Single-loop model predictive control method for loading system

Abstract

The invention relates to the technical field of loading system control, and provides a single-loop model prediction control method for a loading system, and the method comprises the steps: collecting data, and carrying out the processing of the data, and obtaining a state variable; constructing a prediction model output load and displacement prediction sequence including a product term of the displacement change rate and the coupling coefficient; estimating redundant force interference through a Kalman filter by using a state observer in combination with a prediction sequence and a real-time feedback signal; constructing a quadratic objective function containing a feed-forward compensation item in a rolling optimization period, and solving a constrained optimization problem to obtain an optimal control increment; and converting the control increment into a driving signal to control a servo mechanism to output a loading force, and integrating a safety monitoring mechanism. According to the method, system dynamic coupling, state observer real-time interference identification and feedforward compensation active offset influence are represented through the prediction model, redundant force interference generated by active motion of a tested product is effectively inhibited, and the load tracking precision and the anti-interference capability of the loading system are improved.

Description

Technical Field

[0001] This invention relates to the field of loading system control technology, and in particular to a single-loop model predictive control method for loading systems. Background Technology

[0002] In the servo loading test technology of aircraft control surfaces, the single-loop model serves as the control architecture of the loading system and uses a single feedback loop to simulate the load. The model drives the servo mechanism to adjust the output force based on the deviation between the command signal and the measured load signal, so that the loading process approximates the real aerodynamic environment. Its simple structure helps to reduce the complexity of the system, while the direct error correction mechanism improves the dynamic tracking capability, thus meeting the high-fidelity reproduction requirements of rapidly changing loads in control surface testing.

[0003] Existing single-loop model predictive control for loading systems suffers from the following technical challenges: Due to the direct coupling and interaction between the loading system and the test product (DPT), a strong dynamic coupling relationship is formed. When the DPT, such as the control surfaces of an aircraft, actively moves, its motion changes generate redundant force interference in real time. This interference stems from the inertial force and coupling effect caused by the control surface deflection, making it difficult for the loading system to eliminate dynamic deviations when tracking commanded loads. This leads to phase lag and amplitude errors in the control loop, thereby reducing the accuracy of the simulated aerodynamic loads. For example, in control surface servo loading tests, the redundant torque introduced by the rapid extension and retraction of the control surface is superimposed on the loading output, interfering with the accurate reproduction of the load spectrum and affecting the validity of the test. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a single-loop model predictive control method for loading systems, which solves the technical problem of large dynamic response errors and reduced control accuracy caused by redundant force interference generated by the active movement of the test product.

[0005] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0006] The present invention provides a single-loop model predictive control method for a loaded system, comprising: Step 1: Collect signals from the force sensor and displacement sensor in the loading system and obtain the desired load command. Extract the load tracking error, displacement change rate and historical control sequence from the collected signals. The load tracking error is calculated based on the desired load command and the collected load signal. Define the load tracking error, displacement change rate and historical control sequence as state variables. Step 2: Construct a prediction model. The prediction model is driven by state variables. The prediction model performs calculations and outputs load prediction sequences and displacement prediction sequences. Step 3: Input the load prediction sequence, displacement prediction sequence, first analog voltage signal collected by the force sensor, and second analog voltage signal collected by the displacement sensor into the state observer. The state observer performs calculations and outputs the estimated value of the redundant force disturbance. Step 4: During the rolling optimization cycle, construct an objective function based on the prediction model, the estimated value of the redundant force disturbance, and the expected load command. The objective function includes a term to offset the redundant force disturbance with a feedforward compensation term. Solve the constrained optimization problem to obtain the optimal control increment. Step 5: Convert the optimal control increment into a drive signal. Apply the drive signal to the servo mechanism of the loading system. The servo mechanism outputs a loading force according to the drive signal. The loading force acts on the test product. The force sensor detects the magnitude of the loading force, and the displacement sensor detects the positional change of the loading force.

[0007] Furthermore, in the single-loop model predictive control method for a loading system of the present invention, step 1 includes: Receive a first analog voltage signal from the force sensor and a second analog voltage signal from the displacement sensor; The received first analog voltage signal and second analog voltage signal are synchronously sampled and converted from analog to digital, and the load digital signal and position digital signal are output. Collect and send control commands to the servo mechanism to obtain digital signals of the control commands; The output load digital signal, position digital signal, and acquired control command digital signal are timestamped based on the same time base and then merged to form the original data stream.

[0008] Furthermore, in the single-loop model predictive control method for a loading system of the present invention, step 1 further includes: The generated raw data stream is parsed, and the parsed load digital signal, parsed position digital signal, and parsed control command digital signal are output. The parsed load digital signal is subjected to digital filtering processing, and the filtered load signal is output. The parsed position digital signal is subjected to digital filtering processing, and the filtered position signal is output. Calculate the difference between the filtered load signal and the desired load command, and output the load tracking error; Calculate the difference of the filtered position signal at consecutive time points, perform sliding window averaging on the difference results, and output the rate of change of displacement. Extract the signal value with the most recent preset time length from the parsed control command digital signal, and cache it to form a historical control sequence; The output load tracking error, displacement change rate, and historical control sequence are combined into the state vector at the current moment.

[0009] Furthermore, in the single-loop model predictive control method for a loading system of the present invention, step 2 includes: Establish a discrete-time state-space equation that includes the parameter matrix to be identified and the coupling coefficient to be identified. The discrete-time state-space equation takes the state vector as input and includes a product term of the displacement rate of change and the coupling coefficient. To identify the values ​​of the parameter matrix and coupling coefficients, a known excitation signal is injected into the loading system, the response signal output by the loading system is collected, and the value of the state vector during the injection of the known excitation signal is recorded. The recorded state vector, known excitation signal, and acquired response signal are used as inputs to the recursive least squares algorithm, which outputs the parameter matrix and coupling coefficient values.

[0010] Furthermore, the single-loop model predictive control method for a loading system of the present invention, wherein the predictive model performs calculations and outputs load prediction sequences and displacement prediction sequences, includes: Substitute the parameter matrix values, coupling coefficient values, and current state vector output by the recursive least squares algorithm into the discrete-time state-space equation. Using the discrete-time state-space equation with input parameter matrix values, coupling coefficient values, and state vectors, iterative calculations are performed starting from the current moment according to the sampling period to output load values ​​and displacement values ​​at multiple future moments, generating load prediction sequences and displacement prediction sequences.

[0011] Furthermore, in the single-loop model predictive control method for a loaded system of the present invention, the state observer performs calculations and outputs an estimate of the redundant force disturbance, including: Obtain the load prediction value at the current moment from the generated load prediction sequence, and obtain the displacement prediction value at the current moment from the generated displacement prediction sequence; The actual load feedback value at the current moment is obtained from the filtered load signal, and the actual displacement feedback value at the current moment is obtained from the filtered position signal; Calculate the difference between the predicted load value and the actual load feedback value, and output the load residual; calculate the difference between the predicted displacement value and the actual displacement feedback value, and output the displacement residual. The load residual, displacement residual, and the estimated value of redundant force disturbance output from the previous calculation cycle of the state observer are input into the Kalman filter. The Kalman filter executes the state update equation calculation and outputs the estimated value of redundant force disturbance at the current moment.

[0012] Furthermore, in the single-loop model predictive control method for a loading system of the present invention, step 4 includes: Using the generated load prediction sequence, the estimated value of redundant force disturbance output by the state observer, and the expected load command as inputs, and the future control increment sequence as decision variables, a quadratic objective function is constructed. The quadratic objective function includes a first calculation term, a second calculation term, and a third calculation term. The first calculation term is the weighted sum of the squared errors of the load prediction sequence minus the expected load command. The second calculation term is the weighted sum of the squared rates of change of the future control increment sequence. The third calculation term is the sum of the products of the estimated redundant force disturbance value after transformation by the feedforward gain matrix and the first N control increments of the future control increment sequence, where N is an integer greater than zero. Solve the quadratic objective function of the physical constraints of the additional servo mechanism to obtain the optimal solution of the future control increment sequence. Extract the first control increment from the optimal solution of the future control increment sequence as the optimal control increment of the current rolling optimization cycle.

