A method and algorithm system for evaluating intrinsic controllability of a spatial precision pointing mechanism and design guidance

Abstract

This invention discloses a method and algorithm system for evaluating the intrinsic controllability and providing design guidance for space precision pointing mechanisms. Belonging to the field of space precision pointing mechanism evaluation and simulation technology, it solves the technical problems of misaligned evaluation dimensions and limited control compensation capabilities. The algorithm system includes a frequency domain data processing module, a virtual open-loop module, and a result output module that sequentially transmit information data. The frequency domain data processing module receives input structural frequency response function data and performs dimension unification and benchmark calibration of amplitude and phase. The virtual open-loop module is used for intrinsic controllability evaluation and engineering controllability simulation. The intrinsic controllability evaluation and design guidance method includes the following steps: data reading and format normalization, phase benchmark calibration, construction of a virtual open-loop module, dual-dimensional evaluation mode switching logic, multi-crossing point index extraction, and intrinsic controllability evaluation and design guidance. This invention is used for the controllability evaluation and design of space precision pointing mechanisms.

Description

Technical Field

[0001] This invention belongs to the field of space precision pointing mechanism evaluation and simulation technology, specifically involving an intrinsic controllability evaluation and design guidance method and algorithm system for space precision pointing mechanisms. Background Technology

[0002] The pointing accuracy of precision pointing mechanisms in space (such as laser communication turntables and remote sensing payload stabilization platforms) is directly limited by the disturbance suppression capability of the servo control system. To achieve pointing accuracy at the micro-radian level, the control system must possess a sufficiently high closed-loop bandwidth (typically covering external micro-vibration frequencies). However, bandwidth improvement is limited by the system's stability metrics, namely phase margin (PM) and amplitude margin (GM). Once the system's open-loop cutoff frequency approaches the resonant frequency of the mechanical structure, the phase lag and amplitude gain caused by the structural modes will lead to a deterioration in stability metrics, thereby causing system oscillations or divergence. Therefore, the frequency response function (FRF) of the mechanical structure is the physical basis for determining the final pointing accuracy.

[0003] Currently, the design process for mechanisms generally adopts a sequential design model of "structural design → control design". This model has the following problems:

[0004] 1. Misalignment of evaluation dimensions

[0005] Structural design typically focuses on optimizing natural frequency (fundamental frequency) and static stiffness. However, from a precision control perspective, the true determinants of system stability are phase margin and amplitude margin. Current processes lack an evaluation tool that can directly translate structural characteristics into PM / GM indicators during the design phase. Focusing solely on the fundamental frequency often results in structures with high stiffness but introducing significant phase lag and amplitude amplification near the resonance peak, making it difficult to guarantee stability margins near the control bandwidth.

[0006] 2. The physical limits of control compensation capability

[0007] The ability of control algorithms to compensate for structural defects is limited. Due to limitations such as sensor noise amplification and actuator saturation, controllers cannot generate infinite phase lead or notch depth. In serial mode, once the structural design is fixed, if the resonant peaks in its frequency response characteristics are too strong or the phase lag is too large, exceeding the compensability limit of the control algorithm, the system will fail to meet delivery specifications. Modifying the structural design at this point often means restarting finite element modeling and prototype verification, significantly extending the development cycle and increasing engineering costs. Summary of the Invention

[0008] To overcome the shortcomings of misaligned evaluation dimensions and limited control compensation capabilities in space precision pointing mechanisms, this invention proposes an intrinsic controllability assessment and design guidance method and algorithm system for space precision pointing mechanisms.

[0009] The technical solution adopted by this invention to solve its technical problem is:

[0010] An intrinsic controllability evaluation and design guidance algorithm system for a spatial precision pointing mechanism includes a frequency domain data processing module, a virtual open-loop module, and a result output module.

[0011] The frequency domain data processing module is used to receive the input structure frequency response function (FRF) data and to unify the dimensions of amplitude and phase and perform reference calibration.

[0012] The virtual open-loop module includes a proportional gain. With equivalent delay It is used for intrinsic controllability assessment and engineering controllability simulation.

[0013] The output module outputs the intrinsic controllability assessment and design guidance of the spatial precision pointing mechanism, namely the intrinsic controllability assessment and engineering controllability simulation results of the virtual open-loop module.

[0014] The frequency domain data processing module, the virtual open-loop module, and the result output module transmit information data in sequence.

[0015] The aforementioned intrinsic controllability assessment and design guidance algorithm system outputs an intrinsic controllability frequency domain characteristic spectrum and a tolerance curve of the available bandwidth of the project as a function of the equivalent time delay of the project via the result output module.

[0016] The aforementioned intrinsic controllability assessment and design guidance algorithm system, wherein the intrinsic controllability assessment mode does not introduce engineering equivalent time delay constraints, and constructs a virtual open-loop model based on the structural frequency response function to evaluate the upper limit of stable control bandwidth that a spatial precision pointing mechanism can support at the physical level.

[0017] The engineering controllability verification mode introduces engineering time delay constraints to verify whether the current spatial precision pointing mechanism can meet the preset stability margin and bandwidth requirements under real engineering conditions.

[0018] Among them, the engineering delay constraint is formed by the equivalent of sampling, calculation and communication factors.

