Leg template multi-freedom vibration control method for random disturbance

Abstract

The application provides an active vibration control system and method. By collecting displacement, velocity and acceleration information of the lifting rod, the transverse moving rod and the overturning shaft, and synchronously collecting the amplitude of external vibration disturbance acting on the trolley structure; based on the connection mode of the trolley rod, the joint friction characteristics, the component inertia parameters and the coupling torque parameters between joints, a multi-degree-of-freedom mechanical model of the trolley is established or updated; the real-time state input of the state collection step is input into the mechanical model, the coupling vibration amplitude of each degree of freedom under the current disturbance is calculated, and vibration evaluation is performed; a multi-axis cooperative control algorithm is used to determine a set of coordinated control quantities for reducing the coupling vibration amplitude; the control quantities obtained in the control quantity generation step are output to the lifting rod, the transverse moving rod and the overturning shaft at the same time to drive the coordinated action of each degree of freedom to suppress vibration, so that the vibration amplitude of the corbel formwork trolley is kept within the preset vibration threshold.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering equipment control technology, specifically to a multi-degree-of-freedom vibration reduction control method for corbel formwork oriented towards random disturbances. Background Technology

[0002] Corbel formwork trolleys are widely used in cast-in-place tunnel lining structures, undertaking the critical task of forming the top corbel and sidewall concrete. However, tunnel construction sites simultaneously experience random disturbances such as shield tunneling, trolley transportation, and ventilation, characterized by wide frequency bands, high amplitudes, and random directions; the corbel formwork trolley also possesses three types of actuators: lifting, lateral movement, and tilting, resulting in strong structural coupling. Traditional passive reinforcement or single-axis control measures have revealed the following shortcomings:

[0003] Coupled vibration amplification: The degrees of freedom are mutually restrained, and single-axis commands often excite additional torque, making it difficult to suppress high-frequency resonance; lack of real-time performance: manual or offline equalization cannot track second-level disturbance fluctuations; insufficient adaptability: the performance of fixed damping or rubber pads degrades significantly under extreme conditions such as temperature and humidity, geothermal heat, and high-speed airflow; large noise interference: tunnel dust and high humidity environments cause sensor measurement noise to increase, and traditional filtering strategies are prone to introducing phase lag, thereby reducing control stability.

[0004] In recent years, advanced control methods such as multi-axis cooperative control, model predictive control (MPC), and state observers have achieved good results in the fields of industrial robots and precision machine tools. However, there is still a lack of systematic and engineering-based integrated solutions for the random disturbance vibration reduction of tunnel corbel template trolleys.

[0005] In view of the above-mentioned shortcomings, there is an urgent need for a multi-degree-of-freedom vibration reduction method and supporting system that can integrate mechanical modeling, collaborative control, real-time filtering and disturbance compensation, so as to maintain the high-precision and low-vibration operation of the corbel formwork trolley under random disturbance environment, thereby ensuring the quality of concrete pouring and construction safety. Summary of the Invention

[0006] This disclosure provides a multi-degree-of-freedom vibration reduction control method and system for corbel templates oriented to random disturbances, as well as a computer-readable storage medium.

[0007] In a first aspect, this disclosure provides a multi-degree-of-freedom vibration reduction control method for corbel formwork trolleys resistant to random disturbances, applicable to corbel formwork trolleys with lifting rods, lateral movement rods, and tilting shafts, characterized in that it includes:

[0008] Status acquisition steps: Acquire the displacement, velocity and acceleration information of the lifting rod, the horizontal moving rod and the tilting shaft, and simultaneously acquire the amplitude of external vibration disturbances acting on the trolley structure;

[0009] Mechanical modeling steps: Based on the connection method of the trolley rods, joint friction characteristics, component inertial parameters, and joint coupling torque parameters, establish or update a multi-degree-of-freedom mechanical model for the trolley;

[0010] Vibration assessment steps: Input the real-time state from the state acquisition step into the mechanical model, calculate the coupled vibration amplitude of each degree of freedom under the current disturbance, and conduct vibration assessment under the stroke and torque limitations of the actuator.

[0011] Control quantity generation step: Based on the vibration assessment results, a set of coordinated control quantities for reducing the amplitude of the coupled vibration is determined using a multi-axis cooperative control algorithm;

[0012] Control execution and closed-loop update steps: Simultaneously output the control quantities obtained in the control quantity generation step to the lifting rod, the horizontal moving rod and the flipping axis to drive the coordinated action of each degree of freedom to suppress vibration, so that the vibration amplitude of the corbel template trolley is kept within the preset vibration threshold, and the state acquisition step is restarted.

[0013] Optionally, the multi-axis cooperative control algorithm includes a multi-axis cooperative algorithm based on model predictive control, specifically:

[0014] The lifting rod, the lateral rod, and the tilting axis are mapped to a common virtual reference axis, and the cooperative weight vector is calculated based on the real-time load and coupling torque of each degree of freedom.

[0015] The cooperative weight vector is introduced into the objective function of the model predictive control so that the predicted displacement error of each degree of freedom and the control increment simultaneously obey cooperative constraints.

[0016] The optimal set of control quantities that satisfy the travel, torque and coordination constraints is obtained through rolling optimization, and the first moment control quantity in the set is output to drive the synchronous action of each degree of freedom.

[0017] Optionally, the multi-axis cooperative control algorithm includes a state observer-based multi-axis cooperative algorithm, specifically:

[0018] A state observer is set in the feedback loop of each degree of freedom of the lifting rod, the lateral rod and the tilting axis. The observer estimates the unmeasured coupled vibration state and instantaneous coupled torque of each degree of freedom based on the real-time displacement, velocity and acceleration signals.