[0013] Furthermore, the single-loop model predictive control method for a loading system of the present invention solves the quadratic objective function of the physical constraints of the additional servo mechanism by: The preset maximum output force limit and maximum motion speed limit of the servo mechanism are expressed as a set of linear inequality constraints with respect to the future control increment sequence; In each rolling optimization cycle, the generated load prediction sequence, the estimated value of redundant force disturbance output by the state observer, and the expected load command are used as determining parameters. A set of linear inequality constraints is added to the quadratic objective function to solve the constrained optimization problem and obtain the optimal solution of the future control increment sequence. Extract the first control increment from the optimal solution of the future control increment sequence, and use it as the optimal control increment for the current rolling optimization cycle.

[0014] Furthermore, the single-loop model predictive control method for a loading system of the present invention converts the optimal control increment into a drive signal, and the drive signal is applied to the servo mechanism of the loading system, including: Extract the optimal control increment from the current rolling optimization cycle, extract the control command value from the previous rolling optimization cycle, add the optimal control increment to the control command value, and obtain the control command value for the current cycle. Perform digital-to-analog conversion on the current cycle control command value and output an analog voltage drive signal; The analog voltage drive signal is transmitted to the servo mechanism of the loading system. The servo mechanism outputs a loading force according to the analog voltage drive signal. The loading force is applied to the test product. The force sensor detects the magnitude of the loading force, and the displacement sensor detects the positional change of the loading force.

[0015] Furthermore, the single-loop model predictive control method for a loading system of the present invention further includes: Monitor the current cycle control command value and compare it with the preset safety limit value; Monitor load tracking error, compare the load tracking error with the preset load error alarm threshold, monitor the excess force interference estimate, and compare the excess force interference estimate with the preset interference alarm threshold. When the current cycle control command value is greater than the preset safety limit value, or the load tracking error is greater than the preset load error alarm threshold, or the estimated value of redundant force interference is greater than the preset interference alarm threshold, a protection signal is generated. After the protection signal is triggered, the output of analog voltage drive signal to the servo mechanism is stopped, the loading system is controlled to enter the preset safety state, and the loading force is stopped from being applied to the test product.

[0016] The beneficial effects of this invention are: This invention collects signals from force and displacement sensors in a loading system, extracts load tracking error, displacement change rate, and historical control sequences as state variables, constructs a predictive model including the product of displacement change rate and coupling coefficient, and outputs predicted load and displacement sequences. Using a state observer, combined with the predicted sequences and real-time feedback signals, a Kalman filter is used to estimate redundant force interference. Within the rolling optimization cycle, a quadratic objective function with feedforward compensation terms is constructed, and the constrained optimization problem is solved to obtain the optimal control increment. This control increment is then converted into a drive signal to control the servo mechanism's output loading force, and a safety monitoring mechanism is integrated. This invention explicitly characterizes the dynamic coupling relationship between the control surface motion and the loading system through a predictive model. The state observer identifies the amplitude and phase characteristics of redundant force interference in real time. A feedforward compensation term is introduced into the objective function to actively counteract the interference. Combined with rolling optimization, the optimal control command is generated, enabling the servo mechanism to synchronously correct phase lag and amplitude errors caused by interference when outputting loading force. This effectively suppresses redundant force interference caused by the active movement of the test product, improves the load tracking accuracy and dynamic anti-interference capability of the loading system, and ensures system reliability through safety monitoring. Attached Figure Description

[0017] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on the accompanying drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a single-loop model predictive control method for a loading system. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The technical solutions provided by various embodiments of this invention will be described in detail below with reference to the accompanying drawings.

[0020] To better understand the purpose of this invention, the invention will be described in further detail below.

[0021] Please see Figure 1 The present invention provides a single-loop model predictive control method for a loading system, comprising: Step 1: Collect signals from the force sensor and displacement sensor in the loading system and obtain the desired load command. Extract the load tracking error, displacement change rate and historical control sequence from the collected signals. The load tracking error is calculated based on the desired load command and the collected load signal. Define the load tracking error, displacement change rate and historical control sequence as state variables. Step 2: Construct a prediction model. The prediction model is driven by state variables. The prediction model performs calculations and outputs load prediction sequences and displacement prediction sequences. Step 3: Input the load prediction sequence, displacement prediction sequence, first analog voltage signal collected by the force sensor, and second analog voltage signal collected by the displacement sensor into the state observer. The state observer performs calculations and outputs the estimated value of the redundant force disturbance. Step 4: During the rolling optimization cycle, construct an objective function based on the prediction model, the estimated value of the redundant force disturbance, and the expected load command. The objective function includes a term to offset the redundant force disturbance with a feedforward compensation term. Solve the constrained optimization problem to obtain the optimal control increment. Step 5: Convert the optimal control increment into a drive signal. Apply the drive signal to the servo mechanism of the loading system. The servo mechanism outputs a loading force according to the drive signal. The loading force acts on the test product. The force sensor detects the magnitude of the loading force, and the displacement sensor detects the positional change of the loading force.

[0022] During the loading system control process, step 1 involves real-time acquisition of the system's mechanical and motion feedback signals using force and displacement sensors. The force sensor outputs a first analog voltage signal, and the displacement sensor outputs a second analog voltage signal. After synchronous sampling and analog-to-digital conversion, these two types of signals generate load digital signals and position digital signals, respectively. Simultaneously, the system acquires the control command digital signals sent to the servo mechanism, aligns the three types of digital signals with timestamps according to a unified time base, and merges them to form the original data stream. The load digital signals and position digital signals obtained from parsing the original data stream are digitally filtered to extract the filtered load and position signals. The filtered load signal is compared with the externally input desired load command to calculate the load tracking error. The filtered position signal undergoes continuous time-point differential calculation and is then averaged using a sliding window to obtain the displacement change rate. Historical values ​​of the most recent preset time length are extracted from the parsed control command digital signals to form a historical control sequence. Finally, the load tracking error, displacement change rate, and historical control sequence are combined to form the state variable for the current moment.

[0023] Step 2: Constructing a prediction model based on state variables. First, a discrete-time state-space equation is established, including the matrix of parameters to be identified and coupling coefficients. This equation takes the state vector as input and includes a product term consisting of the displacement rate of change multiplied by the coupling coefficient, used to characterize the dynamic coupling characteristics between the loading system and the test product. A known excitation signal is injected into the loading system, while the system's output response signal is collected, and the state vector values ​​during the excitation period are recorded. A recursive least squares algorithm is used to process the recorded state vector, excitation signal, and response signal to identify the parameter matrix values ​​and coupling coefficient values ​​in the state-space equation online. The identified parameters and the current state vector are substituted into the discrete-time state-space equation, and the load and displacement values ​​at multiple future time points are iteratively calculated according to the sampling period, generating load prediction sequences and displacement prediction sequences.

[0024] Step 3 fuses the predicted sequences with real-time sensor feedback. The predicted values ​​for the current moment are extracted from the generated load and displacement prediction sequences, while the actual feedback values ​​for the current moment are obtained from the filtered load and position signals. The difference between the predicted load value and the actual feedback value is calculated to obtain the load residual, and the difference between the predicted displacement value and the actual feedback value is calculated to obtain the displacement residual. The load residual, displacement residual, and the estimated redundant force disturbance output from the previous calculation cycle of the state observer are input into a Kalman filter, and the estimated redundant force disturbance value for the current moment is calculated using the state update equation.

[0025] Step 4 implements feedforward compensation control within the rolling optimization cycle. Using the load prediction sequence, the estimated value of redundant force disturbance, and the desired load command as inputs, and the future control increment sequence as the decision variable, a quadratic objective function is constructed, comprising three terms: the first term is the weighted sum of the squared errors between the load prediction sequence and the desired command; the second term is the weighted sum of the squared rates of change of the control increment; and the third term is the sum of the products of the estimated value of redundant force disturbance after transformation by the feedforward gain matrix and the first N terms of the control increment sequence. The maximum output force limit and maximum motion speed limit of the servo mechanism are transformed into a set of linear inequality constraints. The constrained optimization problem is solved within each rolling cycle to obtain the optimal solution for the future control increment sequence, and the first control increment is extracted as the optimal control increment for the current cycle.

[0026] Step 5 completes the execution of control commands and system safety monitoring. The optimal control increment of the current rolling optimization cycle is added to the control command value of the previous cycle to obtain the absolute control command value for the current cycle. After digital-to-analog conversion, an analog voltage drive signal is generated. This drive signal is transmitted to the servo mechanism, which outputs a corresponding loading force based on the voltage signal. The loading force acts on the tested product to form a closed-loop control. Simultaneously, the system continuously monitors whether the control command value exceeds the safety limit, and monitors whether the load tracking error and the estimated value of redundant force interference exceed the alarm threshold. When any parameter exceeds the limit, a protection signal is immediately generated, the drive signal output is stopped, and the loading system is controlled to enter a safe state.

