A power coordination and limit protection control method for a turbo-electric power system

Abstract

The application discloses a power coordination and limit protection control method of a turbo-electric power system, and belongs to the technical field of control of an aviation hybrid electric propulsion system, and comprises the following steps: establishing a nonlinear component-level model of a series turbo-electric power system, and analyzing the influence mechanism of a constant-power load on the stability of a power turbine shaft system based on the nonlinear component-level model; designing a gain-scheduled multi-input multi-output inner loop pre-stabilization controller based on the influence mechanism; constructing an outer loop model predictive reference instruction regulator based on the multi-input multi-output inner loop pre-stabilization controller; and outputting the reference instruction of the multi-input multi-output inner loop pre-stabilization controller and the outer loop model predictive reference instruction regulator to the series turbo-electric power system. The method effectively suppresses the shaft system instability caused by the negative damping effect of the constant-power load, reduces transient power mismatch, strictly limits the surge margin and turbine front temperature, and can be deployed in real time on a low-cost embedded platform.

Description

Technical Field

[0001] This application relates to the field of control technology for aviation hybrid electric propulsion systems, and in particular to a power coordination and limit protection control method for a turbine electric power system. Background Technology

[0002] As aerospace propulsion systems evolve towards electrification, turbine-electric propulsion systems (consisting of a turboshaft engine, generator, DC bus, and propulsion motor) achieve higher power density by eliminating large-capacity energy storage batteries. However, this also causes the DC bus to lose its transient power buffering capability. In this configuration, the propulsion motor and its converter exhibit constant power load (CPL) characteristics within a certain frequency range, exhibiting negative incremental impedance characteristics: when the power turbine speed decreases, in order to maintain a constant load power, the electromagnetic load torque of the generator actually increases, further exacerbating the speed droop; and the subsequent rapid fuel compensation will cause the turbine inlet temperature and compressor surge margin to approach the safety boundary.

[0003] Existing transient protection mechanisms for aero-engines mostly employ Min-Max constraint logic. Previous research has indicated that while the traditional Min-Max structure can limit the engine from entering unsafe regions, the transient response may be dominated by the most conservative constraint path, easily leading to disruption of input coordination and transient power mismatch in turbine-electric power systems without energy storage buffers. On the other hand, while centralized model predictive control (MPC) can explicitly handle constraints, its online computational burden is too heavy when dealing with high-order models involving turbomachinery, power electronics, and motor dynamics, making real-time deployment on low-cost embedded platforms difficult.

[0004] It is worth noting that existing predictive control methods involving hybrid electric propulsion (such as the coordinated MPC proposed by Seok et al.) are typically based on system architectures equipped with large-capacity energy storage batteries. In such architectures, the energy storage component can absorb power oscillations and provide a buffer time for engine fuel response; therefore, the core of its control strategy lies in power distribution rather than shaft stability. However, for series configurations without energy storage, the DC bus lacks power buffering, and the negative damping effect of the CPL directly acts on the power turbine rotor, leading to shaft instability. Due to the fundamental difference in physical architecture, the aforementioned energy storage-dependent MPC methods cannot be directly applied to this system through simple modifications, and their control logic cannot resolve the deep conflict between rapid power balancing and rotor dynamic stability under conditions without energy storage.

[0005] Therefore, there is an urgent need for a control method that can quickly compensate for CPL negative damping disturbances, coordinate multiple safety constraints online, and has embedded real-time execution capabilities. Summary of the Invention

[0006] To address the aforementioned shortcomings in the prior art, this application provides a power coordination and limit protection control method for a turbine electric power system. This method solves the problems in existing turbine electric power systems without energy storage, where the negative damping effect of constant power load leads to a decrease in shaft stability, and the traditional Min-Max protection logic is prone to transient power mismatch and exceeding of critical safety parameters under conditions without energy storage buffer.

[0007] To achieve the aforementioned objectives, the technical solution adopted in this application is as follows: This application provides a power coordination and limit protection control method for a turbine-electric power system, including: S1: Establish a nonlinear component-level model of the series turbine electric power system, and analyze the influence mechanism of constant power load on the stability of the power turbine shaft system based on the nonlinear component-level model; S2: Based on the influence mechanism, design a gain-scheduled multi-input multi-output inner-loop pre-stabilized controller; S3: Construct an outer loop model predictive reference command regulator based on a multi-input multi-output inner loop pre-stabilized controller; S4: Outputs the reference commands of the multi-input multi-output inner loop pre-stabilizer and the outer loop model prediction reference command regulator to the series turbine electric power system.

[0008] Further, S1 includes: S101: Construct a nonlinear mechanism model of a series turbine-electric power system including a turboshaft engine, a generator, a DC bus, and a propulsion motor; the input vector of the nonlinear mechanism model includes fuel flow rate and motor load torque, the state vector includes power turbine speed, gas turbine speed and motor speed, and the output vector includes power turbine speed, gas turbine speed and motor speed, as well as surge margin, turbine inlet total temperature and engine output shaft torque. S102: Based on the nonlinear mechanism model, under the ground test conditions, multiple typical power operating points are selected, and the gas turbine speed is used as the scheduling variable to obtain the discrete linear time-invariant state space model under each operating condition, and then a global linear variable parameter model cluster is constructed. S103: Based on the global linear variable parameter model cluster, extract the local linear variable parameter model cluster, and analyze the equivalent torque-speed reverse coupling relationship of constant power load from the shaft side of the power turbine.

[0009] Further, S103 includes: By transferring the generator-side load to the power turbine shaft side, the shaft system dynamic equations are established, and the calculation formula is as follows:

[0010] In the formula, To calculate the equivalent moment of inertia on the power turbine shaft side, For the angular velocity of the power turbine, For the power turbine to output torque, This represents the actual electromagnetic load torque of the generator. For mechanical loss torque, For time; The equivalent torque-speed relationship of a constant power load is analyzed from the shaft side of the power turbine, and linearized near the steady-state operating point to obtain the contribution of the constant power load to the speed disturbance. The calculation formula is as follows:

[0011] In the formula, This represents the disturbance to the electromagnetic load torque of the generator. To calculate the equivalent load power converted to the power turbine shaft side, For steady-state angular velocity, This is for speed disturbance.