[0019] Based on the coupled vibration state output by the observer, the synchronous action ratio of each degree of freedom is written into the coordination matrix to generate a coordination correction factor that is dynamically updated over time.

[0020] The collaborative correction factor is applied to the control quantity generation process, so that the lifting rod, the horizontal moving rod and the flipping axis are output synchronously according to the correction ratio under the same time reference, which further reduces the coupling vibration amplitude between multiple degrees of freedom of the corbel template.

[0021] Optionally, a disturbance observer is embedded in the multi-axis collaborative control process executed using the multi-axis collaborative control algorithm. The disturbance observer is used to estimate the external random disturbance force or disturbance torque acting on the lifting rod, the lateral rod, and the tilting axis, and to generate a compensation amount based on the estimation result. The compensation amount is superimposed with the coordinated control amount output by the multi-axis collaborative control to jointly drive the actuators of each degree of freedom, so as to counteract the coupled vibration effect of the external random disturbance on the corbel template.

[0022] Optionally, a filtering module is set in the multi-axis collaborative control link executed by the multi-axis collaborative control algorithm. The filtering module is located between the real-time status signals of the lifting rod, the traverse rod and the flip axis and the collaborative controller. It is used to suppress noise and reduce high-frequency interference of the displacement, velocity and acceleration signals collected by each degree of freedom, so as to improve the anti-interference ability of multi-axis collaborative control against random disturbances and measurement noise.

[0023] Optionally, the filtering process of the filtering module is a signal processing step combining Kalman filtering and frequency domain filtering, and further includes:

[0024] Kalman filtering is first performed on the displacement, velocity, and acceleration signals of each degree of freedom to obtain estimated state values ​​with measurement noise removed;

[0025] The estimated state value is subjected to real-time frequency domain analysis, and frequency domain filtering is applied to suppress high-frequency components that exceed the preset frequency band threshold.

[0026] The signal processed by Kalman filtering and frequency domain filtering is used as the feedback input of the multi-axis collaborative control loop to improve the anti-interference ability of multi-axis collaborative control against random disturbances and measurement noise.

[0027] Secondly, this disclosure provides a multi-degree-of-freedom vibration reduction control system for corbel formwork oriented towards random disturbances, including:

[0028] Status acquisition module: used to acquire displacement, velocity and acceleration information of lifting rod, horizontal moving rod and tilting shaft, and simultaneously acquire the amplitude of external vibration disturbances acting on the trolley structure;

[0029] Mechanical modeling module: used to establish or update a multi-degree-of-freedom mechanical model for the trolley;

[0030] Vibration assessment module: used to calculate the coupled vibration amplitude of each degree of freedom under the current disturbance, and to perform vibration assessment under the conditions of stroke and torque limitations of the actuator;

[0031] Control quantity generation module: Based on the evaluation results of the vibration evaluation module, it is used to determine a set of coordinated control quantities for reducing the amplitude of the coupled vibration;

[0032] Control execution and closed-loop update module: used to simultaneously output the obtained control quantities to the lifting rod, the traverse rod and the tilting axis to drive the coordinated movement of each degree of freedom to suppress vibration.

[0033] Optionally, the system further includes:

[0034] The state observation module is used to observe real-time displacement, velocity and acceleration signals, and estimate the unmeasured coupled vibration state and instantaneous coupled torque of each degree of freedom;

[0035] The correction module is used to write the synchronous action ratio of each degree of freedom into the coordination matrix based on the coupled vibration state output by the observation module, and generate a coordination correction factor that is dynamically updated over time.

[0036] The correction module is also used to apply the collaborative correction factor to the control quantity generation stage, so that the lifting rod, the horizontal moving rod and the flipping axis are output synchronously according to the correction ratio under the same time reference, further reducing the coupling vibration amplitude between multiple degrees of freedom of the corbel template.

[0037] Optionally, the system further includes a disturbance observation module for estimating the external random disturbance force or disturbance torque acting on the lifting rod, the lateral rod, and the tilting axis, and generating a compensation amount based on the estimation result; the compensation amount and the coordinated control amount output by the multi-axis collaborative control are superimposed to jointly drive the actuators of each degree of freedom to counteract the coupled vibration effect of the external random disturbance on the corbel template.

[0038] Thirdly, this disclosure provides a computer-readable storage medium having a computer program stored thereon to implement the methods of this disclosure.

[0039] The beneficial effects of this disclosure are that, compared with the prior art, this disclosure has the following advantages:

[0040] 1) This invention acquires dynamic signals and external disturbance amplitudes of the lifting rod, lateral rod, and flipping shaft synchronously at the millisecond level. Combined with a multi-degree-of-freedom mechanical model based on real-time parameter online updates, it can quickly and accurately capture and quantify the actual impact of coupled vibration modes between multiple degrees of freedom and external random disturbances. This lays a high-precision foundation for subsequent evaluation and control, and overcomes the problems of response lag and model inaccuracy in traditional methods.

[0041] 2) This invention integrates two types of multi-axis cooperative control, including cooperative control based on model predictive control (MPC), which maps the three degrees of freedom to virtual reference axes and dynamically calculates cooperative weight vectors based on real-time load and coupling torque. Within the rolling optimization framework of MPC, this weight vector is introduced into the objective function and constraints to ensure that, under the premise of satisfying the hard limits of stroke and torque of each actuator, the optimal control command sequence that enables multi-degree-of-freedom cooperative action and effectively suppresses coupled vibration is generated, thus avoiding secondary resonance caused by single-axis action. The invention also includes cooperative control based on state observers, which embed state observers in the feedback loops of each degree of freedom to estimate the unmeasured coupled vibration state and instantaneous coupled torque in real time. Based on this, a cooperative correction factor that is dynamically updated over time is generated and applied to the control quantity generation stage, so that the lifting, lateral, and tilting axes can accurately and synchronously output control quantities at the same time reference in the optimal proportion, further weakening the coupled vibration between multiple degrees of freedom.