[0027] Specifically, the single-loop model predictive control method for a loading system of the present invention includes step 1 as follows: Receive a first analog voltage signal from the force sensor and a second analog voltage signal from the displacement sensor; The received first analog voltage signal and second analog voltage signal are synchronously sampled and converted from analog to digital, and the load digital signal and position digital signal are output. Collect and send control commands to the servo mechanism to obtain digital signals of the control commands; The output load digital signal, position digital signal, and acquired control command digital signal are timestamped based on the same time base and then merged to form the original data stream.

[0028] In the single-loop model predictive control method for a loading system, the core task of step 1 is to lay the foundation for subsequent state variable extraction through multi-source sensor data acquisition and preprocessing. This process begins with receiving a first analog voltage signal from a force sensor, which directly reflects the real-time load applied to the test product by the loading system; simultaneously, a second analog voltage signal is received from a displacement sensor to capture the motion displacement changes of the test product. The two analog voltage signals are typically transmitted in a differential input mode to suppress common-mode interference. For example, in aircraft control surface testing, a force sensor may be installed between the actuator and the test control surface, while a displacement sensor monitors the control surface deflection angle, thereby obtaining realistic mechanical and kinematic feedback.

[0029] Next, synchronous sampling and analog-to-digital conversion (ADC) operations are performed on the received first and second analog voltage signals. Synchronous sampling is achieved by a clock signal allocated by a unified timing controller, ensuring strict alignment of the sampling times of the two channels and avoiding dynamic errors introduced by phase differences. The ADC uses a high-resolution chip to quantize the analog voltage signals into load digital signals and position digital signals. For example, in high-speed data acquisition scenarios, the sampling frequency needs to be set according to the system bandwidth, and the choice of the bit depth in the ADC directly affects the signal quantization accuracy, thus impacting the accuracy of subsequent control.

[0030] Simultaneously, the system acquires and sends control commands to the servo mechanism. These commands are read directly from the servo driver's command register in digital signal form, obtaining the control command digital signal. This step ensures the synchronous acquisition of control commands and sensor data, providing input for subsequent data fusion. In practical applications, the control command digital signal may include the desired position or force control mode parameters of the servo mechanism, and its update frequency is consistent with the sensor sampling period.

[0031] Finally, the output load digital signal, position digital signal, and acquired control command digital signal are timestamped and aligned based on the same time base. The timestamping module eliminates timing jitter between different signal sources by adding precise timestamps to each data packet; the merging operation integrates the three types of digital signals into a single raw data stream, forming a unified input for subsequent processing. This data integration method is particularly crucial in complex loading tests. For example, when the control surface moves rapidly, the raw data stream ensures the instantaneous correspondence between load, displacement, and control commands, providing a reliable data foundation for accurately extracting state variables.

[0032] Specifically, in the single-loop model predictive control method for a loading system of the present invention, step 1 further includes: The generated raw data stream is parsed, and the parsed load digital signal, parsed position digital signal, and parsed control command digital signal are output. The parsed load digital signal is subjected to digital filtering processing, and the filtered load signal is output. The parsed position digital signal is subjected to digital filtering processing, and the filtered position signal is output. Calculate the difference between the filtered load signal and the desired load command, and output the load tracking error; Calculate the difference of the filtered position signal at consecutive time points, perform sliding window averaging on the difference results, and output the rate of change of displacement. Extract the signal value with the most recent preset time length from the parsed control command digital signal, and cache it to form a historical control sequence; The output load tracking error, displacement change rate, and historical control sequence are combined into the state vector at the current moment.

[0033] In the subsequent processing of step 1, parsing the resulting raw data stream is a crucial step. The raw data stream includes timestamp-aligned payload digital signals, position digital signals, and control command digital signals. The parsing process separates these three types of signals according to a predefined data frame structure. For example, in an aerospace control surface testing system, the data frame may use a fixed-length header and payload structure. The parsing module identifies the data start point by recognizing the frame header and extracts the parsed payload digital signals, parsed position digital signals, and parsed control command digital signals, providing structured input for subsequent signal processing.

[0034] Next, digital filtering is performed on the analyzed load digital signal and the analyzed position digital signal. The digital filtering employs a zero-phase filtering algorithm, which eliminates group delay through forward and backward filtering, avoiding the introduction of phase distortion. The filtered load signal and the filtered position signal effectively suppress high-frequency noise and sampling jitter. For example, in scenarios with rapid control surface movement, the filtering process can retain effective dynamic characteristics while removing glitches caused by electromagnetic interference, thus improving signal quality.

[0035] The load tracking error is calculated by measuring the difference between the filtered load signal and the desired load command. The desired load command is given by an external test system and represents the load value expected to be applied to the test product. The load tracking error reflects the deviation between the actual applied force and the command value. For example, when the control surface is subjected to active motion disturbance, this error can characterize the degree of degradation of the system's tracking performance in real time and provide input for subsequent control compensation.

[0036] The filtered position signal undergoes differential calculation at continuous time points, and the differential results are then averaged using a sliding window to output the displacement change rate. The differential operation obtains the displacement increment between adjacent sampling points, and the sliding window averaging smooths instantaneous fluctuations by calculating the arithmetic mean of multiple differential values. The displacement change rate quantifies the motion velocity of the tested product. In control surface testing, this parameter can capture the acceleration characteristics of control surface deflection and is used to characterize the dynamic coupling strength of the system.

[0037] The most recent signal value with a preset time length is extracted from the parsed control command digital signal and cached to form a historical control sequence. The preset time length is set according to the system response characteristics, for example, it may cover a complete motion cycle in a periodic loading test; the historical control sequence stores the most recent control command in a circular buffer, forming a short-term memory of the control history, which is used for the state input of the prediction model.

[0038] Finally, the output load tracking error, displacement rate of change, and historical control sequence are combined to form the state vector at the current moment. The state vector serves as the input to the prediction model, integrating three types of information: system tracking error, motion dynamics, and control history. In servo loading of the control surface, the dimension of the state vector depends on the system order. For example, a second-order system may include load tracking error, displacement rate of change, and two historical control values, fully describing the instantaneous operating point of the system.

[0039] Specifically, in the single-loop model predictive control method for a loading system of the present invention, step 2 includes: Establish a discrete-time state-space equation that includes the parameter matrix to be identified and the coupling coefficient to be identified. The discrete-time state-space equation takes the state vector as input and includes a product term of the displacement rate of change and the coupling coefficient. To identify the values ​​of the parameter matrix and coupling coefficients, a known excitation signal is injected into the loading system, the response signal output by the loading system is collected, and the value of the state vector during the injection of the known excitation signal is recorded. The recorded state vector, known excitation signal, and acquired response signal are used as inputs to the recursive least squares algorithm, which outputs the parameter matrix and coupling coefficient values.

[0040] In the prediction model construction in step 2, the discrete-time state-space equations first need to be established. These equations include the matrix of parameters to be identified and the coupling coefficients to be identified, using the state vector generated in step 1 as input. The discrete-time state-space equations specifically include a product term of the displacement rate of change multiplied by the coupling coefficients, used to characterize the dynamic coupling characteristics between the loaded system and the tested product. For example, in aircraft control surface testing, the inertial force generated by the active motion of the control surface will affect the system dynamics through this coupling term. The order of the equations is usually determined as a second- or third-order model based on the system's dynamic characteristics to accurately describe the transmission relationship between load and displacement.

[0041] To identify the parameter matrix values ​​and coupling coefficient values, a known excitation signal is injected into the loading system. This known excitation signal can take the form of a pseudo-random binary sequence or a step signal, etc., to stimulate the system's full-frequency dynamic response. The injected excitation signal is applied to the loading system through a servo mechanism, while the response signal output by the loading system is simultaneously acquired. The response signal includes load feedback measured by a force sensor and position feedback measured by a displacement sensor. During the injection of the known excitation signal, the state vector values ​​calculated in real time in step 1 are recorded synchronously to ensure the temporal consistency between the input / output data and the system state.

[0042] The recorded state vector, known excitation signal, and acquired response signal are used as input data for the recursive least squares algorithm. The algorithm employs a recursive computation method, updating parameter estimates in real-time based on newly arriving data to avoid repeatedly processing historical data. The algorithm gradually converges to the optimal estimates of the parameter matrix and coupling coefficients by minimizing the sum of squared errors between the predicted output and the actual response. The identified parameters are used to update the discrete-time state-space equations, adapting the prediction model to the current dynamic characteristics of the loaded system and providing an accurate model foundation for subsequent prediction sequence generation.