[0019] A method for assessing the intrinsic controllability and providing design guidance for a space precision pointing mechanism, comprising the following steps:

[0020] Step 1, Data Reading and Format Normalization

[0021] The frequency domain data processing module reads the frequency response data of the mechanical structure. The frequency response data of the mechanical structure is in .txt format and is exported by finite element analysis software or frequency sweep test equipment.

[0022] By using regular expressions, the scientific notation format is corrected, and the frequency, amplitude, and phase columns are extracted.

[0023] Based on the equivalent radius from the measuring point to the rotating shaft The measured linear displacement amplitude Converted to angular displacement amplitude angular displacement amplitude The calculation formula is:

[0024]

[0025] Step 2, Phase reference calibration

[0026] In the frequency response data of the mechanical structure in the frequency domain data processing module, the median phase value is extracted from the low-frequency phase column. The low-frequency band refers to the lowest 5% of the frequency range.

[0027] When the phase median When the absolute value is greater than the threshold, it is determined that the phase sign of the mechanical structure frequency response is opposite to the negative feedback convention of the servo control system. A compensation of ±180° is uniformly superimposed on the phase of the entire frequency band until the low-frequency phase reference returns to ±5°.

[0028] When the phase median When the absolute value is less than or equal to the threshold, the phase reference is not calibrated.

[0029] Step 3, Construct a virtual open-loop module

[0030] In pure structural frequency response function Based on this, a virtual open-loop function containing gain, time delay, and compensator is mathematically synthesized. Virtual open-loop function The calculation formula is as follows:

[0031]

[0032] in, For adjustable proportional gain, The equivalent time delay for the project is given by j, where j is the imaginary unit. Angular frequency, To control the compensator, e is the natural constant. This is an equivalent delay in the engineering process.

[0033] A virtual open-loop module is constructed by introducing proportional gain and engineering equivalent time delay parameters for frequency domain stability margin and bandwidth boundary analysis.

[0034] Step 4, Logic for Switching Between Two-Dimensional Evaluation Modes

[0035] The two-dimensional evaluation model includes the intrinsic controllability evaluation model and the engineering controllability simulation model.

[0036] When the engineering equivalent time delay constraint is not introduced, the intrinsic controllability evaluation mode is executed to obtain the phase crossover point and open-loop gain crossover point corresponding to the phase margin and gain margin.

[0037] When an engineering equivalent time delay constraint is introduced, the engineering controllability simulation mode is executed.

[0038] By switching between intrinsic controllability assessment mode and engineering controllability simulation mode, a unified modeling system is achieved for assessing the upper limit of structural physical controllability and verifying engineering feasibility.

[0039] Step 5, Extraction of indicators from multiple crossing points

[0040] The virtual open-loop module searches for all open-loop gain crossing points and phase crossing points across the entire frequency band.

[0041] A unified comparison is made between the phase margin and the magnitude margin corresponding to each crossing point, and the worst phase margin and the worst magnitude margin are extracted across the entire frequency band.

[0042] Step 6, Intrinsic Controllability Assessment and Design Guidance

[0043] The first step is an assessment of intrinsic controllability.

[0044] When the engineering equivalent delay is zero, evaluate the physical limit bandwidth of the space precision pointing mechanism and propose engineering optimization suggestions for the modal frequency and resonance peak of the space precision pointing mechanism.

[0045] When the equivalent time delay of the project is greater than zero, assess the feasibility of control.

[0046] Step 2, Gain Sweep

[0047] Change the adjustable proportional gain Step value, generating adjustable gain This represents the controllability boundary map, with the horizontal axis representing the controllability and the vertical axis representing the performance index. The performance index is bandwidth. and / or phase margin and / or gain margin .

[0048] The third step is reverse guidance.

[0049] Based on the controllability boundary map, identify the physical bottleneck frequencies that limit bandwidth improvement, and output optimization suggestions for the stiffness, damping, or modal density of the space precision pointing mechanism.

[0050] In the above intrinsic controllability assessment and design guidance method, in step 2, the threshold is... .

[0051] The above-mentioned intrinsic controllability assessment and design guidance method, step 4, further includes:

[0052] Intrinsic controllability assessment mode: Without introducing engineering equivalent time delay constraints, a virtual open-loop model is constructed based on the structural frequency response function to evaluate the upper limit of stable control bandwidth that the spatial precision pointing mechanism body can support at the physical level.

[0053] Engineering controllability simulation mode: Introduces engineering equivalent time delay constraints to verify whether the current spatial precision pointing mechanism can meet the preset stability margin and bandwidth requirements under real engineering conditions.

[0054] The aforementioned intrinsic controllability assessment and design guidance methods also include:

[0055] Step 7: Controllability verification and bandwidth boundary output based on engineering constraints

[0056] By introducing engineering equivalent time delay constraints, controllability verification and bandwidth boundary output are achieved under actual control links. Specifically, this includes:

[0057] The first step is to perform simulation modeling for engineering controllability.

[0058] In the servo control system of a space precision pointing mechanism, there exists an engineering equivalent time delay. .

[0059] Based on the structural frequency response function, a delay element is introduced, resulting in a basic virtual open-loop function. The calculation formula is as follows:

[0060]

[0061] In the above formula, For adjustable proportional gain, Let j be the structural frequency response function, where j is the imaginary unit. Let ω be the angular frequency, and e be the natural constant. This is an equivalent delay in the engineering process.

[0062] The second step is to set the safety red line for the project's stability margin.

[0063] Engineering stability margins include phase margin and magnitude margin.