[0012] The beneficial effects of the above scheme are: it reveals the torque-speed reverse coupling relationship after constant power load conversion from the power turbine shaft side and the mechanism by which the open-loop stability margin is weakened as the operating power increases, clarifies the instability boundary, and provides a theoretical basis for control design.

[0013] Furthermore, the multi-input multi-output inner loop pre-stabilization controller adopts an upper triangular matrix structure, and the calculation formula for the upper triangular matrix structure is as follows:

[0014] In the formula, and It is a proportional-integral controller. This is a proportional feedforward compensation channel. To assist in cross passages, To increase fuel consumption, This represents the motor torque increment. For turbine speed error, This is for motor speed error. The speed of the power turbine. This represents the motor speed.

[0015] Furthermore, the parameter tuning of the multi-input multi-output inner loop pre-stabilized controller employs a non-smooth multi-objective constraint optimization method, including: Set the first constraint condition, and optimize the typical power operating point sequentially based on the first constraint condition, and then optimize the typical power operating point in the first cycle. When optimizing the power operating point, the first power operating point will be... The optimal controller parameters at each power operating point are used as the current initial values ​​for optimization. After all typical power operating points have been optimized, the relationship between the parameters of the multi-input multi-output inner loop pre-stabilized controller and the change of the scheduling variable is fitted to obtain the gain scheduling control law, which is then applied to the multi-input multi-output inner loop pre-stabilized controller.

[0016] Furthermore, the first constraint includes frequency domain loop shaping constraint, main channel tracking performance constraint, and coupling response suppression constraint; The frequency domain loop shaping constraint includes: the peak sensitivity is lower than the preset sensitivity, and the target open-loop crossover frequency is the preset open-loop crossover frequency; The main channel tracking performance constraints include: setting the expected closed-loop response tracking of the two main channels, power turbine speed and motor speed, to a unified first-order reference model that satisfies the following formula, and ensuring that the steady-state relative error is less than a preset error, expressed as:

[0017] In the formula, As the desired reference model, For the Laplace operator, It is a time constant; The coupling response suppression constraint includes that the peak value of the auxiliary cross passage step disturbance is less than the preset peak value of the disturbance and the recovery time is less than the preset recovery time.

[0018] The beneficial effects of the above scheme are: by adopting the upper triangular structure of the gain-scheduled multi-input multi-output inner loop pre-stabilized controller, and by optimizing the tuning parameters through non-smooth multi-objective optimization, sufficient frequency domain robustness and main channel tracking accuracy are maintained in the entire operating range, and the peak value of the cross-channel coupling response is small and the recovery time is small.

[0019] Further, S3 includes: S301: Select the gas turbine speed as the scheduling variable, obtain the linear variable parameter matrix, steady-state reference and multi-input multi-output inner loop pre-stabilization control parameters under the current power condition, and combine them to form a closed-loop prediction matrix; S302: Based on the closed-loop prediction matrix, establish a closed-loop linear variable parameter prediction model. The calculation formula is as follows:

[0020] In the formula, The closed-loop augmented state vector includes the power turbine speed. Gas turbine speed Motor speed And the corresponding inner loop proportional-integral controller Discrete integral sum of error Discrete integral of the error and This is the closed-loop prediction matrix. The reference input vector includes the virtual motor speed command and the power turbine speed command, which are corrected by the outer loop model prediction reference command regulator. As a steady-state reference, For sampling discrete time intervals, This is the steady-state reference input matrix; S303: Define the prediction time domain, specify that the initial prediction value at the current sampling time is constructed jointly by the measured or estimated state and the inner loop integral state, define the output bias, and use the output bias to correct all prediction outputs of the closed-loop linear variable parameter prediction model within the prediction time domain. The formula for calculating the output bias is:

[0021] In the formula, For output deviation, For the measured or estimated true output, The model predicts the output; S304: Based on the closed-loop linear variable parameter prediction model, the outer-loop model prediction reference command regulator is determined by solving a finite-time quadratic programming optimization problem at each sampling time to obtain the optimization objective function. The calculation formula is as follows:

[0022] In the formula, To optimize the objective function, This is the corrected virtual reference command for motor speed. The original instructions given externally. , , For the corresponding weighting coefficients, This is the relaxation variable corresponding to the deviation of the power turbine speed from the limit. Let be the slack variable for surge margin. Let be the relaxation variable for the turbine inlet temperature. For surge margin, This refers to the total temperature before the turbine. To predict the index of future steps in the time domain, To predict the total number of steps in the time domain; S305: Set decision variables and a second constraint. The decision variables include the virtual reference command sequence for motor speed in the prediction time domain, as well as relaxation variables corresponding to the deviation limit of power turbine speed, the surge margin, and the turbine inlet temperature. The second constraint includes the power turbine speed deviation limit, the lower limit of surge margin, the upper limit of turbine inlet temperature, and a reference rate of change constraint. The calculation formula for the second constraint is as follows:

[0023]

[0024]

[0025]

[0026] In the formula, To normalize the power turbine speed, To normalize the breathing range, Normalized turbine inlet temperature, The maximum permissible disturbance amount, This is the lower limit of the surge margin safety. This is the upper limit of the safe temperature before the turbine. The preset upper limit for the reference change in motor speed; S306: The finite-time quadratic programming optimization problem is rearranged into a standard quadratic programming form to obtain the standard quadratic programming problem. Based on the second constraint, the standard quadratic programming problem is solved using the effective set method or the interior point method. The calculation formula for the standard quadratic programming problem is:

[0027] In the formula, For the decision variable vector, For Hessian matrix, The gradient vector, with superscript For transpose; S307: In each sampling period, if the standard quadratic programming problem is solved successfully, the first step of the optimal motor speed virtual command is taken as the corrected motor speed virtual command; if the problem fails to be solved, the motor speed virtual command applied in the previous sampling period is retained. S308: Restore the virtual motor speed command corrected for the current sampling period to the motor speed command value, and send it to the multi-input multi-output inner loop pre-stabilization controller for tracking.

