>1rad / s, negative mismatch of load inductance parameter less than 50% or any positive mismatch in EAST fast control power supply.

[0068] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0069] Figure 1 This is a flowchart illustrating the EAST fast control power supply current tracking control method based on disturbance suppression proposed in an embodiment of the present invention.

[0070] Figure 2 This is a block diagram illustrating the principle of EAST fast control power supply current tracking control based on disturbance suppression in an embodiment of the present invention.

[0071] Figure 3 This is a schematic diagram comparing the tracking response of the reference signal tracking under three disturbance suppression strategies: PI control, LESO+MPC, and ILESO+MPC, in an embodiment of the present invention. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] like Figure 1 As shown, the first embodiment of the present invention proposes an EAST fast control power supply current tracking control method based on disturbance suppression, the method comprising the following steps:

[0074] S10. Predict the single-step output current based on the sampled value of the EAST fast control power supply output current, and obtain the optimal control law at the current moment based on the single-step output current and apply it to the EAST fast control system.

[0075] S20. For extended state observation, separate the low-frequency external disturbance and high-frequency disturbance current in the lumped disturbance, wherein the lumped disturbance includes external disturbance and load inductance mismatch;

[0076] S30. Observe low-frequency disturbances from the expanded disturbance state and reduce observation errors caused by high-frequency disturbances based on an adaptive input gain term.

[0077] This embodiment divides the lumped disturbance of the EAST fast control power supply H-bridge load circuit into low-frequency disturbance and high-frequency disturbance. The low-frequency part is observed through the extended state with low bandwidth gain, while the high-frequency disturbance is reduced by the adaptive input gain improved LESO proposed in this embodiment, which reduces the system state observation error caused by it. Under similar bandwidth gain, ILESO has a lower observation error, thereby effectively reducing the observation stability problem of EAST fast control power supply caused by parameter mismatch in the lumped disturbance containing high-frequency components in the control input part.

[0078] In one embodiment, step S10: predicting the single-step output current based on the sampled value of the EAST fast control power supply output current, and obtaining the optimal control law for the current moment based on the single-step output current and applying it to the EAST fast control system, specifically includes the following steps:

[0079] The output current sampling value of the EAST fast control power supply is predicted based on the discretized output current prediction model to obtain the single-step output current. The discretized output current prediction model is expressed as follows:

[0080]

[0081] In the formula, i H (k+1) is the output current value at time k+1, i H (k) is the output current value at time k, R H It is the equivalent resistance, L H It is the self-inductance of the fast control coil, T s It is the sampling period, u H (k) is the output voltage at time k, u H (k-1) is the output voltage at time k-1, Δu H (k) is the increment of the control quantity at time k;

[0082] MPC solves for the optimal control sequence in the rolling time domain using a prediction model and an evaluation function, and applies the first control variable to the system. The optimal control variable can be represented by an increment, and the increment form of the control variable is:

[0083] u H (k)=u H (k-1)+Δu H (k) (2)

[0084] The formula for the single-step output current is expressed as follows:

[0085]

[0086] In the formula, i Hpre (k+1) is the single-step output current at time k+1, i Hpre (k) is the single-step output current at time k, and μ is the prediction error feedback gain;

[0087] The optimal control law for the current moment is obtained based on the single-step output current and applied to the EAST fast control system.

[0088] Specifically, Model Predictive Control (MPC) is a commonly used optimization strategy due to its fast dynamic response and flexible constraints. Therefore, a mathematical model of the EAST fast-control H-bridge power supply is established:

[0089]

[0090] In the formula, u H It is the output voltage, i H It is the output current, L H It is the self-inductance of the fast control coil, R H It is the equivalent resistance, u Hx It is the output voltage of the xth H-bridge.

[0091] Discretize the mathematical model formula (4) of the power supply to obtain the discretized output current prediction model, i.e., formula (1).