[0042] 3) This invention also provides strong anti-interference and noise suppression for the harsh environment of tunnels, including an embedded interference observer, which effectively cancels the coupled vibration effect of external random disturbances (such as shield advancement and vehicle impact) on the corbel template, and greatly shortens the recovery time after sudden disturbances; it also includes Kalman + frequency domain dual filtering, which significantly purifies the feedback signal, greatly reduces the probability of sensor noise and false triggering of vibration suppression commands, and greatly improves the robustness and control stability of the system in a strong noise environment.

[0043] In summary, this invention provides a reliable state input and dynamic foundation for the cooperative control algorithm through a series of closely coordinated, precise synchronous sensing and real-time modeling. The dual-track cooperative control strategy, consisting of MPC and state observer, achieves multi-degree-of-freedom dynamic optimization and synchronous vibration suppression under physical constraints. Meanwhile, the disturbance observer and dual filtering, from the dimensions of feedforward compensation and feedback purification respectively, effectively ensure the execution of the cooperative control strategy in high-noise, high-random-disturbance environments. This integrated design of "sensing-modeling-cooperative control-disturbance filtering" enables the system to cover the full-frequency vibration suppression requirements from low-frequency coupling to high-frequency impacts, ultimately suppressing the vibration amplitude of the tunnel lining formwork trolley within a preset threshold, significantly improving the pouring quality of tunnel lining concrete and the safety and efficiency of the construction process. This solution effectively addresses many shortcomings of traditional methods in terms of real-time performance, disturbance rejection, coordination, and environmental adaptability. Attached Figure Description

[0044] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0045] Figure 1 This is a schematic diagram of the corbel template trolley structure;

[0046] Figure 2 A schematic diagram illustrating a tunnel application scenario for a multi-degree-of-freedom vibration reduction control method for corbel templates oriented towards random disturbances, provided by an embodiment of this disclosure;

[0047] Figure 3 A schematic diagram of a multi-degree-of-freedom vibration reduction control method for a corbel template oriented towards random disturbances provided in an embodiment of this disclosure;

[0048] Figure 4 This is a schematic diagram illustrating the execution steps of a multi-axis cooperative algorithm based on model predictive control, provided in an embodiment of this disclosure.

[0049] Figure 5 A schematic diagram of a multi-axis cooperative algorithm based on a state observer provided in an embodiment of this disclosure;

[0050] Figure 6 This invention provides a schematic diagram of signal processing steps for a filtering module that combines Kalman filtering and frequency domain filtering, as shown in an embodiment of the present disclosure.

[0051] Figure 7 This is a schematic diagram of a multi-degree-of-freedom vibration reduction control system for a corbel template oriented to random disturbances, provided in an embodiment of this disclosure.

[0052] The accompanying drawings have illustrated specific embodiments of this disclosure, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this disclosure to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0053] The present disclosure will be further described below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solutions of the present disclosure more clearly, and should not be used to limit the scope of protection of the present disclosure.

[0054] The present disclosure will be further described below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solutions of the present disclosure more clearly, and should not be used to limit the scope of protection of the present disclosure.

[0055] Figure 1 A schematic diagram of a corbel formwork trolley structure provided in this embodiment includes: a cast corbel 2, a corbel formwork 32, a corbel formwork trolley main frame 311, a hydraulic auxiliary system 312, and an electric control walking system 313. Figure 2 A schematic diagram illustrating a tunnel application scenario for a multi-degree-of-freedom vibration reduction control method for corbel formwork provided in this disclosure embodiment.

[0056] Figure 3 This is a schematic diagram of a multi-degree-of-freedom vibration reduction control method for a corbel template subjected to random disturbances, provided in an embodiment of this disclosure. This control method can be applied to... Figure 1The corbel template trolley shown. See also... Figure 2 The following is a detailed discussion of each step in conjunction with this embodiment.

[0057] In the status acquisition step S100, the displacement, velocity and acceleration information of the lifting rod, the horizontal moving rod and the tilting shaft are acquired, and the amplitude of the external vibration disturbance acting on the trolley structure is acquired simultaneously.

[0058] The lifting rod and the lateral movement rod, as part of the hydraulic auxiliary system 312, are used to synchronously extend and retract to adjust the height of the formwork in the vertical direction, ensuring precise alignment of the pouring joint between the corbel formwork and the tunnel lining segments; and to fine-tune the width of the formwork through lateral extension and retraction, ensuring the parallelism and fit between the formwork side and the tunnel wall. The tilting shaft is integrated at the upper rotatable connection between the main frame 311 and the corbel formwork 32. Driven by the control signals of the electric walking system 313, it allows the formwork to tilt and open around this shaft, realizing the closing and demolding actions. The tilting shaft not only handles the posture switching of the formwork but also works with the lifting rod and the lateral movement rod to complete complex multi-degree-of-freedom positioning.

[0059] In this embodiment, the state acquisition of the corbel template trolley adopts a "single-frame vector" strategy with unified clock management. Each of the three key execution chains—the lifting rod, the lateral rod, and the tilting axis—is equipped with a set of position-velocity sensors, and triaxial accelerometers are attached to the corresponding nodes, ensuring that the displacement, velocity, and acceleration of each mechanism can be completely captured simultaneously. Simultaneously, to quantify external random disturbances such as shield vibration, transport vehicle impact, and airflow within the tunnel, several additional triaxial accelerometers are arranged on the trolley's main beam or template surface, using their instantaneous peak-to-peak values ​​to characterize the overall vibration amplitude. All sensors are triggered for sampling by a millisecond-level common clock. The raw data, after filtering and denoising, is immediately encapsulated into a single-frame state vector, which contains both three-degree-of-freedom motion information and the current external disturbance amplitude. Thus, at each control cycle, the controller only needs to read the latest frame vector to obtain all the real-time input required for subsequent mechanical modeling and vibration assessment, achieving synchronous, simple, and efficient data acquisition.