[0043] Specifically, the single-loop model predictive control method for a loading system of the present invention includes a predictive model performing calculations and outputting load prediction sequences and displacement prediction sequences, comprising: Substitute the parameter matrix values, coupling coefficient values, and current state vector output by the recursive least squares algorithm into the discrete-time state-space equation. Using the discrete-time state-space equation with input parameter matrix values, coupling coefficient values, and state vectors, iterative calculations are performed starting from the current moment according to the sampling period to output load values ​​and displacement values ​​at multiple future moments, generating load prediction sequences and displacement prediction sequences.

[0044] During the calculation process of the predictive model, the parameter matrix values ​​and coupling coefficient values ​​obtained online by the recursive least squares algorithm are substituted into the discrete-time state-space equation along with the current state vector. The discrete-time state-space equation takes the state vector as input and includes a product term of the displacement rate of change and the coupling coefficient, which is used to characterize the dynamic coupling relationship between the loading system and the test product. The substitution operation involves mapping the numerical values ​​to the corresponding variables in the equation. For example, in aerospace control surface testing, the parameter matrix values ​​reflect the inertial damping characteristics of the system, and the coupling coefficient values ​​quantify the interference intensity of the control surface motion on the loading force. After substitution, the equation has the ability to describe the transient dynamics of the system.

[0045] Using discrete-time state-space equations with substituted parameter matrix values, coupling coefficient values, and state vectors, iterative calculations are performed starting from the current moment and following a fixed sampling period. The iterative process employs numerical integration methods, such as the forward Euler method, using the current state vector as initial conditions to calculate the load and displacement values ​​at the next sampling moment, and using the new state as input to continue predicting subsequent moments. For example, in servo loading of control surfaces, each iteration step outputs predicted load and displacement values ​​for future moments, which are accumulated chronologically to form a load prediction sequence and a displacement prediction sequence. The length of the prediction sequence typically covers the system's step response time, providing a trajectory reference in the future time domain for rolling optimization.

[0046] Through this iterative calculation, the prediction model uses real-time updated parameters and states to generate prediction outputs for multiple consecutive time periods. The load prediction sequence and displacement prediction sequence accurately reflect the dynamic trend of the system, providing key inputs for the state observer and rolling optimization module.

[0047] Specifically, the single-loop model predictive control method for a loaded system of the present invention includes a state observer performing calculations and outputting an estimate of the redundant force disturbance, comprising: Obtain the load prediction value at the current moment from the generated load prediction sequence, and obtain the displacement prediction value at the current moment from the generated displacement prediction sequence; The actual load feedback value at the current moment is obtained from the filtered load signal, and the actual displacement feedback value at the current moment is obtained from the filtered position signal; Calculate the difference between the predicted load value and the actual load feedback value, and output the load residual; calculate the difference between the predicted displacement value and the actual displacement feedback value, and output the displacement residual. The load residual, displacement residual, and the estimated value of redundant force disturbance output from the previous calculation cycle of the state observer are input into the Kalman filter. The Kalman filter executes the state update equation calculation and outputs the estimated value of redundant force disturbance at the current moment.

[0048] During the state observer's calculations, the current load prediction value is first obtained from the generated load prediction sequence. This sequence is a sequence of future load values ​​output by the prediction model based on state variables iteratively. The current prediction value is directly extracted from the corresponding time point in the index sequence. Simultaneously, the current displacement prediction value is obtained from the generated displacement prediction sequence. This sequence is a sequence of future displacement values ​​output by the prediction model, and the current displacement prediction value is extracted in the same way. For example, in an aircraft control surface loading test, the load prediction sequence represents the model's predicted trajectory of force changes on the control surface, while the displacement prediction sequence reflects the predicted trajectory of the control surface's movement position. Obtaining the current prediction value provides a benchmark for subsequent comparison with measured values.

[0049] The actual load feedback value at the current moment is obtained from the filtered load signal. The filtered load signal is the real-time load measurement value after digital filtering of the force sensor signal. The actual value at the current moment is directly read from the signal buffer. The actual displacement feedback value at the current moment is obtained from the filtered position signal. The filtered position signal is the real-time position measurement value after filtering of the displacement sensor signal. The actual feedback value characterizes the true operating state of the system. For example, when the control surface actively moves, the actual load feedback value includes the inertial force interference of the control surface, and the actual displacement feedback value captures the instantaneous deflection of the control surface.

[0050] The difference between the predicted load value and the actual load feedback value is calculated, and the load residual is output. The load residual reflects the deviation between the predicted model output and the actual system response. The difference between the predicted displacement value and the actual displacement feedback value is calculated, and the displacement residual is output. The displacement residual represents the error between the displacement prediction and the actual measurement. The residual calculation highlights dynamic characteristics not covered by the model. For example, during rapid deflection of the control surface, the residual mainly originates from the redundant force interference introduced by the control surface motion, providing input for interference estimation.

[0051] The load residual, displacement residual, and the redundant force disturbance estimate output by the state observer from the previous calculation cycle are input into the Kalman filter. The Kalman filter executes the state update equation to calculate and outputs the current redundant force disturbance estimate. The state update equation uses the residual as the observation variable, combines it with the disturbance estimate from the previous time step, and reduces the influence of process noise and observation noise through weighted fusion to dynamically update the disturbance estimate. For example, in control surface testing, the Kalman filter suppresses sensor noise and model error through recursive calculation, outputting a smooth and accurate redundant force disturbance estimate for feedforward compensation control.

[0052] Specifically, in the single-loop model predictive control method for a loading system of the present invention, step 4 includes: Using the generated load prediction sequence, the estimated value of redundant force disturbance output by the state observer, and the expected load command as inputs, and the future control increment sequence as decision variables, a quadratic objective function is constructed. The quadratic objective function includes a first calculation term, a second calculation term, and a third calculation term. The first calculation term is the weighted sum of the squared errors of the load prediction sequence minus the expected load command. The second calculation term is the weighted sum of the squared rates of change of the future control increment sequence. The third calculation term is the sum of the products of the estimated redundant force disturbance value after transformation by the feedforward gain matrix and the first N control increments of the future control increment sequence, where N is an integer greater than zero. Solve the quadratic objective function of the physical constraints of the additional servo mechanism to obtain the optimal solution of the future control increment sequence. Extract the first control increment from the optimal solution of the future control increment sequence as the optimal control increment of the current rolling optimization cycle.

[0053] Within the rolling optimization cycle of step 4, the generated load prediction sequence, the redundant force disturbance estimate output by the state observer, and the expected load command are first used as input parameters. These parameters collectively define the current state and expected future behavior of the system. The load prediction sequence provides load value predictions for multiple future time points, the redundant force disturbance estimate characterizes the dynamic disturbance amplitude introduced by the active movement of the test product, and the expected load command represents the system's target tracking value. A future control increment sequence is used as the decision variable. This sequence includes a series of control increment values ​​to be optimized, used to adjust the output of the servo mechanism. Based on the input and decision variables, a quadratic objective function is constructed. This function aims to quantify system performance indicators, mathematically integrating tracking accuracy, control smoothness, and disturbance compensation requirements.

[0054] The quadratic objective function comprises three computational terms. The first term is the weighted sum of the squared errors of the predicted load sequence minus the expected load command. This term focuses on optimizing the system's tracking performance, adjusting the importance of the error term through weighting coefficients to prioritize minimizing the deviation between the load command and the actual prediction. The second term is the weighted sum of the squared rates of change of the future control increment sequence. This term aims to suppress drastic fluctuations in the control signal, improving system stability by penalizing the rate of change of the control increment and preventing excessive actuator action. The third term is the sum of the products of the estimated redundant force disturbance (after transformation by the feedforward gain matrix) and the first N control increments of the future control increment sequence, where N is a positive integer. This term implements a feedforward compensation mechanism, mapping the estimated redundant force disturbance to a control correction, actively offsetting the disturbance's impact, and improving the system's disturbance rejection capability. These three terms together constitute the comprehensive performance index of the objective function.