[0092] In one embodiment, the MPC optimization objective is to predict the current to track the reference signal while keeping the control quantity in small increments. Therefore, the evaluation function consists of the tracking error and the increment:

[0093]

[0094] When there are no constraints, the optimal solution of the evaluation function is obtained at the poles, J * (k) for Δu H (k) Taking the derivative, we get:

[0095]

[0096] The duty cycle update of a digital controller has an inherent one-step delay. Typically, the single-step predicted current value is used as the initial value for optimization to calculate the control quantity actually acting at time (k+1, k+2). The optimal control law at the current moment after compensating for the delay is:

[0097]

[0098] In the formula, It is the optimal control law at time k, r * It is a reference signal.

[0099] It should be noted that this embodiment establishes a power supply mathematical model for the EAST fast-control H-bridge power supply through a non-perturbative MPC design, and obtains the output current prediction model after discretization. A non-minimization-described discrete convolutional model is used, resulting in high information redundancy, which is beneficial for improving system robustness. Simultaneously, a rolling optimization strategy is employed, rather than a global one-time optimization, which can promptly compensate for uncertainties caused by model mismatch, distortion, interference, etc., resulting in good dynamic performance. Optimized tracking of the current reference can be achieved through prediction error feedback.

[0100] In one embodiment, step S20: For extended state observation, separating the low-frequency external disturbance and the high-frequency disturbance current in the lumped disturbance, wherein the lumped disturbance includes external disturbance and load inductance mismatch, includes the following steps:

[0101] Based on the lumped disturbance, the equivalent lumped disturbance current f of the power supply is... d Represented as:

[0102]

[0103] The converted disturbance current is referred to as disturbance. Choosing the lumped disturbance as the extended state variable, the system's extended state space is:

[0104]

[0105] Low-frequency external disturbance f in lumped disturbance separation d_lf With high-frequency disturbance current f d_hf for:

[0106]

[0107] Where: ΔL H It is a load inductance mismatch, i H d is the output current, d is the external disturbance, and u is the output current. H It is the output voltage, R H It is the equivalent resistance, L H It is the self-inductance of the fast control coil;

[0108] The expanded state space of the system at this point can be written as:

[0109]

[0110] It should be noted that LESO can progressively observe lumped disturbances when the bandwidth is properly tuned. However, satisfactory tracking performance requires the observer bandwidth to cover the highest frequency disturbance component. In practical applications containing high-frequency disturbances, measurement noise and stability limit the use of high-gain observers. The lumped disturbance of a single-phase CHB inverter power supply includes external disturbances and inductor mismatch. Due to the extremely small equivalent load resistance, the disturbance including external disturbances and the equivalent load resistance is considered low-frequency. However, when the output voltage changes at the equivalent switching frequency, the lumped disturbance contains relatively high-frequency components, thus separating the low-frequency and high-frequency external disturbances within the lumped disturbance.

[0111] In one embodiment, step S30, which involves observing low-frequency disturbances from an expanded disturbance state and reducing observation errors caused by high-frequency disturbances based on an adaptive input gain term, includes the following steps:

[0112] Based on an improved linear extended state observer, the low-frequency external disturbance on the load side of the EAST fast control power supply is observed by the extended disturbance state. The formula for the improved linear extended state observer is expressed as follows:

[0113]

[0114] In the formula, It is a current state observation, f d_lf It is a low-frequency external disturbance. It is the extended perturbation observation state, θ is the adaptive input gain term, and u H It is the output voltage, R H It is the equivalent resistance;

[0115] Using the extended state space of the system as the reference model and the improved linear extended state observer ILESO as the adjustable model, the augmented error state space of ILESO and the EAST fast control system is:

[0116]

[0117] In the formula, It is the first derivative of the observation error, ΔL H It is a load inductance mismatch, L H It is the self-inductance of the fast control coil, A e Here, ε is the Hurwitz matrix, ε is the observation error matrix of the extended state space, and δ... t It is the error between the input gain and the adaptive term, f d_hf It is the high-frequency disturbance current, U is the disturbance input vector, ε0 is the augmentation error, and C e It is the state transition matrix.