[0060] In mechanical modeling step S200, a multi-degree-of-freedom mechanical model is established or updated for the trolley based on the connection method of the trolley rods, joint friction characteristics, component inertial parameters, and joint coupling torque parameters.

[0061] In this embodiment, the construction of the multi-degree-of-freedom mechanical model in step S200 adopts a two-level strategy of "static initialization + online adaptation". First, the following parameters are required to construct the static initial model:

[0062] Connection method of trolley components: The trolley components include hydraulic lifting rods (vertical movement), lateral movement rods (lateral displacement), tilting shafts (angle adjustment), and the main frame. The trolley's 3D CAD design file is imported into dynamics analysis software, which automatically identifies the hinged, sliding, or rigid connection types between the lifting rods, lateral movement rods, tilting shafts, and the main frame using their topology information. Based on this, the software generates corresponding displacement constraint equations for each component.

[0063] Joint friction characteristics: including static friction, Coulomb friction, and viscous friction. The static friction torque and speed-dependent viscous friction coefficient of each joint were measured through a no-load slow-speed servo scan test when the trolley left the factory, and written into the friction parameter array.

[0064] Component inertial parameters include mass, moment of inertia, and product of inertia. The density and elastic modulus, already calibrated in the material library, are used to transform the mass and geometric distribution of each component into lumped mass blocks. A hybrid series-parallel rigid body tree structure is then used to obtain the initial generalized inertial matrix of the system. Finally, test results from a laboratory rotating inertia meter are added to the center of gravity-inertia tensor to ensure the model's inertial accuracy.

[0065] Inter-joint coupling torque: obtained through mechanical model calculation, laboratory static calibration or online dynamic identification, etc., all of which are existing technologies and will not be described in detail here.

[0066] Based on the connection method of the above-mentioned trolley rods, joint friction characteristics, component inertial parameters, and joint coupling torque parameters, a complete set of six-degree-of-freedom Lagrange equations is formed as a static initial model.

[0067] The online adaptive operation for the static chamber model includes the following steps: After the trolley is lowered into the shaft, the controller, in an adaptive loop refreshed every 100ms, substitutes the real-time displacement, velocity, and driving torque obtained from the state acquisition step into the recursive least squares estimator. When an observable deviation is detected between the model output and the measured acceleration, the estimator adjusts the friction coefficient or coupling torque coefficient. Simultaneously, if the temperature sensor indicates a significant increase in hydraulic oil temperature, the fluid-added mass term in the inertia tensor is dynamically corrected. This ensures that the mechanical model continuously conforms to the actual dynamic behavior of the trolley over time, even under shield vibration and high humidity / heat environments, providing an accurate and real-time system description for subsequent vibration assessment and control optimization.

[0068] Vibration assessment step S300: Input the real-time state from the state acquisition step into the mechanical model, calculate the coupled vibration amplitude of each degree of freedom under the current disturbance, and conduct vibration assessment under the stroke and torque limitations of the actuator.

[0069] In this embodiment, when the previous cycle has just ended and the status acquisition module has output a frame containing displacement v and velocity... acceleration When the controller receives the real-time data vector of the external disturbance amplitude A_d, it immediately sends this set of values ​​into the online-updated multi-degree-of-freedom mechanical model M(t).

[0070] The model solves for the instantaneous internal force distribution of the system under a given external disturbance torque τ_d in generalized coordinate form. Then, the Jacobian matrix is ​​used to map the internal forces of each joint to key observation points such as the top plate of the template and the contact surface of the side walls, obtaining the coupling response vector r = [r_z, r_x, r_θ] between the three execution axes. The controller performs a sliding window envelope operation on the vector r, encompassing two system main vibration periods, to extract the peak-to-peak coupled vibration amplitude A = max(r) - min(r) at the current moment. This amplitude is compared with the engineering preset threshold A_ref = 0.20 mm. If A ≤ A_ref, the model outputs "0" indicating acceptable vibration; if A > A_ref, it outputs "1" to trigger subsequent control quantity optimization. Through this rapid evaluation based on real-time mechanical response and combined with sliding window envelope, the system can determine whether the current random disturbance has caused the corbel template vibration to exceed the limit within less than 5ms, thus gaining sufficient computational window for the control quantity generation step.

[0071] In the control quantity generation step S400, based on the vibration assessment results, a set of coordinated control quantities for reducing the amplitude of the coupled vibration is determined using a multi-axis cooperative control algorithm.

[0072] In this embodiment, when the vibration assessment returns a "vibration exceeds limit" flag, the controller immediately enters the coordinated control quantity solution process. First, the system reads the current absolute positions of the three types of actuators: lifting rod, lateral rod, and tilting shaft, and sets stroke constraints according to the design allowance: lifting ±70mm, lateral movement ±35mm, and tilting ±4.5°. Simultaneously, it queries the real-time current of the hydraulic pump station and servo drive to calculate the available remaining torque of each axis, which serves as the upper limit of torque for this cycle. Subsequently, the controller dynamically generates a coordinated weight vector W = [0.5, 0.3, 0.2] based on the proportion of each component in the coupled vibration vector r of the previous cycle, corresponding to the main vibration suppression responsibility of the lifting, lateral movement, and tilting three degrees of freedom.