[0055] When solving the quadratic objective function with additional physical constraints on the servo mechanism, the physical limits of the servo mechanism need to be transformed into mathematical constraints. The preset maximum output force limit and maximum motion speed limit of the servo mechanism are expressed as a set of linear inequality constraints with respect to the future control increment sequence. These constraints ensure that the optimal solution is within the system hardware capability range. In each rolling optimization cycle, the generated load prediction sequence, the estimated redundant force disturbance output by the state observer, and the desired load command are used as determining parameters to attach the set of linear inequality constraints to the quadratic objective function, forming a constrained optimization problem. Numerical optimization algorithms such as the interior-point method or the effective set method are used to solve this problem to obtain the optimal solution for the future control increment sequence. The first control increment is extracted from the optimal solution of the future control increment sequence as the optimal control increment for the current rolling optimization cycle. This value is used for immediate control execution, while subsequent elements of the sequence are used for rolling updates of model predictions.

[0056] Specifically, the single-loop model predictive control method for a loading system of the present invention solves the quadratic objective function of the physical constraints of the additional servo mechanism by: The preset maximum output force limit and maximum motion speed limit of the servo mechanism are expressed as a set of linear inequality constraints with respect to the future control increment sequence; In each rolling optimization cycle, the generated load prediction sequence, the estimated value of redundant force disturbance output by the state observer, and the expected load command are used as determining parameters. A set of linear inequality constraints is added to the quadratic objective function to solve the constrained optimization problem and obtain the optimal solution of the future control increment sequence. Extract the first control increment from the optimal solution of the future control increment sequence, and use it as the optimal control increment for the current rolling optimization cycle.

[0057] During the rolling optimization cycle in step 4, the generated load prediction sequence, the estimated redundant force disturbance output by the state observer, and the desired load command are first used as input parameters. The load prediction sequence provides load value predictions for multiple future time points, the estimated redundant force disturbance characterizes the dynamic disturbance amplitude generated by the active movement of the test product, and the desired load command represents the system's target tracking value. A future control increment sequence is used as the decision variable, comprising a series of control increment values ​​to be optimized, used to adjust the output force of the servo mechanism. Based on the input and decision variables, a quadratic objective function is constructed, which mathematically integrates the system's tracking accuracy, control smoothness, and disturbance compensation requirements.

[0058] The quadratic objective function comprises three computational terms. The first term is the weighted sum of the squared errors of the predicted load sequence minus the expected load command. This term focuses on optimizing the system's tracking performance, adjusting the importance of the error term through weighting coefficients to prioritize minimizing the deviation between the load command and the actual predicted value. The second term is the weighted sum of the squared rates of change of the future control increment sequence. This term aims to suppress drastic fluctuations in the control signal, improving system stability by penalizing the rate of change of the control increment and preventing excessive actuator action. The third term is the sum of the products of the estimated redundant force disturbance (after transformation by the feedforward gain matrix) and the first N control increments of the future control increment sequence, where N is a positive integer. This term implements a feedforward compensation mechanism, mapping the estimated redundant force disturbance into a control correction, actively offsetting the disturbance's impact, and improving the system's disturbance rejection capability.

[0059] When solving the quadratic objective function with added physical constraints on the servo mechanism, the physical limits of the servo mechanism need to be transformed into mathematical constraints. The preset maximum output force limit and maximum motion speed limit of the servo mechanism are expressed as a set of linear inequality constraints with respect to the future control increment sequence. These constraints guarantee that the optimal solution is within the system hardware capability range. In each rolling optimization cycle, the generated load prediction sequence, the estimated redundant force disturbance output by the state observer, and the expected load command are used as determining parameters to attach the set of linear inequality constraints to the quadratic objective function, forming a constrained optimization problem. Numerical optimization algorithms such as the interior-point method are used to solve this problem to obtain the optimal solution for the future control increment sequence. The first control increment is extracted from the optimal solution of the future control increment sequence as the optimal control increment for the current rolling optimization cycle. This value is used for immediate control execution, while subsequent elements of the sequence are used for rolling updates of model predictions.

[0060] Specifically, the single-loop model predictive control method for a loading system of the present invention converts the optimal control increment into a drive signal, and the drive signal is applied to the servo mechanism of the loading system, including: Extract the optimal control increment from the current rolling optimization cycle, extract the control command value from the previous rolling optimization cycle, add the optimal control increment to the control command value, and obtain the control command value for the current cycle. Perform digital-to-analog conversion on the current cycle control command value and output an analog voltage drive signal; The analog voltage drive signal is transmitted to the servo mechanism of the loading system. The servo mechanism outputs a loading force according to the analog voltage drive signal. The loading force is applied to the test product. The force sensor detects the magnitude of the loading force, and the displacement sensor detects the positional change of the loading force.

[0061] In step 5, the optimal control increment is first extracted from the current rolling optimization cycle. This increment is the latest control adjustment obtained by solving the constrained optimization problem. Simultaneously, the historical control command value is extracted from the previous rolling optimization cycle; this value represents the absolute control command at the previous moment. The optimal control increment and the historical control command value are algebraically added together to obtain the control command value for the current cycle. This accumulation process realizes the integral effect of the control command, enabling a smooth transition in the control quantity and avoiding abrupt changes. For example, in an aircraft control surface loading test, the current cycle control command value determines the magnitude of the loading force that the servo mechanism needs to output in this cycle.

[0062] The current cycle control command value undergoes digital-to-analog conversion (DAC) processing, converting the digital quantity into an analog voltage signal. The DAC uses a high-resolution conversion chip to map discrete digital control commands into continuous analog voltage values. Maintaining linearity during the conversion process ensures that changes in the digital command are accurately reflected in the output voltage. The output analog voltage drive signal typically conforms to industry standard voltage ranges; for example, a ±10V voltage signal corresponds to the full-scale output of the servo mechanism. This drive signal carries optimized control command information.

[0063] The analog voltage drive signal is transmitted to the servo mechanism of the loading system. Shielded cables or fiber optic media are used for signal transmission to suppress electromagnetic interference. After receiving the analog voltage signal, the servo mechanism drives the actuator through its built-in power amplifier circuit. For example, in an electro-hydraulic servo system, the voltage signal is amplified by a servo amplifier to adjust the opening of the electro-hydraulic servo valve, controlling the hydraulic oil flow and pressure, thereby outputting the corresponding mechanical loading force. The loading force acts directly on the tested product, such as the control surface structure of an aircraft, simulating a real aerodynamic load environment.

[0064] During the loading force output process, the force sensor detects the magnitude of the loading force in real time and converts the mechanical quantity into an electrical signal. The displacement sensor synchronously detects the positional changes of the loading force and records the motion trajectory of the actuator. The feedback signals from both sensors are collected and sent back to the input of the control system, forming a closed-loop control circuit. The signal conversion and execution processes need to maintain strict timing synchronization to ensure that the control command can complete the entire process from calculation to execution within one sampling period, maintaining the real-time performance and stability of the control system.

[0065] Specifically, the single-loop model predictive control method for a loading system of the present invention further includes: Monitor the current cycle control command value and compare it with the preset safety limit value; Monitor load tracking error, compare the load tracking error with the preset load error alarm threshold, monitor the excess force interference estimate, and compare the excess force interference estimate with the preset interference alarm threshold. When the current cycle control command value is greater than the preset safety limit value, or the load tracking error is greater than the preset load error alarm threshold, or the estimated value of redundant force interference is greater than the preset interference alarm threshold, a protection signal is generated. After the protection signal is triggered, the output of analog voltage drive signal to the servo mechanism is stopped, the loading system is controlled to enter the preset safety state, and the loading force is stopped from being applied to the test product.

[0066] During system operation, the safety monitoring mechanism works continuously in parallel with the main control loop. The system monitors the current cycle control command value in real time, which is derived from the sum of the optimal control increment calculated in the rolling optimization cycle and the historical command values. The monitoring process compares the current cycle control command value with a preset safety limit value using a hardware comparator or a software loop reading method. The preset safety limit value is set according to the maximum allowable output capability of the servo mechanism. For example, in aircraft control surface testing, this limit may correspond to the maximum input voltage range of an electro-hydraulic servo valve to prevent overload of the actuator. The comparison results are updated in real time, providing input for protection decisions.

[0067] Simultaneously, the system monitors two types of parameters: load tracking error and redundant force interference estimate. The load tracking error is calculated from the difference between the filtered load signal and the desired load command, reflecting the deviation between the actual applied force and the target value. The redundant force interference estimate comes from the output of the state observer, characterizing the amplitude of dynamic interference introduced by the active movement of the tested product. The monitoring module compares the load tracking error with a preset load error alarm threshold and the redundant force interference estimate with a preset interference alarm threshold. These thresholds are set according to the system's maximum permissible error range; for example, when the control surface moves violently, the threshold may correspond to the upper limit of the permissible force tracking deviation, ensuring the system operates within a safe range.