[0118] It should be noted that the amplitude-frequency response of the observation error can be calculated as follows:

[0119]

[0120] In the formula, ε1(jω) is the frequency domain form of the observation error. It is the frequency domain form of the external disturbance, δ t (jω) is the frequency domain form of the error between the input gain and the adaptive term. It is the frequency domain form of the output voltage, where ω is the rotational angular frequency and ω0 is the bandwidth.

[0121] The input gain error in the time domain is:

[0122]

[0123] As can be seen from formulas (14) and (15), the low-frequency external disturbances on the load side of the EAST fast control power supply are observed through the expanded disturbance state. When the bandwidth is insufficient to cover the high frequency, ILESO will obtain a lower observation error through adaptive input gain.

[0124] In one embodiment, after step S30: observing low-frequency disturbances from the expanded disturbance state and reducing observation errors caused by high-frequency disturbances based on an adaptive input gain term, the method further includes the following steps:

[0125] The adaptive law for the adaptive input gain term is designed based on the Lyapunov function.

[0126] Specifically, the adaptive law of input gain is derived through the Lyapunov function. In formula (13), A e It is a Hurwitz matrix. For any positive definite matrix Q, the Lyapunov equation PA... e +A e T P = -Q both have positive definite solutions P, therefore the continuously differentiable Lyapunov function is constructed as follows:

[0127]

[0128] In the formula, λ t It is any positive number.

[0129] The derivative of formula (16) along the direction of formula (12) is:

[0130]

[0131] When the adaptive law is designed to eliminate the second and third terms of (17), the Lyapunov function will have a negative derivative. At this point, the observation error and input gain error gradually decrease, and ILESO is stable. The adaptive law is calculated using the Lyapunov function:

[0132]

[0133] In the formula, It is the first derivative of the adaptive input gain term. It is δ t The first derivative, ε0 is the augmented error, U is the perturbation input vector, u H It is the output voltage, λ t It is any positive number, δ t It is the error between the input gain and the adaptive term.

[0134] This embodiment designs an adaptive law for the input gain using Lyapunov functions to ensure observation stability. It's important to note that the adaptive input gain does not necessarily converge to the true value because the system state observations contain an integral term of error, which differs from model reference adaptive online parameter identification. The observation error of ILESO is determined by f... d_lf and u H If the excitation is applied, then the transfer function of the observation error is:

[0135]

[0136] f in formula (10) d_lf Substituting into formula (19), we can obtain the observation error:

[0137]

[0138] The amplitude-frequency response of the observation error is then:

[0139]

[0140] When bandwidth dominates the perturbation observation error, ILESO and LESO have similar observation performance. However, when the bandwidth is insufficient to cover high frequencies, ILESO will achieve a lower observation error through adaptive input gain. Substituting equation (20) into equation (18) and using the inverse Laplace transform, the input gain error in the time domain can be obtained:

[0141]

[0142] In one embodiment, after designing the adaptive law for the adaptive input gain term based on the Lyapunov function, the method further includes:

[0143] By analyzing the closed-loop stability using the transfer function, the stability condition is determined that the negative mismatch of the inductor parameters should be less than 50%.

[0144] Furthermore, by analyzing the closed-loop stability through transfer function analysis, the stability condition that the negative mismatch of inductor parameters should be less than 50% is obtained, specifically including:

[0145] Analyzing the closed-loop stability of ILESO+MPC, the transfer function of ILESO is obtained as follows:

[0146]

[0147] External disturbances and inductance mismatch are compensated for in the optimal control law through feedforward and feedback loops for predicted current:

[0148]

[0149] The transfer function for closed-loop reference tracking can be obtained as follows:

[0150]

[0151] The characteristic equation of the system is Δ = s 3 +(β1+L H θ)s 2 +(2β2+β1-β2L H θ)s+β2=0, according to the Routh criterion, the closed-loop stability condition of the system is:

[0152] β1+L H θ>0

[0153] β2>0

[0154]

[0155] Since the ILESO bandwidth ω0 > 0 and the adaptive input gain θ is a time-varying variable, the system stability depends on θ and ω0. Combining these three conditions, the strict closed-loop stability condition for the system is given as follows:

[0156]

[0157] For any bandwidth ω0 > 1 rad / s, the closed-loop stability of the system requires θ to satisfy the following condition:

[0158]

[0159] It should be noted that the adaptive input gain asymptotically approaches the true value, therefore the mismatch in the load inductance is ΔL. H ≥-0.5L H The final closed-loop stability condition is: for any ω0>1rad / s, the negative mismatch of the load inductance parameter is less than 50% or any positive mismatch, ILESO+MPC is closed-loop stable.

[0160] Furthermore, this embodiment also presents the z-domain form of the improved ESO+MPC for the EAST fast-controllable H-bridge power supply, discretizing the extended state space of the EAST fast-controllable power supply system as follows:

[0161]

[0162] In the formula, i H (k+1) is the output current value at time k+1, i H (k) is the output current value at time k, u H (k) is the output voltage at time k, T s It is the sampling period, ΔL H It is a load inductance mismatch, f d_hf It is a high-frequency disturbance current, f d_lf (k) is the low-frequency perturbation at time k, f d_lf (k+1) is the low-frequency disturbance at time k+1;

[0163] The ILESO of the z-domain is proposed as follows:

[0164]

[0165] In the formula, ε1(k) and ε2(k) are the observation errors at time k, and i H (k) is the output current at time k. The current state observation at time k, It is the current state observation at time k+1, f d_lf (k) represents low-frequency external disturbance. This is the observed state of the expanding perturbation at time k. This is the observed state of the extended perturbation at time k+1, where X(k) is the additional remainder term for the auxiliary Lyapunov stabilization, β3 is the parameter to be tuned for the auxiliary remainder term, and u H (k) is the output voltage at time k. This is the adaptive gain step size, θ(k) is the adaptive input gain term at time k, and b0 is the initial adaptive input gain, which is recommended to be the nominal value of the inductor, such as 1 / L. H β1 + =T s β1, β2 + =T s β2.

[0166] The positive real augmented error state space is obtained from equations (29) and (30):

[0167]

[0168] In the formula, It is the step size of the derivative of the low-frequency perturbation at time k.

[0169] In one embodiment, the Lyapunov function for constructing the z-domain is:

[0170]

[0171] In the formula δ t + (k)=1 / (L H +ΔL H Let )-b0+θ(k) be the input gain error in the z-domain. Proving the observer stability in the z-domain requires the following positive real property theorem: If the discrete state-space system is positive real, then there must exist a positive definite matrix P. e And real matrices K and L, such that:

[0172]

[0173] Therefore, by using the positive real theorem, the increment of the Lyapunov function can be obtained as:

[0174]

[0175] Since X(k)ε1(k) / β3>0, only β3<-1 / 2 needs to be tuned, then ΔV<0 is guaranteed, meaning the z-domain is ILESO stable. External disturbances and inductor mismatch are compensated for in the optimal control law through feedforward and feedback loops:

[0176]

[0177] Furthermore, adopting, such as Figure 2 The EAST fast-control power supply control device shown is used to simulate and analyze the EAST fast-control power supply current tracking control method based on disturbance suppression. The single-branch cascaded H-bridge inverter circuit (CHB) consists of three cascaded inverter H-bridges. The simulation parameters are set as follows: DC supply voltage E = 540V, inductance L = 400mH, inductance internal resistance R = 0.08Ω, triangular carrier frequency = 5kHz, and a 60° carrier phase shift method is selected for phase shift control. An external disturbance d(t) = 10cos(100πt) is set in the load circuit, and the inductance parameter is set to a positive mismatch ΔL. H =25%L H .