[0073] Under the dual constraints of stroke and torque, and the influence of weight vectors, the controller constructs a single-objective rolling optimization problem: using the weighted sum of squared predicted displacement errors of the three axes as the objective function, it solves for the control increment within a future 200ms time window. The optimization algorithm employs real-time quadratic programming, completing in an average time of 3ms. The solution is a set of optimal control quantity sequences ΔU* that satisfy the constraints; the controller extracts only the first control quantity ΔU0 = [-2.3mm, +1.6mm, -0.25°] from this sequence and performs a torque saturation check on it. After confirming that the maximum hydraulic output only accounts for 82% of the allowable value, ΔU0 is immediately superimposed on the existing target pose to generate a new absolute command U_next. This command is synchronously sent to the lifting cylinder proportional valve, the transverse lead screw servo drive, and the tilting cylinder control valve to achieve three-axis coordinated action, thereby reducing the coupled vibration peak to within the threshold.

[0074] In the control execution and closed-loop update step S500, the control quantity obtained in the control quantity generation step is simultaneously output to the lifting rod, the horizontal moving rod and the flipping axis to drive the coordinated action of each degree of freedom to suppress vibration, so that the vibration amplitude of the corbel template trolley is kept within the preset vibration threshold, and the state acquisition step is restarted.

[0075] In the final stage of the control cycle, the controller packages the three-degree-of-freedom coordinated control quantities calculated in the previous stage into a single data message with a unified timestamp, and sends it to the execution layer all at once via the EtherCAT bus. Since the lifting cylinder proportional valve, the traverse screw servo drive, and the tilting cylinder valve group are all locked to the same system clock, this message is simultaneously parsed and activated within microseconds of arriving at each controlled node. Consequently, the three actuators begin to move almost simultaneously: the hydraulic valve core rapidly adjusts its opening with 2kHz pulse width modulation, the servo motor drives the ball screw with a 1kHz position loop, and the tilting cylinder completes precise oscillation within a small displacement. After the movement is completed, the displacement, velocity, and acceleration sensors distributed on each axis immediately read back the new state values; the accelerometers on the main beam and template surface also synchronously provide updated overall vibration peak values. The controller uses an online mechanical model to calculate the coupled amplitude in real time and compares it with a set threshold of 0.20mm: if the peak-to-peak value has dropped below the threshold, only routine monitoring is performed in the next cycle; if it is still too high, optimization is triggered again in the next 20ms cycle. The on-site test lasting half an hour showed that the amplitude of the top plate was always suppressed to within 0.18 mm, and it could recover within 0.6 s after any 0.6 g level pulse disturbance, so that the corbel formwork trolley could maintain a stable and low vibration working state in complex random environment.

[0076] This solution constructs a high-precision vibration sensing system through synchronous acquisition of multi-degree-of-freedom dynamic signals and real-time mechanical modeling, accurately capturing the coupled vibration modes of the corbel formwork trolley during tunnel construction. Based on a dual-track collaborative control strategy of model prediction and state observation, and under strict adherence to the physical constraints of the actuators, it dynamically generates vibration suppression commands, effectively suppressing the mechanical interference effects of the lifting, lateral, and tilting three degrees of freedom. The innovative embedding of interference observation and dual filtering mechanisms significantly improves the system's robustness against dust, temperature changes, and random impacts.

[0077] Furthermore, the multi-axis cooperative control algorithm in the control quantity generation step S400 includes a model predictive control-based multi-axis cooperative algorithm and a state observer-based multi-axis cooperative algorithm. These two algorithms are suitable for different scenarios. In the random disturbance environment of tunnel construction, the model predictive control-based multi-axis cooperative algorithm is suitable for high-frequency vibrations caused by shield tunneling and vehicle passage, generating vibration suppression commands in advance through virtual axis mapping and rolling optimization. The state observer-based multi-axis cooperative algorithm targets low-frequency coupled vibrations such as gradual changes in hydraulic oil temperature and slow changes in joint friction, using a state observer to capture hidden disturbances in real time and dynamically correct the action ratio. The two schemes dynamically switch based on the vibration spectrum characteristics, forming a vibration suppression strategy covering the entire frequency band. The two different algorithms are described in detail below.

[0078] Figure 4 This diagram illustrates the execution steps of a multi-axis cooperative algorithm based on model predictive control, as provided in an embodiment of this disclosure. Now, in conjunction with... Figure 4 The specific steps of the algorithm will be further explained.

[0079] A1. Map the lifting rod, lateral rod, and tilting axis to a common virtual reference axis, and calculate the cooperative weight vector based on the real-time load and coupling torque of each degree of freedom.

[0080] In this embodiment, the controller first introduces a unified "virtual reference axis" for the three execution chains. It converts the vertical displacement, horizontal displacement, and tilt angle into equivalent displacements of the same dimension according to a preset ratio—every 1mm of vertical movement, every 0.8mm of horizontal movement, and every 0.1° of tilt angle is considered as 1 unit on the virtual axis. In this way, the instantaneous motion quantities of the three degrees of freedom can be directly added and compared to form a reference coordinate system that can be uniformly scheduled.

[0081] Next, the controller retrieves the driving torque and the coupling torque calculated from the mechanical model within the same sampling period. First, it divides the real-time load of each degree of freedom by its rated upper limit to obtain the load coefficient after percentage division. Then, it multiplies this coefficient by the absolute value of the corresponding coupling torque to obtain the "comprehensive influence index". The larger the comprehensive influence index, the more sensitive the degree of freedom is to both the high load and the vibration coupling effect of other axes at this moment.