[0064] Phase margin satisfy:

[0065]

[0066] In the above formula, This is the safety margin red line for phase margin.

[0067] Gain Margin satisfy:

[0068]

[0069] In the above formula, This represents the safety margin for amplitude.

[0070] The third step is to extract the maximum amplitude crossover frequency and output design guidance.

[0071] Search for the open-loop gain crossover point and extract the maximum amplitude crossover frequency achievable by the servo control system of the space precision pointing mechanism under the condition of satisfying the engineering stability margin safety red line. Maximum amplitude crossing frequency The calculation formula is as follows:

[0072]

[0073] In the above formula, The open-loop gain crossover frequency refers to the control bandwidth of the servo control system.

[0074] Crossing frequency with maximum amplitude For the vertical axis, the equivalent time delay of the project Plot the delay tolerance curve with the x-axis as the horizontal axis.

[0075] Step 4: Output the results

[0076] Output maximum amplitude crossover frequency Delay tolerance curves and engineering optimization suggestions for the modal frequencies and resonance peaks of spatial precision pointing mechanisms are proposed.

[0077] The intrinsic controllability assessment and design guidance method for the aforementioned space precision pointing mechanism, in step 7, refers to the phase margin safety red line. for Amplitude margin safety red line for .

[0078] The beneficial effects of this invention are:

[0079] An intrinsic controllability assessment and design guidance algorithm system for a spatial precision pointing mechanism takes structural frequency response function (FRF) data as input. First, it completes the benchmark unification of frequency domain data through an automatic phase identification module. Then, it constructs a parameterized virtual open-loop model and searches for key crossing points related to stability across the entire frequency band.

[0080] An intrinsic controllability assessment and design guidance algorithm system for a space precision pointing mechanism provides quantitative basis for structural design and control performance matching through a unified result output module, which gives the intrinsic controllability frequency domain characteristic spectrum and the tolerance curve of the available bandwidth of the project with time delay.

[0081] A method for assessing the intrinsic controllability and guiding the design of a space precision pointing mechanism is proposed. Through automated phase reference unification, virtual open-loop construction, and multi-crossing point stability margin extraction, this method achieves quantitative assessment of the upper limit of the physical controllability of the structural system, frequency domain verification of the control feasibility under the introduced engineering equivalent time delay constraint, and provides a reliable basis for the structural design and control parameter selection of the space precision pointing mechanism without relying on the physical system.

[0082] A method for evaluating the intrinsic controllability and guiding the design of a spatial precision pointing mechanism is proposed. The method adopts a closed-loop evaluation dimension, which directly maps the physical characteristics such as the inherent frequency and resonance peak that are of concern in the structural design stage to the phase margin and amplitude margin indicators that are of concern in the control field. This realizes the direct correlation between structural parameters and control stability indicators, and avoids the problem of indicator mismatch in traditional serial design.

[0083] A method for assessing the intrinsic controllability and guiding the design of a spatial precision pointing mechanism is proposed. The assessment process is brought forward, eliminating the need to write specific control algorithm code or build a physical closed-loop system. Based solely on the structural FRF data, the upper limit of the controllability of the structural configuration in the frequency domain can be predicted. This allows for the early screening of schemes that do not meet the control requirements during the structural design stage, thus shortening the overall R&D cycle.

[0084] A method for assessing the intrinsic controllability and guiding the design of a space precision pointing mechanism is proposed. It adopts diagnostic logic robustness and can effectively cope with complex multimodal flexible structures through multi-crossing point search and automatic phase calibration, avoiding misjudgments caused by traditional single-point linearization assessment.

[0085] An intrinsic controllability assessment and design guidance method for a spatial precision pointing mechanism is proposed. It adopts optimized direction quantization and can intuitively observe the influence trend of engineering time delay and structural resonance peak position on controllable bandwidth through controllability boundary spectrum and time delay-bandwidth relationship curve. This provides a clear physical basis at the frequency and bandwidth levels for the design trade-off between "lightweight and high stiffness".

[0086] An intrinsic controllability assessment and design guidance method for a space precision pointing mechanism is proposed. The method adopts engineering constraint feasibility pre-verification. Based on the intrinsic controllability assessment, it introduces equivalent engineering time delay and stability margin redline constraints, and outputs the upper limit boundary of controllability determined by both structural and engineering conditions. This provides a unified frequency domain criterion for subsequent control index setting and engineering implementation scheme selection, and realizes pre-verification of engineering feasibility in the structural design stage. Attached Figure Description

[0087] Figure 1 This is the system architecture and modules of Embodiment 1 of the present invention;

[0088] Figure 2 This is a flowchart of the intrinsic controllability assessment and design guidance process for the spatial precision pointing mechanism according to Embodiment 1 of the present invention;

[0089] Figure 3 This is the uncalibrated phase frequency diagram of Embodiment 1 of the present invention;

[0090] Figure 4 This is the phase frequency diagram under calibration according to Embodiment 1 of the present invention;

[0091] Figure 5 This is an evaluation of the intrinsic controllability of an embodiment of the present invention;

[0092] Figure 6 This is an authentic controllability boundary map of an embodiment of the present invention;

[0093] Figure 7 This is the curve showing the relationship between the controllable bandwidth and the time delay in Embodiment 1 of the present invention. Detailed Implementation

[0094] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0095] Example 1

[0096] The system functional architecture of the present invention is as follows: Figure 1 As shown, the system takes the structure frequency response function (FRF) data as input, and completes the dimension unification and reference calibration of the amplitude and phase through the frequency domain data processing module; then, a virtual open-loop model including the proportional gain (K_p) and equivalent time delay (T_d) is constructed.