[0028] The beneficial effects of the above scheme are: replacing high-dimensional nonlinear MPC with lightweight quadratic programming, predicting the future trajectory of power turbine speed, surge margin and turbine inlet total temperature online, and actively shaping the motor speed command to ensure that key safety parameters never exceed the limits under complex dynamic conditions.

[0029] The beneficial effects of this application are: This application provides a power coordination and limit protection control method for a turbine electric power system. Based on the negative damping mechanism of constant power load on the turbine shaft side, it designs a gain-dispatch multi-input multi-output inner loop pre-stabilization controller and a non-smoothly optimized model prediction reference command regulator outer loop. While ensuring robustness in the frequency domain under all operating conditions and the tracking accuracy of the main channel, it reduces transient power mismatch under high power step and strictly limits surge margin, turbine inlet temperature and turbine speed to prevent them from exceeding limits. This achieves a unity of shaft stability, coordination of multiple safety constraints and engineering real-time performance. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0031] Figure 1 This is a flowchart illustrating a power coordination and limit protection control method for a turbine electric power system provided in an embodiment of this application.

[0032] Figure 2 This is a schematic diagram of a series turbine electric power system provided in an embodiment of this application.

[0033] Figure 3 This is a component-level model structural block diagram of a series hybrid electric propulsion turboshaft engine provided in an embodiment of this application.

[0034] Figure 4 This is a schematic diagram of the distribution of local open-loop characteristic values ​​of a system under different operating power, provided as an embodiment of this application.

[0035] Figure 5 This is a schematic diagram of the non-smooth optimization tuning result of an inner loop controller provided in an embodiment of this application.

[0036] Figure 6 This is a signal flow diagram of an overall control architecture provided in an embodiment of this application.

[0037] Figure 7 A schematic diagram comparing the dynamic response of a closed-loop LPV prediction model and a nonlinear mechanism model under the transition state, provided in an embodiment of this application.

[0038] Figure 8 This is a schematic diagram illustrating the constraint protection effect of MPRG on a nonlinear component-level model, as provided in an embodiment of this application.

[0039] Figure 9This is a schematic diagram of a common inner loop Min-Max limit protection control architecture provided in an embodiment of this application.

[0040] Figure 10 This is a schematic diagram of the acceleration / deceleration planning and simulation mode switching process of a turbine-electric MIMO system provided in an embodiment of this application.

[0041] Figure 11 This is a schematic diagram comparing the multivariate cooperative performance of MPRG and Min-Max under APRBS random commands and motor load disturbances, provided as an embodiment of this application.

[0042] Figure 12 This is a schematic diagram comparing the transient power mismatch and power change rate of MPRG and Min-Max under motor torque disturbance, provided as an embodiment of this application.

[0043] Figure 13 This is a physical diagram and connection schematic of a CHIL verification platform with an MPRG control architecture provided in an embodiment of this application.

[0044] Figure 14 This is a statistical chart showing the time consumption of controller hardware-in-the-loop simulation calculations, provided as an embodiment of this application.

[0045] Figure 15 This is a schematic diagram showing the consistency between the STM32-CHIL running results and the Simulink desktop simulation results provided in this application embodiment. Detailed Implementation

[0046] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.

[0047] Example 1: This application provides a power coordination and limit protection control method for a turbine-electric power system. This method is applicable to series turbine-electric power systems without large-capacity energy storage buffers, typically with a power level of 1MW. A turboshaft engine drives a permanent magnet synchronous generator via a gearbox. After rectification, the power is supplied to four parallel inverter-motor-ducted fan propulsion units via a DC bus. In this system architecture, the generator and propulsion motor are directly coupled via the DC bus. When changes in the end-propulsion load cause fluctuations in the bus voltage, the generator's electromagnetic torque responds immediately, rigidly transmitting the disturbance to the power turbine shaft. Due to the lack of energy storage to smooth transient power fluctuations, the system must rely on the control strategy itself to dynamically match fuel supply and motor load within a millisecond timescale, rather than relying on physical energy storage devices for absorption and buffering. The method can be found in [reference needed]. Figure 1 ,include: S1: Establish a nonlinear component-level model of the series turbine electric power system, and analyze the influence mechanism of constant power load on the stability of the power turbine shaft system based on the nonlinear component-level model.

[0048] In one embodiment of this application, a nonlinear mechanism model (CLM) of a 1MW series turbine-electric power system including a turboshaft engine, a generator, a DC bus, and a propulsion motor is constructed. Its input vector includes fuel flow rate. With motor load torque The state vector includes the power turbine speed. Gas turbine speed and motor speed The output vector includes the aforementioned rotational speed and surge margin. Turbine front total temperature and engine output shaft torque. This series turbine electric power system, such as Figure 2 As shown, the energy transfer relationships between the turboshaft engine, generator, DC bus, and propulsion motor are illustrated. A component-level model of the series hybrid electric propulsion turboshaft engine is shown below. Figure 3 As shown, where, For gearbox speed, For the torque required by the electric propulsion load, This is the motor load torque command. The design parameters of this system are shown in Table 1 to increase the motor load torque.

[0049] Table 1 Design parameters of series turbine-electric power system

[0050] Under ground test conditions, several typical power operating points were selected, with the gas turbine speed as the benchmark. As scheduling variables, the small perturbation method and system identification are used to obtain discrete linear time-invariant (LTI) state-space models under various operating conditions, and then a global linear variable parameter (LPV) model cluster is constructed.

[0051] Based on this, the equivalent torque-speed reverse coupling relationship of the constant power load (CPL) is analyzed from the turbine shaft side. Specifically, the generator-side load is converted to the turbine shaft side, and the shaft dynamics can be expressed as follows:

[0052] in, To calculate the equivalent moment of inertia on the power turbine shaft side, For the angular velocity of the power turbine, For the power turbine to output torque, This represents the actual electromagnetic load torque of the generator. For mechanical loss torque, For time.

[0053] Analysis of the equivalent torque-speed relationship of CPL from the turbine shaft side: Linearization near the steady-state operating point yields the contribution of the CPL load term to the speed disturbance:

[0054] in, This represents the disturbance (small signal increment change value) of the generator's electromagnetic load torque. To calculate the equivalent load power converted to the power turbine shaft side, For steady-state angular velocity, This is for speed disturbance.