[0082] Finally, the controller normalizes the three combined influence indices proportionally, resulting in a set of time-varying collaborative weights. For example, the calculation results for the current cycle might assign 64% to the lifting rod, 27% to the traverse rod, and only 9% to the tilting shaft. Subsequent control optimization is guided by this set of three weights: the lifting rod first undertakes significant corrections, followed by the traverse rod, and the tilting shaft only makes minor compensations. Through this iterative update, the system can dynamically allocate "vibration suppression responsibility" according to real-time operating conditions in each control cycle, ensuring that the overall amplitude is quickly reduced to the target threshold while preventing any actuator from overtraveling or overloading due to excessive movement.

[0083] A2. Introduce the cooperative weight vector into the objective function of the model predictive control so that the predicted displacement error of each degree of freedom and the control increment simultaneously obey the cooperative constraint.

[0084] In this embodiment, the control system directly writes the cooperative weight vector W = [w1, w2, w3] generated in real time in step A1 into the objective function of the model predictive controller. The predictive time domain of the controller is set to 250ms, and internally it will sequentially calculate the displacement prediction values ​​and control increments of the three degrees of freedom for several discrete time intervals. Specifically, the predicted displacement errors of the lifting, lateral, and flipping axes are multiplied by their corresponding weights w1, w2, and w3, respectively, and then combined with the control increments after being multiplied by the same weights and fed into the same cost accumulator; in other words, the displacement errors and control actions must converge together according to their weight ratios. Taking the current period weight W≈[0.64, 0.27, 0.09] as an example, the optimizer will allocate 64% of the vibration suppression pressure to the lifting rod, 27% to the lateral rod, and the flipping axis will only bear 9% of the fine compensation. In this way, if any degree of freedom wants to reduce its own error by using a larger action during the prediction solution process, it must simultaneously satisfy the "cooperative ratio" limited by the weights, thus avoiding the triggering of new coupled vibrations due to overcompensation of a single axis from the root. The optimal control output of the optimizer at the first moment naturally carries this cooperative constraint, ensuring that the three execution chains can quickly reduce the overall amplitude in subsequent actual actions without exceeding the safe upper limit of their respective stroke and torque.

[0085] A3. The optimal set of control quantities that satisfy the travel, torque and coordination constraints is obtained through rolling optimization, and the first moment control quantity in the set is output to drive the synchronous action of each degree of freedom.

[0086] In this embodiment, the system establishes a rolling optimization framework with a prediction window of 250 milliseconds and a control window of 60 milliseconds. The controller first sends the updated multi-degree-of-freedom mechanical model, cooperative weights, and the remaining stroke and torque limits of each execution chain into the real-time quadratic programming solver. Starting from the current moment, the solver performs a joint search on the lifting, lateral, and flipping displacement trajectories of six discrete points within the prediction window and the control increment. The goal is to reduce the overall coupled vibration peak below the threshold under the allocation ratio limited by the cooperative weights, while ensuring that the displacement command at any given moment does not exceed the remaining stroke and the control command does not exceed the remaining torque. Due to the embedded cooperative weights, the algorithm naturally tends to allow the lifting rod to undertake large corrections, the lateral rod to perform medium-amplitude compensation, and the flipping axis to make only small fine adjustments. The solution iteration takes an average of about 3 milliseconds to converge, obtaining a sequence of optimal control quantities covering the next 60 milliseconds. Subsequently, the controller only takes the first frame instruction of the sequence, that is, the "first moment control quantity", and immediately sends it synchronously to the lifting cylinder proportional valve, the lateral servo drive, and the tilting cylinder valve group; the three execution chains start simultaneously because they share the same time base, ensuring the coordination and consistency of physical actions. When the next 20-millisecond control cycle begins, the system re-optimizes by sliding the window according to the same process, and so on, so that the vibration of the trolley is always suppressed within the set threshold.

[0087] Figure 5 This is a schematic diagram of a multi-axis cooperative algorithm based on a state observer provided in an embodiment of this disclosure. Now, in conjunction with... Figure 5 The specific steps of the algorithm will be further explained.

[0088] B1. Set up state observers in the feedback loops of each degree of freedom of the lifting rod, the lateral rod, and the tilting axis. The observers estimate the unmeasured coupled vibration state and instantaneous coupled torque of each degree of freedom based on the real-time displacement, velocity, and acceleration signals.

[0089] In this embodiment, a software state observer is serially inserted after the servo drive loop of each execution chain. Taking the lifting rod as an example, the observer kernel is a fourth-order discrete state equation. The measured inputs are lifting displacement, velocity, and acceleration, and the outputs are "unmeasured coupled vibration displacement components" and "equivalent coupled torque". The system matrix is ​​composed of offline identified lifting body parameters and coupling coefficients provided by the online mechanical model. The observation gain is configured with poles to keep the error convergence bandwidth above 20Hz. The horizontal movement rod and the flip axis are established with third-order and second-order observers respectively, receiving their respective sensor signals in real time.

[0090] When the tunnel boring machine (TBM) advances or vehicle impacts cause overall vibration of the formwork, the lifting sensor can only detect displacement along its own axis, but cannot directly quantify the coupled disturbances from the lateral or tilting directions. The observer uses the difference between the model prediction and the measurement residual to provide the unmeasured coupled vibration components within less than 10ms; simultaneously, it calculates the transient equivalent coupled torque based on Lagrange mechanical relations. In this way, in addition to conventional position and velocity feedback, the controller can obtain two additional hidden states—"coupled vibration displacement" and "coupled torque"—in each control cycle. Subsequent updates to the coordination matrix and correction factors are based on these two observations: if a sudden increase in the coupled torque on the lifting rod is observed, the system will immediately increase the coordination weight in the lifting direction and allocate more vibration-damping actions to the lifting mechanism in the model prediction optimization; conversely, it will appropriately reduce its motion amplitude. Through continuous iteration, the unmeasured coupled states of the three degrees of freedom are compensated in real time, significantly improving the overall amplitude convergence speed.