[0097] Based on this, the system enters either the intrinsic controllability assessment path or the engineering controllability simulation path according to the different evaluation modes, and finally the result output module provides the structural stability margin, controllable bandwidth and frequency domain visualization results.

[0098] Figure 2 The overall algorithm logic flow of the space precision pointing mechanism controllability evaluation method proposed in this invention is shown.

[0099] The process takes structural frequency response function (FRF) data as input. First, it uses an automatic phase identification module to unify the frequency domain data. Then, it constructs a parameterized virtual open-loop model and searches for key crossover points related to stability across the entire frequency band.

[0100] Based on this, depending on the selection of the evaluation mode, the algorithm enters either the intrinsic controllability evaluation path or the engineering controllability verification path. The intrinsic controllability evaluation path is used to analyze the upper limit of physical controllability that the mechanical structure can support without introducing engineering constraints; the engineering controllability verification path is used to evaluate the achievable bandwidth boundary of the structure in the real control link after introducing equivalent engineering time delay constraints.

[0101] Finally, the system provides a quantitative basis for matching structural design and control performance through a unified output module, which presents the intrinsic controllability frequency domain characteristic spectrum and the tolerance curve of the available bandwidth of the project with time delay.

[0102] It should be noted that, Figure 2 The dual-branch logic is not a conditional judgment during algorithm execution, but rather two evaluation modes configured within the same frequency domain analysis framework for different evaluation objectives. The intrinsic controllability evaluation mode characterizes the physical controllability upper limit of the structure under ideal control conditions; the engineering controllability verification mode verifies the engineering feasibility of this physical upper limit after introducing equivalent engineering constraints. Both modes share the same FRF input and virtual open-loop construction method, differing only in the constraint conditions and the form of the output results.

[0103] An intrinsic controllability assessment and engineering simulation method based on structural frequency response function, through automated phase reference unification, virtual open-loop construction, and multi-crossing point stability margin extraction, achieves the following without relying on the physical system: quantitative assessment of the upper limit of physical controllability of the structural system; frequency domain verification of control feasibility under the introduced engineering equivalent time delay constraint; and provides a reliable basis for the structural design and control parameter selection of space precision pointing mechanisms. The method includes the following steps:

[0104] Step 1: Data Reading and Format Normalization

[0105] Read the frequency response data (.txt format) of mechanical structures exported by finite element analysis software (such as ANSYS) or frequency sweep testing equipment.

[0106] Correct the scientific notation format using regular expressions to extract the frequency, amplitude, and phase columns.

[0107] Physical quantity transformation: Converting the measured linear displacement amplitude Based on the equivalent radius from the measuring point to the rotating shaft Converted to angular displacement amplitude This achieves dimensional unification of electromechanical interfaces.

[0108] Step 2: Automatic Phase Reference Calibration

[0109] To address the overall phase shift issue in the original FRF data caused by differences in coordinate definition or excitation direction, the median phase value of the low-frequency band (e.g., the lowest 5% of the frequency range) is extracted. .

[0110] when Approximately ±180° (e.g.) When the phase sign of the FRF structure is determined to be opposite to that of the negative feedback convention of the control system, a compensation of ±180° is uniformly superimposed on the phase of the entire frequency band to bring the low-frequency phase reference back to ±5°.

[0111] This automatic calibration process ensures that subsequent phase margin and gain margin calculations are performed under a unified reference standard, avoiding misjudgments in stability assessment due to inconsistent phase definitions.

[0112] Figure 3 The figure shows the phase frequency response curves obtained directly from the structural FRF without phase reference calibration. It can be seen that the phase in the low-frequency band is offset to around -180 degrees. This offset is due to the difference between the force-displacement direction definition in the finite element model and the negative feedback convention of the control system.

[0113] Figure 4 The results show the phase-frequency response after introducing the automatic phase calibration algorithm. By automatically identifying the low-frequency phase reference and applying uniform compensation, the phase curve returns to ±5° in the low-frequency range, providing a unified reference for the accurate calculation of subsequent phase margin and amplitude margin.

[0114] Step 3: Construct a virtual open-loop model

[0115] In pure structural frequency response function Based on this, a virtual open-loop function containing gain, time delay, and compensator is mathematically synthesized. :

[0116]

[0117] in, For adjustable proportional gain, The equivalent time delay for the project is given by j, where j is the imaginary unit. Angular frequency, To control the compensator, e is the natural constant. This is an equivalent delay in the engineering process.

[0118] A virtual open-loop model is constructed for controllability assessment, in which proportional gain and equivalent delay parameters are introduced for frequency domain stability margin and bandwidth boundary analysis.

[0119] Step 4: Logic for Switching Between Two-Dimensional Evaluation Modes

[0120] Depending on the evaluation objective, this method supports two controllability evaluation modes within a unified algorithmic framework:

[0121] Intrinsic controllability assessment mode: In this mode, no engineering equivalent time delay constraints are introduced. Instead, a virtual open-loop model is constructed based solely on the structural frequency response function to assess the upper limit of the stable control bandwidth that the mechanical structure itself can support at the physical level.