[0055] because Therefore, the CPL load term and speed disturbance The same sign indicates a negative damping effect—that is, when the speed decreases, the load torque increases, and when the speed increases, the load torque decreases, thus weakening the shaft system's self-recovery capability to speed disturbances. Several typical power operating points (covering the range of 290kW to 799kW) were selected to... As scheduling variables, the small perturbation method and system identification are used to extract LPV model clusters. The spectral radius of the state matrix for each operating condition is calculated. (i.e., the maximum eigenvalue modulus) is used to determine the high-power open-loop instability trend caused by CPL negative damping, where, For the first The state matrix of each power operating point For the first 1 eigenvalue, For feature value index.

[0056] like Figure 4 As shown, further local small disturbance stability analysis indicates that as the operating power increases, the dominant eigenvalue of the system gradually moves out of the unit circle and crosses the unit circle stability boundary near 508kW. That is, when the operating power exceeds 508kW, the system has an open-loop divergent mode under the state of no control intervention.

[0057] S2: Based on the influence mechanism, design a gain-scheduled multi-input multi-output inner-loop pre-stabilized controller.

[0058] In one embodiment of this application, a multiple-input multiple-output (MIMO) inner-loop controller is designed based on the LPV model cluster obtained in S1, with an upper triangular matrix structure:

[0059] in, To increase fuel consumption, This represents the motor torque increment, i.e., the control quantity output to the motor from the inner loop. For turbine speed error, For motor speed error, the main diagonal element and Both are proportional-integral (PI) controllers, which respectively control the power turbine speed. Closed-loop calming and motor speed Zero steady-state error tracking; off-diagonal elements This is a proportional feedforward compensation channel, used to provide compensation to the fuel flow channel when the motor speed command changes, thereby reducing the impact of electrical load changes on the fuel flow channel. The coupling effect; To assist in cross-channel operation and further improve multivariate decoupling performance. Its gain varies with the scheduling variable. (Gas turbine speed) changes synchronously, and is uniformly tuned by non-smooth optimization.

[0060] The controller parameters are tuned using a non-smooth multi-objective constrained optimization method (such as the "systune" tool in MATLAB / Simulink), unifying frequency domain robustness, time domain tracking performance, and cross-channel suppression requirements into optimization objectives and the first constraint condition. The first constraint condition includes the following constraints: (1) Frequency Domain Loop Shaping: A stability margin constraint is applied to the open-loop loops of the two main feedback channels, namely the power turbine speed and the motor speed. The peak sensitivity is lower than the preset sensitivity, such as 6 dB (corresponding to a stability margin greater than 0.5). The target open-loop crossover frequency is approximately 5 rad / s, ensuring that the inner loop closed-loop object has sufficient local robustness near each typical operating point. The sensitivity function is defined as follows: ,in, The magnitude of the open-loop transfer function. For sensitivity, It is an identity matrix.

[0061] (2) Main channel tracking performance constraints: specified and Unified first-order reference model for expected closed-loop dynamic tracking of two main channels In the formula, As the desired reference model, For the Laplace operator, is the time constant. Taking 0.5 seconds, the steady-state relative error is less than 0.01.

[0062] (3) Coupling response suppression constraint: Constraints are imposed on the peak value of the power turbine speed deviation caused by the change of motor speed command (e.g., less than the preset disturbance peak value of 0.6) and the recovery time (less than the preset recovery time of 3 seconds) to set the proportional cross compensation channel. .

[0063] A hot-start strategy is adopted to avoid controller parameter jumps between adjacent operating conditions: in the first When optimizing for each power operating point, adjacent lower power operating points ( The optimal controller parameters are used as the initial values ​​for the current optimization. After optimization at all operating points, the controller parameters are adjusted accordingly. The changing relationships are smoothly fitted to obtain the controller matrix elements. , , Follow A variable gain scheduling control law. The resulting inner-loop controller can provide continuously varying control parameters over a wide operating range and form a pre-stabilized closed-loop object for prediction and constraint supervision by the outer MPRG, such as... Figure 5 As shown, where, This is the power turbine speed command. This is the original command for motor speed. For the augmented / linearized state space matrix block under the current scheduling point, This represents the current scheduling variable, namely the gas turbine speed. , , , Is At this point, the standard state-space coefficient matrix is ​​obtained after linearizing the nonlinear component-level model (CLM). This is the stacked steady-state reference vector at the current scheduling point. As a steady-state baseline, it is included in the current scheduling variables. Below, three state variables ( , , The steady-state value of ) To output a steady-state baseline, it is included in the current scheduling variables. Below are six output variables ( , , , , , The steady-state value of ) As the input steady-state benchmark, it is included in the current scheduling variables. Below, two input variables ( and The steady-state value (corresponding to the steady-state reference fuel flow rate in the figure) and steady-state reference load torque ), For controller parameters, This is the upper limit of the turbine inlet temperature. This is the lower limit of the surge margin. The rate of change of the power turbine speed. This represents the upper limit of the rate of change of the power turbine speed. This is the virtual instruction after the MPRG outer loop correction. For closed-loop system measurement, Let be the state vector of the system. and For the tracking error of the power turbine speed and the tracking error of the motor speed, Main channel controller (fuel-power turbine channel). For cross-decoupling / feedforward compensation channels (non-diagonal). Main channel controller (torque-motor channel). For the closed-loop final fuel flow command, This is the final motor load torque command. Let be the discrete integral state vector of the inner-loop PI controller, with superscript . For transpose, For the corresponding error Discrete integrals, For the corresponding error Discrete integrals.

[0064] The specific constraints are shown in Table 2.

[0065] Table 2 Performance Optimization Constraints for Inner Loop Controller

[0066] S3: Construct an outer loop model predictive reference command regulator (MPRG) based on a multi-input multi-output inner loop pre-stabilized controller.