[0068] When the comparison logic detects that the current cycle control command value exceeds the preset safety limit, or the load tracking error exceeds the preset load error alarm threshold, or the estimated value of redundant force interference exceeds the preset interference alarm threshold, the system immediately generates a protection signal. The protection signal generation employs hardware logic circuitry or software interrupts to ensure rapid response. For example, during a control surface loading test, if the control surface suddenly jams, causing a surge in load error, the comparison circuit will instantly trigger protection.

[0069] Upon triggering of the protection signal, the system executes a series of safety operations. First, it stops outputting analog voltage drive signals to the servo mechanism, achieved by shutting down the power amplifier output stage or zeroing the digital-to-analog converter output. Then, it controls the loading system to enter a preset safety state, including releasing hydraulic system pressure, activating the mechanical braking device, and cutting off the main power supply. These actions ensure that the loading force completely stops acting on the test product, preventing equipment damage or test accidents. The safety monitoring mechanism forms a protection layer independent of the control loop, improving system reliability.

[0070] The specific mathematical expression of the discrete-time state-space equation is as follows: ; ; in, This is a discrete-time index, representing the current sampling time; for The state vector at time t is determined by the load tracking error. Displacement change rate It consists of historical control sequences, including the most recent ones. One control input; ; The state vector is a preset positive integer. The dimension is (include , and (one historical control value); for The control input at any given time is a scalar value; for The rate of change of displacement at time t is the state vector. One of the elements, listed separately here to emphasize its product with the coupling coefficient; for The output vector at time step, including the load value and displacement value ; Right now ; For the system matrix, dimension It describes the dynamic characteristics of the state vector evolving over time; To control the input matrix, the dimension Describes the effect of control inputs on the state; The coupling coefficient matrix has dimensions [missing information]. , representing the rate of change of displacement The coupling effect on the state vector, where The term is the product of the displacement rate of change and the coupling coefficient; For the output matrix, the dimension This maps the state vector to the output vector.

[0071] The data processing path for calculating the predicted sequence using this equation is as follows: The parameter matrix values ​​obtained from the online identification of the recursive least squares algorithm (i.e.) , , , (value) and the current state vector Substitute into the equation.

[0072] For each future sampling time ( , For prediction in the time domain, iterative calculations are performed according to the sampling period: According to the equation Calculate the state vector at the next time step ,in Initially, it is the current control input, and in subsequent time steps... This can be obtained through control strategy assumptions (such as zero maintenance).

[0073] According to the equation Calculate the output vector Extract load values ​​from them and displacement value .

[0074] Repeat step 2 for to Generate a load prediction sequence; and displacement prediction sequence; ; This data processing path is based on iterative prediction, enabling those skilled in the art to calculate the predicted sequence.

[0075] The specific mathematical expression of the quadratic objective function is as follows: ; in, Let be the objective function value, and be a scalar. For the prediction time domain, it represents the number of sampling points for future predictions; for The predicted load value at time 1 is derived from the load prediction sequence output by the prediction model; for The expected load command at any given time; The weighting coefficient for the first calculation term represents the load tracking error at time t. The importance of; For the control time domain, it represents the length of the control increment sequence for optimization decisions; for The control increment at time step is a decision variable, defined as follows: ; for The control increment at any time, for , These are known historical values; The weighting coefficient for the second calculation term represents the rate of change of the control increment at time t. The penalty weight; For the time domain of the feedforward compensation term, ,and Integers greater than zero; The current time-instance estimate of the redundant force disturbance is derived from the state observer output. The feedforward gain matrix has dimensions [missing information]. (Scalar) Maps the estimated value of redundant force disturbance to the control compensation quantity; The weighting coefficient for the third calculation term represents the feedforward compensation at time t. The weights; In the third calculation item; This represents the product of the feedforward compensation and the control increment, which are summed to form the product sum.

[0076] The data processing path for solving the optimal control increment using this objective function is as follows: In each rolling optimization cycle, obtain the load prediction sequence at the current moment; ; Redundant force interference estimate and expected payload command sequence .

[0077] The objective function Represented as decision variables; The quadratic form: The first item can be written as: ; in , , This is a diagonal weight matrix with elements of . ; The second item can be written as: ; in; , This is a diagonal weight matrix with elements of . ; The third item can be written as: ,in , This is a diagonal weight matrix with elements of . .

[0078] Transform the physical constraints of the servo mechanism (such as the maximum output force limit and the maximum motion speed limit) into a set of linear inequality constraints. .

[0079] Solving constrained optimization problems: minimizing ,satisfy The optimal solution for the future control increment sequence is obtained by using numerical algorithms (such as the interior-point method). .

[0080] from Extract the first element This serves as the optimal control increment for the current rolling optimization cycle. This data processing path clarifies the calculation and optimization process of the objective function, enabling those skilled in the art to implement it.

[0081] In the specific implementation of servo loading tests on aircraft control surfaces, this method achieves single-loop model predictive control in the following manner. A force sensor in the loading system is installed between the actuator and the control surface under test to detect the real-time load applied to the control surface; a displacement sensor, using an angular displacement measurement unit, is installed on the control surface shaft to capture the control surface deflection angle. At the start of the test, the force sensor outputs a first analog voltage signal, and the displacement sensor outputs a second analog voltage signal. Both signals are acquired by a synchronous sampling module using the same clock source and converted into load digital signals and position digital signals by a 16-bit analog-to-digital converter. Simultaneously, the controller reads the digital control command signal sent to the electro-hydraulic servo valve from the servo driver register. The three types of signals are integrated into a raw data stream through a timestamp alignment module, with the timestamp accuracy consistent with the sampling period of the control system.

[0082] The raw data stream parsing module separates the load digital signal, position digital signal, and control command digital signal based on the frame header identifier. The load digital signal is processed by a zero-phase digital filter to remove high-frequency noise, resulting in a filtered load signal; the position digital signal undergoes the same filtering process to obtain a filtered position signal. The filtered load signal is compared with the externally input expected load command to calculate the load tracking error in real time. A first-order difference operation is performed on the filtered position signal, and then a sliding window averaging algorithm is used to process the difference result, outputting the displacement change rate parameter. Historical data for the most recent 200 milliseconds is extracted from the parsed control command digital signal and stored in a circular buffer to form a historical control sequence. Finally, the load tracking error, displacement change rate, and historical control sequence are combined to form the current state vector, which serves as the input to the prediction model.

[0083] The prediction model employs a second-order discrete-time state-space equation, which includes a product term of the displacement rate of change and the coupling coefficient. To identify the model parameters, a step excitation signal with gradually varying amplitude is injected into the electro-hydraulic servo valve, while simultaneously recording the response data from the force and displacement sensors. A recursive least squares algorithm is used to process the state vector and response data during the excitation period, updating the parameter matrix and coupling coefficients online. Substituting the identified parameters into the state-space equation, and using the current state vector as initial conditions, the forward Euler method is used to iteratively calculate the load and displacement prediction sequences for the next 20 time points at a sampling period of 1 millisecond.

[0084] The state observer extracts the predicted load and displacement values ​​for the current moment from the prediction sequence and compares them with the filtered sensor measurements to generate load and displacement residuals. The residual signals and the previous cycle's estimated redundant force disturbance are input into a Kalman filter, and the estimated redundant force disturbance for the current moment is calculated using the state update equation. In the rolling optimization stage, a quadratic objective function is constructed, including a tracking error weighting term, a control increment rate of change penalty term, and a feedforward compensation term. The maximum output force of the servo mechanism (10kN) and maximum speed (50mm / s) are transformed into linear constraints. The interior-point method is used to solve the constrained optimization problem, obtaining the optimal sequence for the next 10 control increments. The first element is extracted as the optimal control increment for the current moment.

[0085] The optimal control increment is accumulated with the control command value of the previous cycle and generated as a ±10V analog voltage drive signal via a 16-bit digital-to-analog converter. This signal is transmitted to the electro-hydraulic servo valve through a shielded cable, driving the hydraulic cylinder to output the corresponding load. Force and displacement sensors detect the load magnitude and control surface deflection angle in real time, forming a closed-loop control. The safety monitoring system operates in parallel. When the control command voltage exceeds 8V, the load tracking error is greater than 200N, or the estimated value of redundant force interference exceeds 150N, a protection signal is immediately triggered to cut off the power source of the servo mechanism, and the system enters a safe state. This invention effectively suppresses redundant force interference caused by active control surface movement in aircraft control surface flutter testing, improving the accuracy of load simulation.