[0091] B2. Based on the coupled vibration state output by the observer, the synchronous action ratio of each degree of freedom is written into the coordination matrix to generate a coordination correction factor that is dynamically updated over time.

[0092] In actual operation, each time the controller receives the "coupled vibration displacement" and "equivalent coupled torque" output from the state observer, it immediately reassesses the relative importance of the three execution chains in the current vibration mode. The process involves: first, taking the absolute values ​​of the observed coupled displacement amplitudes for the three degrees of freedom (lifting, lateral, and flipping), and then multiplying them by the corresponding observed coupled torque amplitudes to obtain three comprehensive indices. The larger the index, the more significantly the degree of freedom is affected by coupled vibration and plays a dominant role in the transmission of vibration energy. The controller then normalizes these three indices proportionally and writes them into a 3×3 diagonal "coordination matrix," where the diagonal elements represent the latest synchronization ratio. Compared to the matrix of the previous cycle, if the index of a certain degree of freedom increases, the controller increases its diagonal elements and correspondingly decreases the others, with each adjustment limited to within 10% to avoid excessive oscillation. The sum of the diagonal elements of the matrix remains 1, ensuring that the total amount of motion of the three execution chains remains constant while the distribution ratio changes in real time. The controller refers to the proportional vector extracted from this determinant as the "cooperative correction factor," and directly multiplies it into the objective function during the next round of model prediction optimization. Thus, the cooperative weights dynamically drift over time: once the dominant vibration direction changes from vertical to horizontal, the horizontal weight automatically increases, while the vertical weight decreases synchronously. This rolling update ensures that the correction factor always closely follows the observed coupling state, maintaining consistency between the distribution ratio of the three-degree-of-freedom synchronous actions and the actual vibration mode on site. This allows for the suppression of coupled amplitudes with the most suitable master-slave relationship within each control cycle.

[0093] B3. Apply the aforementioned collaborative correction factor to the control quantity generation stage, so that the lifting rod, the horizontal moving rod, and the flipping axis are output synchronously according to the correction ratio under the same time reference, further reducing the coupling vibration amplitude between multiple degrees of freedom of the corbel template.

[0094] In the latest control cycle of this embodiment, the correction factor generated by the iterative coordination matrix is ​​resolved into a proportional vector C = [0.58, 0.31, 0.11], corresponding to the lifting rod, the lateral rod, and the tilting axis, respectively. The controller then directly embeds this vector into the control quantity generation stage: the model predictive optimizer first obtains the original optimal control increment sequence ΔU* of the three degrees of freedom using a conventional algorithm, and then simultaneously weights these three increments according to the proportions in C, retaining 58% in the lifting direction, 31% in the lateral direction, and only 11% in the tilting direction; in order not to change the overall vibration suppression amplitude, the three values ​​are normalized proportionally and then subjected to a saturation check with the actuator stroke and torque upper limit. The control quantity after correction is encoded into a message with the same timestamp and sent to the lifting valve group, the lateral servo drive, and the tilting valve group all at once via the EtherCAT bus. Since the three drives share the timestamp, they move synchronously within a few hundred microseconds: the lifting cylinder depresses by 1.9mm, the lateral screw moves by 1.0mm, and the tilting axis rotates by 0.12°.

[0095] The above describes the specific execution steps of two multi-axis cooperative control algorithms. After generating the instructions for the multi-axis cooperative control algorithm, it is necessary to further overcome the coupled vibrations caused by unmodeled random disturbances in the tunnel environment, such as shield impact and transport vehicle vibration. Therefore, this solution introduces an embedded disturbance observer as a parallel disturbance rejection module. The implementation steps are detailed below with reference to the disturbance observation flowchart:

[0096] An interference observer is embedded in the multi-axis collaborative control process. The interference observer is used to estimate the external random disturbance force or disturbance torque acting on the lifting rod, the lateral rod and the tilting axis, and generate a compensation amount based on the estimation result. The compensation amount is superimposed with the coordinated control amount output by the multi-axis collaborative control to jointly drive the actuators of each degree of freedom to counteract the coupled vibration effect of the external random disturbance on the corbel template.

[0097] In one specific embodiment, the three actuator chains of the gantry crane—the lifting cylinder, the lateral lead screw, and the tilting cylinder—still coordinate their movements according to the target torque output by the coordinating controller. However, an additional software module, the "interference observer," is inserted between the controller and the actuators. As soon as the coordinating controller calculates the target torque for the next moment, the interference observer immediately calls the crane's real-time mechanical model to predict the acceleration that these torques should produce under ideal conditions. Simultaneously, sensors have collected the actual accelerations of each axis; the residual obtained by subtracting the two, after high-speed low-pass filtering, directly reflects the magnitude and direction of the external random disturbance torque. The system takes the opposite of this "disturbing torque," generates a compensation amount, and then adds it vector-wise to the original target torque of the coordinating controller. The synthesized torque command is sent to the same timestamped data message, simultaneously delivering it to the three actuator chains within a microsecond delay. In this way, the lifting, lateral, and tilting axes not only maintain synchronization according to their coordination weights but also have a counter-torque to offset external impacts "pre-embedded" at the same instant of movement.

[0098] In this embodiment, an embedded disturbance observer is introduced as a parallel disturbance rejection module. This module estimates the external disturbance torque acting on the three-axis actuator in real time within the same control cycle and generates a reverse compensation amount. This compensation amount and the cooperative control output are synthesized into the final drive command through a vector superposition unit, forming a dual-track mechanism of "active vibration suppression - dynamic disturbance rejection".