[0067] Based on the already stable inner loop of S2, an outer loop MPRG is added for online correction of the motor speed reference command. This ensures that the load-side power demand is constrained by the engine's safety margin during transitions, achieving power coordination and multi-constraint protection without altering the inner loop controller structure. Figure 6 As shown, from Mapping by operating point ( This represents the first starting / lowest power operating point within the gain scheduling range. This represents the last end / highest power operating point within the gain scheduling range, illustrating the cascade relationship and signal interaction between the inner-loop controller and the outer-loop MPRG of the gain-scheduled MIMO. Figure 6 The first row, R1(a), shows the sensitivity function of the power turbine speed feedback loop under various operating conditions, verifying that it meets the robustness requirements. This is a sensitivity function of the power turbine speed loop, used to evaluate the robustness of this channel. This is the sensitivity stability margin index for the power turbine speed circuit. Figure 6 The first row, R1(b), shows the sensitivity function of the motor speed feedback loop under various operating conditions, verifying that it has a good stability margin. This is a sensitivity function for the motor speed loop, used to evaluate the robustness of this channel. This is the sensitivity stability margin index for the motor speed circuit. Figure 6 The first line, R1(c), shows a comparison between the open-loop frequency response and the target envelope under various operating conditions, demonstrating that the controller meets the expected bandwidth design. The magnitude of the open-loop transfer function. The open-loop frequency response is used to specify the controller bandwidth in the design target; Figure 6 The second line, R2(d), shows the step tracking response of the power turbine speed to the reference command, verifying its fast tracking performance. For the increase in power turbine speed, This is the increment of the reference command for the power turbine speed. This is a reference command for the power turbine speed; Figure 6 The second line, R2(e), demonstrates the motor speed's step tracking response to the reference command, verifying its good dynamic performance. For the motor speed increment, This is the increment of the motor speed reference command. This is a reference command for motor speed; Figure 6 The second row, R2(f), displays the statistical results of tracking errors under various operating conditions, demonstrating that the system can achieve high tracking accuracy. The transient tracking error of the main channel. The statistical results of tracking errors under various operating conditions; Figure 6The third line R3 (h) shows the cross-coupling response of the power turbine speed command change to the motor speed, verifying that the coupling effect is small; Figure 6 The third line R3 (g) shows the cross-coupling response of the motor speed command change to the power turbine speed, verifying that the cross disturbance is effectively suppressed; Figure 6 The third row, R3(k), shows the peak distribution of cross-coupling for each operating condition, indicating that all operating conditions meet the coupling constraint requirements. This refers to the peak cross-coupling index in the direction of power turbine speed → motor speed. This refers to the peak cross-coupling index in the direction of motor speed → power turbine speed. This is to meet the peak constraint requirements for cross-coupling.

[0068] Specific sub-steps include: S301: Constructing a closed-loop linear variable parameter (LPV) prediction model and correcting output bias.

[0069] Read the current measurement value: , , and airborne model estimation , Select As a scheduling variable, based on the current LPV matrix in interpolation S1 The steady-state reference and inner-loop controller parameters are obtained by interpolation from adjacent operating points and then combined to form the closed-loop prediction matrix. , .

[0070] The closed-loop LPV prediction model used by MPRG is:

[0071] in, For sampling discrete time intervals, The steady-state reference input matrix and the closed-loop augmented state vector are given. Includes: power turbine speed Gas turbine speed Motor speed And the two integral states of the inner loop PI controller (corresponding to respectively) Discrete integral of error and Discrete integral of error ).

[0072] Reference input vector Includes: power turbine speed command (constant value 20000 rpm, normalized to 1) and virtual motor speed command corrected by MPRG. Corresponding steady-state reference. It is also obtained by interpolation.

[0073] To reduce the impact of model mismatch, a one-step output bias correction method is adopted: the initial prediction value at the current sampling time is constructed jointly by the measurement or estimation state and the inner loop integral state, and the output bias is defined. And in the prediction time domain, this deviation is used to correct all subsequent prediction outputs, so that the constraint determination of MPRG is based on the current real feedback, wherein, The true output of the current measurement / estimation. The current model predicts the output, with the following accuracy: Figure 7 As shown, where, Figure 7 (a) is to show the response comparison between the component-level model and the LPV prediction model under the motor speed step command, and to verify the accuracy of motor speed prediction; Figure 7 (b) is to demonstrate the comparison of the power turbine speed response and verify the predictive ability of the LPV prediction model for power turbine dynamics. Figure 7 (c) is to show the comparison of gas turbine speed response and verify that the LPV prediction model can accurately reflect the changes in engine core speed. Figure 7 (d) is to show the comparison of compressor surge margin response and verify the prediction accuracy of LPV prediction model for safety margin; Figure 7 (e) shows the comparison of turbine inlet temperature response, verifying that the LPV prediction model can accurately predict engine thermodynamic dynamics. Figure 7 (f) illustrates the switching process of the LPV model index as the operating conditions change, reflecting the online scheduling of the prediction model based on the operating conditions.

[0074] S302: Construct and solve the MPRG optimization problem.

[0075] Based on the closed-loop prediction model, MPRG solves a finite-time quadratic programming (QP) optimization problem at each sampling time, with the objective function being... for:

[0076] The first item is to make the modified motor speed a virtual reference command. As close as possible to the original instructions given externally. Items two through four are penalties. , , For the corresponding weighting coefficients, , , These are three types of non-negative relaxation variables, corresponding to the degree of relaxation of the power turbine speed, surge margin, and turbine inlet temperature constraints, respectively. Among them, the relaxation variable corresponding to the deviation of the power turbine speed from the limit... Allow a larger range (because)N p (For performance indicators rather than safety limits), while surge margin and turbine inlet temperature The slack variables are subject to large weighting coefficients , Strict restrictions to ensure that in the vast majority of cases SM and T 4. Constraints are strictly satisfied, with only a minimal amount of relaxation allowed in cases of short-term conflicts among multiple constraints to ensure the feasibility of QP solutions. To predict the index of future steps in the time domain, To predict the total number of steps in the time domain (i.e., the look-ahead window width for the optimization problem).

[0077] Decision variables are determined by the prediction time domain. The virtual reference instruction sequence for motor speed within a step, along with three types of slack variables, constitute the system.

[0078] The constraints include: (1) The power turbine speed deviates from the limit:

[0079] in, To normalize the power turbine speed, This represents the maximum permissible disturbance.