[0178] Disturbance suppression current reference tracking is compared in PI controllers, conventional LESO+MPC controllers, and ILESO+MPC controllers, respectively. Figure 3 As shown. The parameters for conventional LESO+MPC are tuned as follows: bandwidth ω0 = 2000π rad / s, prediction error feedback gain μ = 0.1. The parameters for ILESO+MPC are tuned as follows: bandwidth ω0 = 2000π rad / s, adaptive step size λ t =1600, auxiliary residual term gain β3 = -0.52.

[0179] Figure 3 The reference tracking performance of the three disturbance suppression strategies for inductor abrupt changes is shown, with four waveforms representing the reference signal, PI control, LESO+MPC, and ILESO+MPC. It can be seen that the PI controller, tuned with a large integral gain to achieve zero steady-state tracking, suffers from a large time delay, resulting in a large overshoot of 71.5% and a long settling time of 2.2ms. LESO+MPC exhibits strong disturbance suppression performance, but it is not ideal in the high-frequency range due to inductor mismatch, still showing an overshoot of 8.75% and a settling time of 1.045ms. ILESO+MPC demonstrates satisfactory disturbance suppression performance, with no overshoot and a settling time of 0.55ms. It can be seen that initially, ILESO+MPC has similar tracking performance to LESO+MPC, but as the adaptive input gain is continuously adjusted, ILESO+MPC shows lower overshoot and a faster tracking settling time.

[0180] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0181] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0182] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A current tracking control method for EAST fast control power supply based on disturbance suppression, characterized in that, The method includes: The single-step output current is predicted based on the sampled value of the EAST fast control power supply output current, and the optimal control law at the current moment is obtained based on the single-step output current and applied to the EAST fast control system. For extended state observation, the low-frequency external disturbance and high-frequency disturbance current in the lumped disturbance are separated, wherein the lumped disturbance includes external disturbance and load inductance mismatch, including: Based on the lumped disturbance, the equivalent lumped disturbance current of the power supply is... Represented as: Low-frequency external disturbances in lumped disturbances With high-frequency disturbance current for: In the formula: It's a load inductance mismatch. It is the output current. It is an external disturbance. It is the output voltage. It is the equivalent resistance. It is the self-inductance of the fast control coil; Low-frequency disturbances are observed from the expanded disturbance state, and observation errors caused by high-frequency disturbances are reduced based on an adaptive input gain term. The method further includes: Discretizing the extended state space of the EAST fast control system after separating the low-frequency external disturbance and the high-frequency disturbance current from the lumped disturbance, we obtain: In the formula, , It is the first k+ Output current value at time 1 It is the first k Output current value at time , yes k Output voltage at any given time It is the sampling period. It's a load inductance mismatch. It is a high-frequency disturbance current. yes k Low-frequency disturbances at any given moment yes k+ Low-frequency disturbance at time 1; The z-domain form of the improved linearly extended state observer is as follows: In the formula, , It is the observation error at time k. yes k Output current at time , The current state observation at time k, It is a low-frequency external disturbance. yes k The observation state of the constant expansion of the perturbation. yes k+ Observational state of the expanding perturbation at time 1. It is an additional residual term that assists in the stability of Lyapunov. These are the parameters to be tuned for the auxiliary remainder term. It is the adaptive gain step size. It is the adaptive input gain at time k. It is the initial adaptive input gain. β 1 + = T s β 1, β 2 + = T s β 2.