[0122] Engineering controllability verification mode: In this mode, an engineering delay constraint equivalent to that formed by factors such as sampling, calculation and communication is introduced to verify whether the current structure can meet the preset stability margin and bandwidth requirements under real engineering conditions.

[0123] Through the aforementioned mode switching mechanism, this method achieves unified modeling for the assessment of the upper limit of structural physical controllability and the verification of engineering feasibility without changing the main structure of the algorithm, providing a reusable frequency domain analysis framework for structure-control co-design.

[0124] Step 5: Extracting Indicators from Multiple Crossing Points

[0125] To address the characteristics of space precision pointing mechanisms, which exhibit multiple flexible modes and complex frequency domain features, this method automatically searches for all open-loop gain crossing points and phase crossing points across the entire frequency band.

[0126] Based on this, the phase margin and amplitude margin corresponding to each crossing point are compared in a unified manner, and the worst phase margin and worst amplitude margin in the entire frequency band are extracted as the sole criterion for system stability assessment, thereby avoiding the problem of missed detection of high-frequency instability risks that may be caused by the traditional single crossing point analysis method.

[0127] Step 6: Intrinsic Controllability Assessment and Design Guidance

[0128] Model switching: In terms of "intrinsic controllability" Evaluate the physical limit bandwidth of the mechanical structure under "engineering controllability" ( ) The feasibility of control measures will be assessed.

[0129] Gain Sweep: Automatically changes Step value, generated with For the horizontal axis, performance indicators ( The "controllability boundary map" is represented by the vertical axis.

[0130] Reverse guidance: Based on the obtained spectrum, identify the physical bottleneck frequency that limits bandwidth improvement, and output optimization suggestions for structural stiffness, damping, or modal density.

[0131] Figure 5The figure shows the virtual open-loop frequency domain response constructed based on the structural FRF under the intrinsic controllability evaluation mode (i.e., without introducing the equivalent time delay condition). The figure marks the open-loop amplitude-frequency response, phase-frequency response, and the corresponding phase margin, gain margin, and dominant structural resonance peak position, which are used to evaluate the upper limit of the stable control bandwidth that the structure itself can support at the physical level.

[0132] Figure 6 This represents the intrinsic controllability boundary map obtained through sweep analysis of the proportional gain (K_p). The figure shows the relationship curves of bandwidth, worst-case phase margin, and worst-case gain margin as a function of gain, which are used to identify the stability evolution trend of the structure under different control intensities, thereby revealing the structural intrinsic bottlenecks that limit the improvement of system bandwidth.

[0133] Step 7: Controllability verification and bandwidth boundary output based on engineering constraints

[0134] After completing the frequency response function of the structure body After assessing the intrinsic controllability, in order to realize the engineering applicability of the method in real aerospace servo control systems, this invention further introduces engineering constraints to verify the achievable bandwidth of the space precision pointing mechanism under actual control links.

[0135] Engineering delay constraint modeling

[0136] In the actual closed-loop system of a space precision pointing mechanism, factors such as sampling period, controller calculation delay, communication bus transmission, and driver response will inevitably introduce equivalent time delay. .

[0137] This invention introduces a delay element based on the structural frequency response function:

[0138]

[0139] This step will cause the open-loop phase to lag as the frequency increases, thereby compressing the system's stability margin.

[0140] Engineering stability margin red line criteria

[0141] To ensure the robust stability of aerospace servo systems, this invention sets a stability margin safety red line for engineering controllability, including:

[0142] Phase margin satisfies:

[0143]

[0144] The gain margin is satisfied:

[0145]

[0146] The aforementioned red line indicators can be set according to mission requirements, such as those commonly used for aerospace precision turntables. , .

[0147] Engineering available bandwidth extraction and design guidance output

[0148] After introducing time delay constraints and margin limits, this invention extracts the maximum amplitude crossover frequency that the system can achieve under the engineering redline conditions by automatically searching for the open-loop gain crossover point.

[0149]

[0150] It should be noted that the upper limit of the available bandwidth for this project is the frequency domain controllability boundary obtained by considering only the structural frequency response characteristics, equivalent engineering time delay, and stability margin red line. It reflects the theoretical controllable upper limit allowed by the coupling between the structure and the control link, rather than the actual closed-loop operating bandwidth of the final engineering system. The actual engineering bandwidth is further limited by factors such as actuator capability, sensor noise, and high-frequency unmodeled dynamics.

[0151] Finally, the output of this invention is:

[0152] Available bandwidth for the project

[0153] Delay tolerance curve

[0154] Recommendations for engineering optimization of structural modal frequencies and resonance peaks

[0155] This enables pre-constraints on control performance and closed-loop verification of engineering feasibility during the structural design phase.

[0156] Figure 7 The curves showing the relationship between the system's controllable bandwidth and time delay under the condition of introducing equivalent engineering delay are illustrated. Among them, This represents the upper limit of controllability, determined by the structure's frequency response characteristics and time delay constraints, under the condition of meeting the preset engineering stability margin. This represents the theoretical limit bandwidth obtained solely based on stability conditions.

[0157] It should be noted that this type of bandwidth index is used to characterize the controllable boundary of the frequency domain under the combined effect of structural and engineering constraints. Its main function is to provide performance upper limit determination and optimization direction guidance for the structural design stage, rather than directly serving as the final closed-loop bandwidth setting value of the engineering system.