[0080] (2) Lower limit of surge margin:

[0081] in, To normalize the breathing range, This represents the lower limit of the surge margin safety.

[0082] (3) Upper limit of turbine inlet temperature:

[0083] in, Normalized turbine inlet temperature, This is the upper limit of the safe temperature before the turbine.

[0084] (4) Reference rate of change constraint:

[0085] In the formula, This is a preset upper limit for the reference change in motor speed, meaning that the reference change in motor speed in adjacent sampling periods must not exceed the preset upper limit to avoid sudden changes in commands.

[0086] The introduction of slack variables is used to avoid the optimization problem becoming infeasible due to model errors or short-term conflicts of multiple constraints, and the degree of constraint relaxation is limited by a large-weight penalty term in the objective function.

[0087] The MPRG optimization problem can be simplified into a standard quadratic programming form:

[0088] in, For the decision variable vector, For Hessian matrix, The gradient vector, with superscript This is a transpose.

[0089] Within each sampling period, if the quadratic programming solution is successful, the first step of the optimal reference sequence is taken as the corrected command, and a reference rate of change limit is applied; if the solution fails, the reference applied in the previous sampling period is retained as the command, and a warning flag is set. Finally, the corrected normalized motor speed reference is restored to a physical quantity (motor speed command value with actual engineering units and dimensions) and sent to the inner loop controller for tracking. The constraint protection effect of MPRG on the nonlinear component-level model is as follows: Figure 8 As shown, where, Figure 8 (a) gives the power turbine speed. The dynamic response, under the action of the MPRG correction reference command, the component-level nonlinear model and the LPV prediction model remain highly consistent and always meet the lower limit constraint of the power turbine speed. It recovers quickly after only a small transient deviation in the early stage of the step. Figure 8 (b) shows the motor speed. And the MPRG corrected reference command shows that MPRG shapes the original step command into a smooth feasible reference. The component-level model can stably track the corrected reference command and eventually converge to the target speed. Figure 8 (c) gives the turbine inlet temperature According to the response results, the LPV prediction model can accurately predict the dynamic changes of the component-level model and always meet the upper temperature limit constraint throughout the entire transition process, thus achieving engine thermal safety protection. Figure 8 (d) indicates the compressor surge margin. With its dynamic response, MPRG can effectively ensure that the surge margin is always higher than the safety lower limit, while the LPV prediction model and the nonlinear model maintain good consistency.

[0090] In one embodiment of this application, to highlight the advantages of this application, a comparison is made between an MPRG outer loop and a traditional lookup table-type Min-Max limiter under the same inner loop controller. The inner loop Min-Max limit protection control architecture is as follows: Figure 9 As shown, where, This is an anti-integral saturation trigger signal (frequency / integrator reset). For load compensation components, This is the safe torque value after amplitude limiting. The acceleration / deceleration plan and simulation mode switching process of the turbine-electric MIMO system are as follows: Figure 10 As shown, (a) are the acceleration, deceleration, and steady-state curves of fuel flow rate varying with motor speed. The acceleration and deceleration plans are generated by offline MPC optimization to ensure that the engine meets the constraints of power turbine speed, surge margin, and turbine inlet temperature at different operating stages; (b) are the acceleration, deceleration, and steady-state curves of load torque varying with motor speed, maintaining a one-to-one correspondence with the fuel flow plan to ensure coordinated matching between engine output power and propulsion load; (c) is the switching process of the fuel flow control channel between acceleration, PI control, and deceleration modes. When the system detects transient acceleration, the controller briefly switches to the acceleration plan and then returns to PI closed-loop control to achieve smooth adjustment of fuel flow; (d) is the mode switching process of the load torque control channel, which synchronously switches between acceleration plan and PI control with the fuel channel to maintain coordination between fuel input and motor load input. The test included APRBS (Amplitude Modulated Pseudo-Random Binary Sequence) continuous acceleration and deceleration conditions, with motor load torque disturbance superimposed at 50s. The results are as follows: Figures 11-12 As shown, where, Figure 11 (a) compares the speed of the power turbine under random motor speed command and load disturbance. The response results show that MPRG can effectively suppress the speed drop caused by sudden load changes, keeping the power turbine speed close to 99.5% of the safety constraint, while Min-Max control shows a larger transient drop. Figure 11 (b) gives the motor speed. Both control strategies can track random speed commands, but MPRG achieves a smoother speed adjustment process through reference shaping. Figure 11 (c) shows the turbine inlet temperature. With its dynamic response, MPRG maintains the temperature below the maximum allowable value while ensuring a fast response, and has better constraint retention capability compared with the Min-Max scheme. Figure 11 (d) gives the compressor surge margin. During the change process, both methods can ensure that the surge margin is higher than the safety boundary, but MPRG has a more stable dynamic recovery capability during the load change phase. Figure 11 (e) shows the propulsion motor load torque. In response to changes in load reference, MPRG achieves smoother load regulation by correcting the load reference online, while Min-Max uses actuator limiting to complete the control. Figure 11 (f) gives the fuel flow rate With its control input response, MPRG can coordinate the relationship between fuel compensation and load changes, making fuel regulation more continuous, thereby reducing transient power mismatch between the engine and the propulsion system. Figure 12 (a) and (c) represent the power difference and power change rate of the outer loop of MPRG. Figure 12 (b) and (d) represent the power difference and power change rate of a traditional lookup table-based Min-Max limiter. The results show that under the Min-Max scheme... There was a clear deviation from the limit (the lowest level dropped to approximately 98.7%), resulting in power mismatch (engine output power). With electric propulsion load power difference ,in, The negative peak value for power loss in the electric drive link is approximately -128kW; however, the MPRG in this application remains constrained and feasible. (Basically maintained above 99.5% of the constraint boundary), the peak power mismatch was only about -47kW, a reduction of 63%. During deceleration, due to... and For invalid constraints (far from the boundary), the two behave similarly.

[0091] S4: Outputs the reference commands of the multi-input multi-output inner loop pre-stabilizer and the outer loop model prediction reference command regulator to the series turbine electric power system.