2. The EAST fast control power supply current tracking control method based on disturbance suppression as described in claim 1, characterized in that, The step of predicting the single-step output current based on the sampled output current value of the EAST fast control power supply, and obtaining the optimal control law for the current moment based on the single-step output current and applying it to the EAST fast control system, includes: The output current sampling value of the EAST fast control power supply is predicted based on the discretized output current prediction model to obtain the single-step output current. The discretized output current prediction model is expressed as follows: In the formula, It is the first k+ Output current value at time 1 It is the first k Output current value at time , It is the equivalent resistance. It is the self-inductance of the fast control coil. It is the sampling period. yes k Output voltage at any given time , yes k- Output voltage at time 1 yes k Control the increment of quantity at all times; The formula for the single-step output current is expressed as follows: In the formula, yes k+ Single-step output current at time 1 yes k Single-step output current at any given moment It is the prediction error feedback gain; The optimal control law for the current moment is obtained based on the single-step output current and applied to the EAST fast control system.

3. The EAST fast control power supply current tracking control method based on disturbance suppression as described in claim 2, characterized in that, The formula for the optimal control law at the current moment, obtained based on the single-step output current, is expressed as follows: In the formula, Yes, yes k The optimal control law at time t. r It is a reference signal.

4. The EAST fast control power supply current tracking control method based on disturbance suppression as described in claim 1, characterized in that, The method of observing low-frequency disturbances from an expanded disturbance state and reducing observation errors caused by high-frequency disturbances based on an adaptive input gain term includes: Based on an improved linear extended state observer, the low-frequency external disturbance on the load side of the EAST fast control power supply is observed by the extended disturbance state. The formula for the improved linear extended state observer is expressed as follows: In the formula, and It is the observation error of the extended state space. It is the output current. It is a current state observation. It is a low-frequency external disturbance. This is the observation state of the extended perturbation. θ It is an adaptive input gain term. It is the output voltage. It is the equivalent resistance. and This is the LESO observation gain; The augmented error state space of the improved linear extended state observer and the EAST fast control system is: In the formula, , It is the first derivative of the observation error. It's a load inductance mismatch. It is the self-inductance of the fast control coil. It is a Hurwitz matrix. It is the observation error matrix of the extended state space. It is the error between the input gain and the adaptive term. It is a high-frequency disturbance current. It is the perturbation input vector. It is augmentation error. It is the state transition matrix.

5. The EAST fast control power supply current tracking control method based on disturbance suppression as described in claim 4, characterized in that, After observing low-frequency disturbances by the expanded disturbance state and reducing observation errors caused by high-frequency disturbances based on an adaptive input gain term, the method further includes: The adaptive law for the adaptive input gain term is designed based on the Lyapunov function, and the formula is expressed as: In the formula, It is the first derivative of the adaptive input gain term. It is the first derivative of the error between the input gain and the adaptive term. It is augmentation error. It is the output voltage. It is any positive number. It is the error between the input gain and the adaptive term.

6. The EAST fast control power supply current tracking control method based on disturbance suppression as described in claim 5, characterized in that, After designing the adaptive law for the adaptive input gain term based on the Lyapunov function, the method further includes: Analyzing the stability of the closed-loop control, the transfer function of the closed-loop reference tracking is obtained, expressed by the formula: In the formula, It is the output current. r It is a reference signal. s It is a complex variable in the transfer function. and It is the LESO observation gain. The system characteristic equation is Δ=s 3 +( β 1+ L H θ )s 2 +(2 β 2+ β 1- β 2L H θ )s+ β 2 = 0; Based on the transfer function of closed-loop reference tracking, the closed-loop stability condition is obtained as follows: In the formula, ω 0 represents bandwidth. It is the self-inductance of the fast control coil. θ It is an adaptive input gain term.

7. The EAST fast control power supply current tracking control method based on disturbance suppression as described in claim 1, characterized in that, The method further includes: Constructing Lyapunov functions for the z-domain for: In the formula, It is the observation error matrix of the expanded state space at time k. It is a positive definite matrix. It is the z-domain input gain error. T It is the transpose symbol.

8. The EAST fast control power supply current tracking control method based on disturbance suppression as described in claim 1, characterized in that, The method further includes: In the optimal control law, the lumped disturbance is compensated through feedforward and feedback loops, as expressed by the following formula: in, r It is a reference signal.

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