[0158] Example 2

[0159] An intrinsic controllability assessment and design guidance algorithm system for a space precision pointing mechanism, such as Figure 1As shown, it includes a frequency domain data processing module, a virtual open-loop module, and a result output module.

[0160] The frequency domain data processing module is used to receive the input structure frequency response function (FRF) data and to unify the dimensions of amplitude and phase and perform reference calibration.

[0161] The virtual open-loop module includes a proportional gain. With equivalent delay It is used for intrinsic controllability assessment and engineering controllability simulation.

[0162] Intrinsic controllability assessment mode: Without introducing engineering equivalent time delay constraints, a virtual open-loop model is constructed based on the structural frequency response function to evaluate the upper limit of stable control bandwidth that a spatial precision pointing mechanism can support at the physical level.

[0163] Engineering controllability verification mode: Introducing engineering time delay constraints to verify whether the current space precision pointing mechanism can meet the preset stability margin and bandwidth requirements under real engineering conditions.

[0164] Among them, the engineering delay constraint is formed by the equivalent of sampling, calculation and communication factors.

[0165] The output module outputs the intrinsic controllability assessment and design guidance of the spatial precision pointing mechanism, the intrinsic controllability frequency domain characteristic spectrum, and the tolerance curve of the engineering available bandwidth as a function of the engineering equivalent time delay.

[0166] Intrinsic controllability assessment and design guidance refers to the intrinsic controllability assessment of virtual open-loop modules and the simulation results of engineering controllability.

[0167] The frequency domain data processing module, the virtual open-loop module, and the result output module transmit information data in sequence.

[0168] A method for assessing the intrinsic controllability and providing design guidance for a space precision pointing mechanism, the flowchart of which is shown below. Figure 2 As shown, it includes the following steps:

[0169] Step 1, Data Reading and Format Normalization

[0170] The frequency domain data processing module reads the frequency response data of the mechanical structure. The frequency response data of the mechanical structure is in .txt format and is exported by finite element analysis software or frequency sweep test equipment.

[0171] By using regular expressions, the scientific notation format is corrected, and the frequency, amplitude, and phase columns are extracted.

[0172] Based on the equivalent radius from the measuring point to the rotating shaft The measured linear displacement amplitude Converted to angular displacement amplitude angular displacement amplitude The calculation formula is:

[0173]

[0174] Step 2, Phase reference calibration

[0175] In the frequency response data of the mechanical structure in the frequency domain data processing module, the median phase value is extracted from the low-frequency phase column. The low-frequency band refers to the lowest 5% of the frequency range.

[0176] When the phase median When the absolute value is greater than the threshold, it is determined that the phase sign of the mechanical structure frequency response is opposite to the negative feedback convention of the servo control system. A compensation of ±180° is uniformly superimposed on the phase of the entire frequency band until the low-frequency phase reference returns to ±5°.

[0177] When the phase median When the absolute value is less than or equal to the threshold, the phase reference is not calibrated.

[0178] Threshold is .

[0179] Step 3, Construct a virtual open-loop module

[0180] In pure structural frequency response function Based on this, a virtual open-loop function containing gain, time delay, and compensator is mathematically synthesized. Virtual open-loop function The calculation formula is as follows:

[0181]

[0182] in, For adjustable proportional gain, The equivalent time delay for the project is given by j, where j is the imaginary unit. Angular frequency, To control the compensator, e is the natural constant. This is an equivalent delay in the engineering process.

[0183] By introducing proportional gain and engineering equivalent time delay parameters for frequency domain stability margin and bandwidth boundary analysis, a virtual open-loop module for controllability assessment is constructed.

[0184] Step 4, Logic for Switching Between Two-Dimensional Evaluation Modes

[0185] The two-dimensional evaluation model includes the intrinsic controllability evaluation model and the engineering controllability simulation model.

[0186] When the engineering equivalent time delay constraint is not introduced, the intrinsic controllability evaluation mode is executed to obtain the phase crossover point and open-loop gain crossover point corresponding to the phase margin and gain margin.

[0187] When an engineering equivalent time delay constraint is introduced, the engineering controllability simulation mode is executed.

[0188] By switching between intrinsic controllability assessment mode and engineering controllability simulation mode, a unified modeling system is achieved for assessing the upper limit of structural physical controllability and verifying engineering feasibility.

[0189] Intrinsic controllability assessment mode: Based on the structural frequency response function, a virtual open-loop model is constructed to evaluate the upper limit of the stable control bandwidth that the spatial precision pointing mechanism body can support at the physical level.

[0190] Engineering controllability simulation mode: used to verify whether the current space precision pointing mechanism can meet the preset stability margin and bandwidth requirements under real engineering conditions.

[0191] Step 5, Extraction of indicators from multiple crossing points

[0192] The virtual open-loop module searches for all open-loop gain crossing points and phase crossing points across the entire frequency band.

[0193] A unified comparison is made between the phase margin and the magnitude margin corresponding to each crossing point, and the worst phase margin and the worst magnitude margin are extracted across the entire frequency band.

[0194] Step 6, Intrinsic Controllability Assessment and Design Guidance

[0195] The first step is an assessment of intrinsic controllability.

[0196] When the equivalent delay of the project is zero, that is At the same time, the physical limit bandwidth of the space precision pointing mechanism is evaluated, and engineering optimization suggestions for the modal frequency and resonance peak of the space precision pointing mechanism are proposed.