[0092] In one embodiment of this application, the control algorithms described in S2 and S3 are generated into C code using an Embedded Coder and deployed on an STM32H743ZIT6 development board (64MHz main frequency, 20ms control cycle). The host computer runs a nonlinear component-level model (Simulink) and communicates with the development board via a UART serial port (115200bps) to perform hardware-in-the-loop (CHIL) verification of the controller. A schematic diagram of the physical CHIL verification platform for the MPRG control architecture and its connections is shown below. Figure 13 As shown, where, The output vector is a 6-dimensional vector fed back from the nonlinear component-level model or the controlled object to the STM32 controller, representing the current true response value of the system; This is the virtual reference command for motor speed that is finally output to the inner loop controller after online correction by the MPRG (Model Predictive Reference Command Regulator). The single-step calculation time for the current control cycle (the most recent step); This represents the maximum single-step calculation time recorded during the entire operation. The experiment was set to a total duration of 100 seconds, with a sudden motor load torque disturbance applied at 50 seconds, and the responses of all channels were recorded. The test results are as follows: Figure 14As shown in Table 3, the average single-step calculation time is 0.322ms, the maximum single-step calculation time is 2.955ms, the control cycle is 20ms, the real-time margin (control cycle / maximum calculation time) is approximately 6.77 times, and the hardware output waveform completely overlaps with the desktop simulation, with each channel error approaching zero. Figure 15 As shown, (a) displays the power turbine speed. and its lower bound constraint boundary The comparison shows that the maximum absolute error Max|e| between the embedded hardware and the simulation curve is only 0.015% (occurring at t=88.26s), indicating that the hard constraint protection logic runs correctly on the hardware side; (b) shows the motor speed. The tracking response comparison showed a maximum absolute error of 7.08 rpm (occurring at t=88.54s), indicating that the STM32 hardware's tracking of the motor speed command was highly consistent with the desktop simulation; (c) showed the gas turbine speed. The state response comparison showed a maximum absolute error of 46.03 rpm (occurring at t=88.48s), verifying the real-time calculation accuracy of the hardware on key state variables; (d) demonstrates the compressor surge margin. and its lower bound The maximum absolute error was only 1.100% (occurring at t=88.00s), indicating that the embedded algorithm was completely consistent with the simulation results in terms of constraint relaxation variable protection; (e) shows the total temperature before the turbine. and its upper safety limit The protection status showed a maximum absolute error of 1.552% (occurring at t=70.26s), indicating that the embedded controller operated effectively and maintained temperature safety in the critical constraint region; (f) shows the virtual instructions after MPRG outer loop correction. The comparison of the motor speed shaping reference command shows a maximum absolute error of 19.88 rpm (occurring at t=70.24s), indicating that the real-time quadratic programming MPRG algorithm running on the STM32 can successfully output shaping commands consistent with the outer loop simulation. It is evident that the method proposed in this application can achieve online quadratic programming solution for MPRG on a low-cost STM32H743 microcontroller with a main frequency of only 64MHz, with a maximum single-step calculation time of 2.955ms. In contrast, a centralized MPC of the same scale on the same hardware platform cannot complete the solution within a 20ms control cycle due to the need to simultaneously optimize two inputs: fuel flow and motor torque. This demonstrates the embedded deployment advantage of the low-degree-of-freedom MPRG architecture proposed in this application, which does not rely on high-computing-power industrial controllers.

[0093] Table 3. Statistical Results of CHIL Verification Real-Time Performance

[0094] This application clarifies the instability boundary through the analysis of the negative damping mechanism of constant power load on the shaft side of the power turbine, and designs a gain-scheduled multi-input multi-output inner loop pre-stabilization controller and a non-smoothly optimized model prediction reference command regulator outer loop. While ensuring robustness in the frequency domain under all operating conditions and the tracking accuracy of the main channel, it reduces the transient power mismatch under high power step by 63%, and strictly limits the surge margin, turbine inlet temperature and power turbine speed to prevent them from exceeding the limits. The measured maximum single-step calculation time of this dual-layer architecture on a low-cost embedded microcontroller is only 2.955ms, which is much less than the 20ms control cycle, and the one-step output deviation correction effectively compensates for the model mismatch, thus taking into account shaft stability, coordination of multiple safety constraints, transient response performance and engineering real-time performance.

[0095] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping readers understand the principles of this application, and should be understood as not limiting the scope of protection of this application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this application without departing from the essence of this application, and these modifications and combinations are still within the scope of protection of this application.

Claims

1. A power coordination and limit protection control method for a turbine electric power system, characterized in that, include: S1: Establish a nonlinear component-level model of the series turbine electric power system, and analyze the influence mechanism of constant power load on the stability of the power turbine shaft system based on the nonlinear component-level model; S2: Based on the influence mechanism, design a gain-scheduled multi-input multi-output inner-loop pre-stabilized controller; S3: Construct an outer loop model predictive reference command regulator based on a multi-input multi-output inner loop pre-stabilized controller; S4: Outputs the reference commands of the multi-input multi-output inner loop pre-stabilizer and the outer loop model prediction reference command regulator to the series turbine electric power system.

2. The power coordination and limit protection control method for a turbine electric power system according to claim 1, characterized in that, S1 includes: S101: Construct a nonlinear mechanism model of a series turbine-electric power system including a turboshaft engine, a generator, a DC bus, and a propulsion motor; the input vector of the nonlinear mechanism model includes fuel flow rate and motor load torque, the state vector includes power turbine speed, gas turbine speed and motor speed, and the output vector includes power turbine speed, gas turbine speed and motor speed, as well as surge margin, turbine inlet total temperature and engine output shaft torque. S102: Based on the nonlinear mechanism model, under the ground test conditions, multiple typical power operating points are selected, and the gas turbine speed is used as the scheduling variable to obtain the discrete linear time-invariant state space model under each operating condition, and then a global linear variable parameter model cluster is constructed. S103: Based on the global linear variable parameter model cluster, extract the local linear variable parameter model cluster, and analyze the equivalent torque-speed reverse coupling relationship of constant power load from the shaft side of the power turbine.