[0086] In a specific embodiment of the servo loading test of an aircraft control surface, the present invention is implemented in the following manner. The loading system is equipped with a high-precision strain gauge force sensor and a magnetostrictive displacement sensor. The force sensor is installed between the electro-hydraulic actuator and the control surface under test to detect the applied real-time load; the displacement sensor is installed on the control surface shaft to monitor the deflection angle. At the start of the test, the force sensor outputs a first analog voltage signal, and the displacement sensor outputs a second analog voltage signal. Both signals are synchronously acquired at a sampling frequency of 10kHz and converted into load digital signals and position digital signals by a 16-bit analog-to-digital converter. Simultaneously, control command digital signals are read from the servo driver register. The three types of signals are merged into a raw data stream after timestamp alignment. After parsing the raw data stream, zero-phase filtering is performed on the load and position digital signals to extract the filtered load and position signals. The difference between the filtered load signal and the desired load command is calculated to obtain the load tracking error; first-order difference and sliding window averaging are performed on the filtered position signal to output the displacement change rate; the most recent 200ms historical data is extracted from the control command signal to form a historical control sequence. The variables are combined into a state vector to drive the prediction model. The prediction model employs a second-order discrete-time state-space equation, including a product term of the displacement rate of change and the coupling coefficient. By injecting a step excitation signal with gradually varying amplitude into the system and collecting response data, a recursive least squares algorithm is used to identify the parameter matrix and coupling coefficients online. Substituting the identified parameters and the current state vector into the equation, the load prediction sequence and displacement prediction sequence for the next 20 time steps are iteratively calculated at a 1ms sampling period. The state observer obtains the current time step prediction value from the prediction sequence, compares it with the sensor's measured values ​​to obtain the load residual and displacement residual, and combines it with the previous time step disturbance estimate to output the redundant force disturbance estimate through a Kalman filter. Within the rolling optimization cycle, a quadratic objective function is constructed, including a weighted sum of squared errors, a penalty term for the control increment rate of change, and a feedforward compensation term, where the feedforward term maps the disturbance estimate to the control correction. The maximum output force of 10kN and the maximum speed of 50mm / s of the servo mechanism are transformed into linear constraints, and the constrained optimization problem is solved to obtain the optimal solution for the future control increment sequence. The first element is extracted as the optimal control increment. After the control increment is accumulated with the historical command value, a ±10V analog drive signal is generated through digital-to-analog conversion to drive the electro-hydraulic servo valve to output the loading force. Force and displacement sensors provide real-time feedback on load and position, forming a closed loop. The safety monitoring system operates in parallel; when the control command value exceeds 8V, the load tracking error is greater than 200N, or the estimated interference value exceeds 150N, a protection signal is triggered, stopping the drive output and entering a safe state. In rapid deflection tests of the control surface, this implementation effectively suppressed the excess torque caused by inertial force coupling through feedforward compensation, improving load tracking accuracy.

[0087] In another embodiment of the high-dynamic flutter test of large aircraft control surfaces, the loading system adopts a multi-channel synchronous acquisition scheme. High-frequency response strain gauge sensors are used as force sensors, and high-resolution magnetostrictive sensors are used as displacement sensors. The sampling clock is allocated by a unified timing source to ensure phase synchronization. The raw data stream is parsed using a frame structure, and a zero-phase filter is used to eliminate group delay. An adaptive window adjustment mechanism is introduced in the calculation of the displacement change rate in the state variables. The window size dynamically changes according to the control surface movement speed to adapt to the violent motion caused by flutter. The prediction model is constructed as a third-order state-space equation to more accurately describe the high-frequency dynamic characteristics. The coupling coefficient is dynamically updated through real-time system identification, and the excitation signal uses a composite waveform of step and sine waves to excite the system's full-frequency response. The state observer is designed as a multi-input structure to simultaneously process load and displacement residuals. The Kalman filter noise covariance is tuned online based on the signal-to-noise ratio. In the rolling optimization objective function, the weight of the feedforward compensation term is correlated with the confidence level of the disturbance estimate. The optimization solution uses the interior-point method to handle constraints, and the control increment output undergoes anti-saturation processing before being processed. The execution stage employs an 18-bit digital-to-analog converter, and the drive signal is transmitted to the servo mechanism via an isolation amplifier to reduce ground loop interference. Safety monitoring uses multi-level thresholds and a hysteresis comparison strategy to avoid false triggering. In control surface flutter testing, this system significantly reduces interference errors introduced by violent motion, ensuring the realism of aerodynamic load simulation. During implementation, this invention ensures control accuracy and system stability under high dynamic conditions by real-time identification and compensation for redundant force interference.

[0088] This invention establishes a discrete-time state-space equation including the product of displacement change rate and coupling coefficient, explicitly characterizing the dynamic coupling relationship between the control surface motion and the loading system in the prediction model. In aerospace control surface testing scenarios, when the control surface actively deflects, the inertial force generated by its motion is transmitted to the loading system through mechanical connections, forming redundant force interference. The prediction model maps the control surface motion acceleration, quantified by the displacement change rate, into its impact on the system dynamics through real-time updated parameter matrices and coupling coefficients, thereby reflecting this coupling effect in advance in the load prediction sequence and displacement prediction sequence.

[0089] The state observer identifies dynamic characteristics not covered by the model by comparing the residuals of the predicted sequence with the real-time feedback signals from the sensors. The Kalman filter uses the load residuals and displacement residuals as observed variables, combined with the disturbance estimate from the previous moment, to dynamically calculate the estimate of the current redundant force disturbance through the state update equation. This process essentially attributes the deviation between the actual system response caused by the control surface motion and the model prediction to the effect of the redundant force disturbance, and quantifies its amplitude and phase characteristics.

[0090] In the rolling optimization phase, the estimated redundant force disturbance is introduced as a feedforward compensation term into the quadratic objective function. The feedforward gain matrix maps the disturbance estimate to a control correction, forming a feedforward channel in the product term with the future control increment sequence. When solving constrained optimization problems, this compensation term guides the optimization algorithm to generate control commands that can actively counteract the disturbance. For example, when the rudder sharply turns to the right, generating a positive disturbance force, the feedforward term will generate a corresponding negative control correction, pre-compensating for its impact before the disturbance force occurs.

[0091] Meanwhile, by transforming the physical limits of the servo mechanism into linear inequality constraints, the optimal solution is ensured to remain within the system's safety range. The final generated optimal control increment is then converted into a drive signal through integration, enabling the servo mechanism to synchronously correct phase lag and amplitude errors caused by disturbances when outputting applied force. This feedforward and feedback composite control structure allows the system to perform feedforward compensation based on the foresight of the predictive model, while also correcting residual errors in real time through sensor feedback, thereby significantly improving its ability to suppress dynamic disturbances.

[0092] The recursive least squares algorithm is a parameter estimation method that updates parameter estimates in real time based on newly arriving data through recursive calculations, avoiding redundant processing of historical data. In this invention, the recursive least squares algorithm is used to identify the parameter matrix values ​​and coupling coefficient values ​​in the prediction model. The algorithm input includes the recorded state vector, the known excitation signal, and the acquired response signal. By minimizing the sum of squared errors between the predicted output and the actual response, it gradually converges to the optimal estimates of the parameter matrix values ​​and coupling coefficient values. The output results are used to update the discrete-time state-space equations.

[0093] The Kalman filter is a recursive state estimator that reduces the impact of process noise and observation noise by fusing observed variables and previous time-step estimates through a state update equation. In this invention, the Kalman filter is used by the state observer to calculate the estimated value of redundant force disturbances. The algorithm input includes load residuals, displacement residuals, and the estimated value of redundant force disturbances output by the state observer in the previous calculation cycle. By executing the state update equation, the algorithm dynamically updates and outputs the estimated value of redundant force disturbances at the current time step.

[0094] Interior-point methods are numerical algorithms for solving constrained optimization problems, iteratively approximating the optimal solution by processing the internal paths of constraints. In this invention, the interior-point method is used to solve a quadratic objective function with additional physical constraints on the servo mechanism. The algorithm uses the generated load prediction sequence, the estimated redundant force disturbance output by the state observer, and the desired load command as determining parameters, attaches a set of linear inequality constraints to the objective function, and obtains the optimal solution for the future control increment sequence through iterative calculation.