[0197] When the equivalent delay of the project is greater than zero, that is At that time, assess the feasibility of control.

[0198] Step 2, Gain Sweep

[0199] Change the adjustable proportional gain Step value, generating adjustable gain This represents the controllability boundary map, with the horizontal axis representing the controllability and the vertical axis representing the performance index. The performance index is bandwidth. and / or phase margin and / or gain margin .

[0200] The third step is reverse guidance.

[0201] Based on the controllability boundary map, identify the physical bottleneck frequencies that limit bandwidth improvement, and output optimization suggestions for the stiffness, damping, or modal density of the space precision pointing mechanism.

[0202] Step 7: Controllability verification and bandwidth boundary output based on engineering constraints

[0203] By introducing engineering equivalent time delay constraints, bandwidth controllability verification can be achieved under actual control link conditions. Specifically, this includes:

[0204] The first step is to perform simulation modeling for engineering controllability.

[0205] In the servo control system of a space precision pointing mechanism, there exists an engineering equivalent time delay. .

[0206] Based on the structural frequency response function, a delay element is introduced, resulting in a basic virtual open-loop function. The calculation formula is as follows:

[0207]

[0208] In the above formula, For adjustable proportional gain, Let j be the structural frequency response function, where j is the imaginary unit. Let ω be the angular frequency, and e be the natural constant. This is an equivalent delay in the engineering process.

[0209] The second step is to set the safety red line for the project's stability margin.

[0210] Engineering stability margins include phase margin and magnitude margin.

[0211] Phase margin satisfy:

[0212]

[0213] In the above formula, This is the safety margin red line for phase margin.

[0214] Gain Margin satisfy:

[0215]

[0216] In the above formula, This represents the safety margin for amplitude.

[0217] The third step is to extract the maximum amplitude crossover frequency and output design guidance.

[0218] Search for the open-loop gain crossover point and extract the maximum amplitude crossover frequency achievable by the servo control system of the space precision pointing mechanism under the condition of satisfying the engineering stability margin safety red line. Maximum amplitude crossing frequency The calculation formula is as follows:

[0219]

[0220] In the above formula, The open-loop gain crossover frequency refers to the control bandwidth of the servo control system.

[0221] Crossing frequency with maximum amplitude For the vertical axis, the equivalent time delay of the project Plot the delay tolerance curve with the x-axis as the horizontal axis.

[0222] Step 4: Output the results

[0223] Output maximum amplitude crossover frequency Delay tolerance curves and engineering optimization suggestions for the modal frequencies and resonance peaks of spatial precision pointing mechanisms are proposed.

Claims

1. An algorithm system for evaluating the intrinsic controllability and guiding the design of a spatial precision pointing mechanism, characterized in that, It includes a frequency domain data processing module, a virtual open-loop module, and a result output module; The frequency domain data processing module is used to receive the input structure frequency response function (FRF) data and to unify the dimensions of the amplitude and phase and perform reference calibration. The virtual open-loop module includes a proportional gain. With equivalent delay It is used for intrinsic controllability assessment and engineering controllability simulation; The output module outputs the intrinsic controllability assessment and design guidance of the spatial precision pointing mechanism, namely the intrinsic controllability assessment and engineering controllability simulation results of the virtual open-loop module. The frequency domain data processing module, the virtual open-loop module, and the result output module transmit information data in sequence.

2. The intrinsic controllability assessment and design guidance algorithm system for the spatial precision pointing mechanism according to claim 1, characterized in that, The result output module outputs the intrinsic controllability frequency domain characteristic spectrum and the tolerance curve of the engineering available bandwidth as a function of the engineering equivalent time delay.

3. The intrinsic controllability assessment and design guidance algorithm system for the space precision pointing mechanism according to claim 1, characterized in that, The intrinsic controllability evaluation mode: without introducing engineering equivalent time delay constraints, based on the structural frequency response function, constructs a virtual open-loop model to evaluate the upper limit of stable control bandwidth that the spatial precision pointing mechanism can support at the physical level; The engineering controllability verification mode introduces engineering time delay constraints to verify whether the current spatial precision pointing mechanism can meet the preset stability margin and bandwidth requirements under real engineering conditions. Among them, the engineering delay constraint is formed by the equivalent of sampling, calculation and communication factors.