3. The power coordination and limit protection control method for a turbine electric power system according to claim 2, characterized in that, S103 includes: By transferring the generator-side load to the power turbine shaft side, the shaft system dynamic equations are established, and the calculation formula is as follows: In the formula, To calculate the equivalent moment of inertia on the power turbine shaft side, For the angular velocity of the power turbine, For the power turbine to output torque, This represents the actual electromagnetic load torque of the generator. For mechanical loss torque, For time; The equivalent torque-speed relationship of a constant power load is analyzed from the shaft side of the power turbine, and linearized near the steady-state operating point to obtain the contribution of the constant power load to the speed disturbance. The calculation formula is as follows: In the formula, This represents the disturbance to the electromagnetic load torque of the generator. To calculate the equivalent load power converted to the power turbine shaft side, For steady-state angular velocity, This is for speed disturbance.

4. The power coordination and limit protection control method for a turbine electric power system according to claim 3, characterized in that, The multi-input multi-output inner loop pre-stabilization controller adopts an upper triangular matrix structure, and the calculation formula for the upper triangular matrix structure is as follows: In the formula, and It is a proportional-integral controller. This is a proportional feedforward compensation channel. To assist in cross passages, To increase fuel consumption, This represents the motor torque increment. For turbine speed error, This is for motor speed error. The speed of the power turbine. This represents the motor speed.

5. The power coordination and limit protection control method for a turbine electric power system according to claim 4, characterized in that, The parameter tuning of the multi-input multi-output inner loop pre-stabilized controller employs a non-smooth multi-objective constraint optimization method, including: Set the first constraint condition, and optimize the typical power operating point sequentially based on the first constraint condition, and then optimize the typical power operating point in the first cycle. When optimizing the power operating point, the first power operating point will be... The optimal controller parameters at each power operating point are used as the current initial values ​​for optimization. After all typical power operating points have been optimized, the relationship between the parameters of the multi-input multi-output inner loop pre-stabilized controller and the change of the scheduling variable is fitted to obtain the gain scheduling control law, which is then applied to the multi-input multi-output inner loop pre-stabilized controller.

6. The power coordination and limit protection control method for a turbine electric power system according to claim 5, characterized in that, The first constraint conditions include frequency domain loop shaping constraint, main channel tracking performance constraint, and coupling response suppression constraint; The frequency domain loop shaping constraint includes: the peak sensitivity is lower than the preset sensitivity, and the target open-loop crossover frequency is the preset open-loop crossover frequency; The main channel tracking performance constraints include: setting the expected closed-loop response tracking of the two main channels, power turbine speed and motor speed, to a unified first-order reference model that satisfies the following formula, and ensuring that the steady-state relative error is less than a preset error, expressed as: In the formula, As the desired reference model, For the Laplace operator, It is a time constant; The coupling response suppression constraint includes that the peak value of the auxiliary cross passage step disturbance is less than the preset peak value of the disturbance and the recovery time is less than the preset recovery time.

7. The power coordination and limit protection control method for a turbine electric power system according to claim 6, characterized in that, S3 includes: S301: Select the gas turbine speed as the scheduling variable, obtain the linear variable parameter matrix, steady-state reference and multi-input multi-output inner loop pre-stabilization control parameters under the current power condition, and combine them to form a closed-loop prediction matrix; S302: Based on the closed-loop prediction matrix, establish a closed-loop linear variable parameter prediction model. The calculation formula is as follows: In the formula, The closed-loop augmented state vector includes the power turbine speed. Gas turbine speed Motor speed And the corresponding inner loop proportional-integral controller Discrete integral sum of error Discrete integral of the error and This is the closed-loop prediction matrix. The reference input vector includes the virtual motor speed command and the power turbine speed command, which are corrected by the outer loop model prediction reference command regulator. As a steady-state reference, For sampling discrete time intervals, This is the steady-state reference input matrix; S303: Define the prediction time domain, specify that the initial prediction value at the current sampling time is constructed jointly by the measured or estimated state and the inner loop integral state, define the output bias, and use the output bias to correct all prediction outputs of the closed-loop linear variable parameter prediction model within the prediction time domain. The formula for calculating the output bias is: In the formula, For output deviation, For the measured or estimated true output, The model predicts the output; S304: Based on the closed-loop linear variable parameter prediction model, the outer-loop model prediction reference command regulator is determined by solving a finite-time quadratic programming optimization problem at each sampling time to obtain the optimization objective function. The calculation formula is as follows: In the formula, To optimize the objective function, This is the corrected virtual reference command for motor speed. The original instructions given externally. , , For the corresponding weighting coefficients, This is the relaxation variable corresponding to the deviation of the power turbine speed from the limit. Let be the slack variable for surge margin. Let be the relaxation variable for the turbine inlet temperature. For surge margin, This refers to the total temperature before the turbine. To predict the index of future steps in the time domain, To predict the total number of steps in the time domain; S305: Set decision variables and a second constraint. The decision variables include the virtual reference command sequence for motor speed in the prediction time domain, as well as relaxation variables corresponding to the deviation limit of power turbine speed, the surge margin, and the turbine inlet temperature. The second constraint includes the power turbine speed deviation limit, the lower limit of surge margin, the upper limit of turbine inlet temperature, and a reference rate of change constraint. The calculation formula for the second constraint is as follows: In the formula, To normalize the power turbine speed, To normalize the breathing range, Normalized turbine inlet temperature, The maximum permissible disturbance amount, This is the lower limit of the surge margin safety. This is the upper limit of the safe temperature before the turbine. The preset upper limit for the reference change in motor speed; S306: The finite-time quadratic programming optimization problem is rearranged into a standard quadratic programming form to obtain the standard quadratic programming problem. Based on the second constraint, the standard quadratic programming problem is solved using the effective set method or the interior point method. The calculation formula for the standard quadratic programming problem is: In the formula, For the decision variable vector, For Hessian matrix, The gradient vector, with superscript For transpose; S307: In each sampling period, if the standard quadratic programming problem is solved successfully, the first step of the optimal motor speed virtual command is taken as the corrected motor speed virtual command; if the problem fails to be solved, the motor speed virtual command applied in the previous sampling period is retained. S308: Restore the virtual motor speed command corrected for the current sampling period to the motor speed command value, and send it to the multi-input multi-output inner loop pre-stabilization controller for tracking.

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