[0095] The effective set method is a constraint optimization algorithm that handles inequality constraints by identifying active constraint sets and iteratively solving subproblems. In this invention, the effective set method is used as an alternative to the interior point method to solve constrained quadratic objective functions. The algorithm processes linear inequality constraint sets within a rolling optimization cycle, using the future control increment sequence as the decision variable, and obtains the optimal control increment through effective set updates and subproblem solving.

[0096] Discrete-time state-space equations are a dynamic system modeling method that uses state vectors to describe the system's behavior at discrete time points. In this invention, the discrete-time state-space equations serve as the core of the prediction model. Taking state variables as input, the equations include a product term of the displacement rate of change and the coupling coefficient. By substituting the parameter matrix values, coupling coefficient values, and state vectors, the model iteratively calculates the load and displacement values ​​at multiple future time points according to the sampling period, outputting a load prediction sequence and a displacement prediction sequence.

Claims

1. A single-loop model predictive control method for a loaded system, characterized in that, include: Step 1: Collect signals from the force sensor and displacement sensor in the loading system and obtain the desired load command. Extract the load tracking error, displacement change rate and historical control sequence from the collected signals. The load tracking error is calculated based on the desired load command and the collected load signal. Define the load tracking error, displacement change rate and historical control sequence as state variables. Step 2: Construct a prediction model. The prediction model is driven by state variables. The prediction model performs calculations and outputs load prediction sequences and displacement prediction sequences. Step 3: Input the load prediction sequence, displacement prediction sequence, first analog voltage signal collected by the force sensor, and second analog voltage signal collected by the displacement sensor into the state observer. The state observer performs calculations and outputs the estimated value of the redundant force disturbance. Step 4: During the rolling optimization cycle, construct an objective function based on the prediction model, the estimated value of the redundant force disturbance, and the expected load command. The objective function includes a term to offset the redundant force disturbance with a feedforward compensation term. Solve the constrained optimization problem to obtain the optimal control increment. Step 5: Convert the optimal control increment into a drive signal. Apply the drive signal to the servo mechanism of the loading system. The servo mechanism outputs a loading force according to the drive signal. The loading force acts on the test product. The force sensor detects the magnitude of the loading force, and the displacement sensor detects the positional change of the loading force.

2. The single-loop model predictive control method for a loading system according to claim 1, characterized in that, Step 1 includes: Receive a first analog voltage signal from the force sensor and a second analog voltage signal from the displacement sensor; The received first analog voltage signal and second analog voltage signal are synchronously sampled and converted from analog to digital, and the load digital signal and position digital signal are output. Collect and send control commands to the servo mechanism to obtain digital signals of the control commands; The output load digital signal, position digital signal, and acquired control command digital signal are timestamped based on the same time base and then merged to form the original data stream.

3. The single-loop model predictive control method for a loading system according to claim 2, characterized in that, Step 1 also includes: The generated raw data stream is parsed, and the parsed load digital signal, parsed position digital signal, and parsed control command digital signal are output. The parsed load digital signal is subjected to digital filtering processing, and the filtered load signal is output. The parsed position digital signal is subjected to digital filtering processing, and the filtered position signal is output. Calculate the difference between the filtered load signal and the desired load command, and output the load tracking error; Calculate the difference of the filtered position signal at consecutive time points, perform sliding window averaging on the difference results, and output the rate of change of displacement. Extract the signal value with the most recent preset time length from the parsed control command digital signal, and cache it to form a historical control sequence; The output load tracking error, displacement change rate, and historical control sequence are combined into the state vector at the current moment.

4. The single-loop model predictive control method for a loading system according to claim 3, characterized in that, Step 2 includes: Establish a discrete-time state-space equation that includes the parameter matrix to be identified and the coupling coefficient to be identified. The discrete-time state-space equation takes the state vector as input and includes a product term of the displacement rate of change and the coupling coefficient. To identify the values ​​of the parameter matrix and coupling coefficients, a known excitation signal is injected into the loading system, the response signal output by the loading system is collected, and the value of the state vector during the injection of the known excitation signal is recorded. The recorded state vector, known excitation signal, and acquired response signal are used as inputs to the recursive least squares algorithm, which outputs the parameter matrix and coupling coefficient values.

5. The single-loop model predictive control method for a loading system according to claim 4, characterized in that, The prediction model performs calculations and outputs load prediction sequences and displacement prediction sequences, including: Substitute the parameter matrix values, coupling coefficient values, and current state vector output by the recursive least squares algorithm into the discrete-time state-space equation. Using the discrete-time state-space equation with input parameter matrix values, coupling coefficient values, and state vectors, iterative calculations are performed starting from the current moment according to the sampling period to output load values ​​and displacement values ​​at multiple future moments, generating load prediction sequences and displacement prediction sequences.

6. The single-loop model predictive control method for a loading system according to claim 5, characterized in that, The state observer performs calculations and outputs estimates of redundant force disturbances, including: Obtain the load prediction value at the current moment from the generated load prediction sequence, and obtain the displacement prediction value at the current moment from the generated displacement prediction sequence; The actual load feedback value at the current moment is obtained from the filtered load signal, and the actual displacement feedback value at the current moment is obtained from the filtered position signal; Calculate the difference between the predicted load value and the actual load feedback value, and output the load residual; calculate the difference between the predicted displacement value and the actual displacement feedback value, and output the displacement residual. The load residual, displacement residual, and the estimated value of redundant force disturbance output from the previous calculation cycle of the state observer are input into the Kalman filter. The Kalman filter executes the state update equation calculation and outputs the estimated value of redundant force disturbance at the current moment.

7. The single-loop model predictive control method for a loading system according to claim 6, characterized in that, Step 4 includes: Using the generated load prediction sequence, the estimated value of redundant force disturbance output by the state observer, and the expected load command as inputs, and the future control increment sequence as decision variables, a quadratic objective function is constructed. The quadratic objective function includes a first calculation term, a second calculation term, and a third calculation term. The first calculation term is the weighted sum of the squared errors of the load prediction sequence minus the expected load command. The second calculation term is the weighted sum of the squared rates of change of the future control increment sequence. The third calculation term is the sum of the products of the estimated redundant force disturbance value after transformation by the feedforward gain matrix and the first N control increments of the future control increment sequence, where N is an integer greater than zero. Solve the quadratic objective function of the physical constraints of the additional servo mechanism to obtain the optimal solution of the future control increment sequence. Extract the first control increment from the optimal solution of the future control increment sequence as the optimal control increment of the current rolling optimization cycle.

8. The single-loop model predictive control method for a loading system according to claim 7, characterized in that, Solving the quadratic objective function for the physical constraints of the additional servo mechanism includes: The preset maximum output force limit and maximum motion speed limit of the servo mechanism are expressed as a set of linear inequality constraints with respect to the future control increment sequence; In each rolling optimization cycle, the generated load prediction sequence, the estimated value of redundant force disturbance output by the state observer, and the expected load command are used as determining parameters. A set of linear inequality constraints is added to the quadratic objective function to solve the constrained optimization problem and obtain the optimal solution of the future control increment sequence. Extract the first control increment from the optimal solution of the future control increment sequence, and use it as the optimal control increment for the current rolling optimization cycle.

9. The single-loop model predictive control method for a loading system according to claim 8, characterized in that, The optimal control increment is converted into a drive signal, and the drive signal is applied to the servo mechanism of the loading system, including: Extract the optimal control increment from the current rolling optimization cycle, extract the control command value from the previous rolling optimization cycle, add the optimal control increment to the control command value, and obtain the control command value for the current cycle. Perform digital-to-analog conversion on the current cycle control command value and output an analog voltage drive signal; The analog voltage drive signal is transmitted to the servo mechanism of the loading system. The servo mechanism outputs a loading force according to the analog voltage drive signal. The loading force is applied to the test product. The force sensor detects the magnitude of the loading force, and the displacement sensor detects the positional change of the loading force.

10. The single-loop model predictive control method for a loading system according to claim 9, characterized in that, Also includes: Monitor the current cycle control command value and compare it with the preset safety limit value; Monitor load tracking error, compare the load tracking error with the preset load error alarm threshold, monitor the excess force interference estimate, and compare the excess force interference estimate with the preset interference alarm threshold. When the current cycle control command value is greater than the preset safety limit value, or the load tracking error is greater than the preset load error alarm threshold, or the estimated value of redundant force interference is greater than the preset interference alarm threshold, a protection signal is generated. After the protection signal is triggered, the output of analog voltage drive signal to the servo mechanism is stopped, the loading system is controlled to enter the preset safety state, and the loading force is stopped from being applied to the test product.

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