4. A method for evaluating the intrinsic controllability and guiding the design of a space precision pointing mechanism, using the algorithm system for evaluating the intrinsic controllability and guiding the design of a space precision pointing mechanism as described in any one of claims 1 to 3, characterized in that, Includes the following steps: Step 1, Data Reading and Format Normalization The frequency domain data processing module reads the frequency response data of the mechanical structure, which is in .txt format and is exported by finite element analysis software or frequency sweep test equipment. By using regular expressions, the scientific notation format can be corrected to extract the frequency, amplitude, and phase columns. Based on the equivalent radius from the measuring point to the rotating shaft The measured linear displacement amplitude Converted to angular displacement amplitude angular displacement amplitude The calculation formula is: ； Step 2, Phase reference calibration In the frequency response data of the mechanical structure in the frequency domain data processing module, the median phase value is extracted from the low-frequency phase column. Among them, the low-frequency band is the lowest 5% frequency point within the frequency range; When the phase median When the absolute value is greater than the threshold, it is determined that the phase sign of the mechanical structure frequency response is opposite to the negative feedback convention of the servo control system. A compensation of ±180° is uniformly superimposed on the phase of the entire frequency band until the low-frequency phase reference returns to ±5°. When the phase median When the absolute value is less than or equal to the threshold, the phase reference is not calibrated; Step 3, Construct a virtual open-loop module In pure structural frequency response function Based on this, a virtual open-loop function containing gain, time delay, and compensator is mathematically synthesized. Virtual open-loop function The calculation formula is as follows: ； in, For adjustable proportional gain, The equivalent time delay for the project is given by j, where j is the imaginary unit. Angular frequency, To control the compensator, e is the natural constant. This is an equivalent delay in the engineering process; A virtual open-loop module is constructed by introducing proportional gain and engineering equivalent time delay parameters for frequency domain stability margin and bandwidth boundary analysis. Step 4, Logic for Switching Between Two-Dimensional Evaluation Modes The two-dimensional evaluation model includes the intrinsic controllability evaluation model and the engineering controllability simulation model; When the engineering equivalent time delay constraint is not introduced, the intrinsic controllability evaluation mode is executed to obtain the phase crossing point and open-loop gain crossing point corresponding to the phase margin and gain margin. When introducing engineering equivalent time delay constraints, execute the engineering controllability simulation mode; By switching between intrinsic controllability assessment mode and engineering controllability simulation mode, a unified modeling system for assessing the upper limit of structural physical controllability and verifying engineering feasibility is achieved. Step 5, Extraction of indicators from multiple crossing points The virtual open-loop module searches for all open-loop gain crossing points and phase crossing points across the entire frequency band. A unified comparison is made between the phase margin and the magnitude margin corresponding to each crossing point, and the worst phase margin and the worst magnitude margin in the entire frequency band are extracted. Step 6, Intrinsic Controllability Assessment and Design Guidance The first step is an assessment of intrinsic controllability. When the engineering equivalent delay is zero, evaluate the physical limit bandwidth of the space precision pointing mechanism and propose engineering optimization suggestions for the modal frequency and resonance peak of the space precision pointing mechanism. When the equivalent time delay of the project is greater than zero, assess the feasibility of control. Step 2, Gain Sweep Change the adjustable proportional gain Step value, generating adjustable gain The controllability boundary map is plotted with the horizontal axis representing the controllability and the performance index representing the performance index representing the performance index. The performance index is the bandwidth. and / or phase margin and / or gain margin ; The third step is reverse guidance. Based on the controllability boundary map, identify the physical bottleneck frequencies that limit bandwidth improvement, and output optimization suggestions for the stiffness, damping, or modal density of the space precision pointing mechanism.

5. The method for intrinsic controllability assessment and design guidance of the space precision pointing mechanism according to claim 4, characterized in that, In step 2, the threshold is .

6. The method for intrinsic controllability assessment and design guidance of the space precision pointing mechanism according to claim 4, characterized in that, Step 4 further includes: Intrinsic controllability assessment mode: Without introducing engineering equivalent time delay constraints, a virtual open-loop model is constructed based on the structural frequency response function to assess the upper limit of stable control bandwidth that the spatial precision pointing mechanism body can support at the physical level; Engineering controllability simulation mode: Introduces engineering equivalent time delay constraints to verify whether the current spatial precision pointing mechanism can meet the preset stability margin and bandwidth requirements under real engineering conditions.

7. The method for intrinsic controllability assessment and design guidance of the space precision pointing mechanism according to claim 4, characterized in that, Also includes: Step 7: Controllability verification and bandwidth boundary output based on engineering constraints By introducing engineering equivalent time delay constraints, controllability verification and bandwidth boundary output are achieved under actual control links. Specifically, this includes: The first step is to perform simulation modeling for engineering controllability. In the servo control system of a space precision pointing mechanism, there exists an engineering equivalent time delay. ; Based on the structural frequency response function, a delay element is introduced, resulting in a basic virtual open-loop function. The calculation formula is as follows: ； In the above formula, For adjustable proportional gain, Let j be the structural frequency response function, where j is the imaginary unit. Let ω be the angular frequency and e be the natural constant. This is an equivalent delay in the engineering process; The second step is to set the safety red line for the project's stability margin. Engineering stability margins include phase margin and magnitude margin; Phase margin satisfy: ； In the above formula, This represents the safety margin for phase margin. Gain margin satisfy: ； In the above formula, This represents the safety margin for amplitude. The third step is to extract the maximum amplitude crossover frequency and output design guidance. Search for the open-loop gain crossover point and extract the maximum amplitude crossover frequency achievable by the servo control system of the space precision pointing mechanism under the condition of satisfying the engineering stability margin safety red line. Maximum amplitude crossing frequency The calculation formula is as follows: ； In the above formula, The open-loop gain crossover frequency refers to the control bandwidth of the servo control system. Crossing frequency with maximum amplitude For the vertical axis, the equivalent time delay of the project Plot the delay tolerance curve with the x-axis as the horizontal axis; Step 4: Output the results Output maximum amplitude crossover frequency Delay tolerance curves and engineering optimization suggestions for the modal frequencies and resonance peaks of spatial precision pointing mechanisms are proposed.

8. The method for evaluating the intrinsic controllability and providing design guidance for the spatial precision pointing mechanism according to claim 7, characterized in that, In step 7, the phase margin safety red line for Amplitude margin safety red line for .

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