[0099] Furthermore, sensor noise caused by factors such as dust adhesion and hydraulic pulsation directly threatens vibration suppression stability, necessitating improved signal reliability of multi-axis collaborative control in high-interference tunnel environments. To address this, this solution incorporates a filtering module within the multi-axis collaborative control system. This module is located between the real-time status signals of the lifting rod, lateral rod, and tilting axis and the collaborative controller. It suppresses noise and reduces high-frequency interference in the displacement, velocity, and acceleration signals acquired for each degree of freedom, thereby enhancing the multi-axis collaborative control's resistance to random disturbances and measurement noise.

[0100] In this embodiment, the sensor signals from the lifting cylinder, the lateral lead screw, and the tilting cylinder are not directly sent to the collaborative controller. Instead, they first pass through an independent filtering module. This module operates at a 5ms cycle time, synchronized with the fieldbus. It aggregates the raw displacement, velocity, and acceleration data from the three degrees of freedom into a single frame, which is then processed in two stages.

[0101] The first stage is Kalman filtering: using the known actuator motion equations and measurement noise covariance, displacement and velocity are recursively estimated, thereby suppressing electromagnetic noise and sensor quantization errors. The second stage is real-time frequency reduction: the small window sequence of the Kalman output is subjected to a Fast Fourier Transform (FFT). If an energy peak is detected above 25Hz, it indicates the presence of high-frequency disturbances from the tunnel boring machine or cutting machine. The system then attenuates the amplitude of that frequency band by 20dB before inversely transforming it back to the time domain. The signal processed in this way is not only smoother, but also significantly weakens high-frequency interference.

[0102] Figure 6 This diagram illustrates the signal processing steps of a filtering module combining Kalman filtering and frequency domain filtering, as provided in an embodiment of this disclosure. Now, in conjunction with... Figure 6 The specific embodiments of this application are further described below.

[0103] S510. First, perform Kalman filtering on the displacement, velocity, and acceleration signals of each degree of freedom to obtain estimated state values ​​after removing measurement noise.

[0104] In this embodiment, during each control cycle of field operation, the system first "translates" the three physical execution axes onto a unified virtual reference axis for subsequent coordinated scheduling. Specifically, the vertical displacement is denoted as the original coordinate Z, the horizontal displacement as X, and the rotation angle as Θ. To ensure comparability within the same dimension, the controller defines "1 virtual unit" as corresponding to 1mm of vertical displacement, 0.8mm of horizontal displacement, or 0.1° of rotation. Then, Z, X, and Θ are successively divided by their respective conversion factors. The resulting three dimensionless numbers are geometrically located in the same coordinate system and are combined into a common virtual reference axis.

[0105] After unifying the dimensions, the system reads the output torques of the three execution chains at that moment and converts them into equivalent loads on the template surface using the mechanical model. Simultaneously, it obtains the three pairs of coupling torques calculated by the model. The program divides the real-time load by its respective rated upper limit to obtain the "load coefficient," and then multiplies it by the absolute value of the coupling torque to generate a set of three values—these values ​​not only reflect the magnitude of the force on each degree of freedom at that moment but also its sensitivity to overall coupled vibration. For example, during a shield tunneling impact, the product result might show 0.48 for the lifting axis, 0.20 for the lateral axis, and 0.06 for the tilting axis. The controller normalizes these three numbers proportionally to obtain a weight vector [0.64, 0.27, 0.09]. The 0.64 in the vector indicates that in subsequent vibration suppression operations, the lifting cylinder will undertake approximately 60% of the correction task; the lateral screw will share less than 30%; and the tilting cylinder only needs to perform minor compensation. The weight vector drifts in real time with the load and coupling state, updating every twenty milliseconds to ensure that the motion distribution of the three physical axes always matches the on-site vibration mode.

[0106] S520. Perform real-time frequency domain analysis on the estimated state value, and implement frequency domain filtering suppression on high-frequency components that exceed the preset frequency band threshold.

[0107] In this embodiment, after obtaining smooth state values ​​using Kalman filtering, the control system immediately sends the latest 256 sampling points (corresponding to a 1.28s historical window, sampling rate 200Hz) into a real-time Fast Fourier Transform (FFT) program. After the transform, the spectrum is mapped to the positive frequency range of 0–100Hz. To suppress high-frequency interference caused by shield gear squealing and the cutting machine, the system presets 25Hz as a threshold: any amplitude peak appearing above 25Hz is multiplied by an attenuation factor of 0.1; useful vibration information below 25Hz retains its original amplitude. Subsequently, the program performs an inverse FFT on the attenuated spectrum to restore it to the time domain. The resulting "frequency-domain reduced version" signal is sent back to the co-controller within 5ms, serving as feedback input along with the low-frequency Kalman estimation. After this real-time frequency domain suppression, the root mean square value of the high-frequency noise in the three axes of lifting, lateral movement, and flipping is reduced from 0.018g to 0.010g, avoiding high-frequency spikes from misleading subsequent vibration assessment and control optimization.

[0108] S530: The signal processed by Kalman filtering and frequency domain filtering is used as the feedback input of the multi-axis collaborative control loop to improve the anti-interference ability of multi-axis collaborative control against random disturbances and measurement noise.

[0109] In this embodiment, the original measurement data of the lifting cylinder, the lateral lead screw, and the tilting cylinder are first filtered by Kalman filtering to remove sensor white noise, and then the amplitude of components above 25Hz is attenuated by 90% within the 0–100Hz frequency spectrum. After this processing, the acceleration RMS noise of each actuator axis has been reduced from 0.018g to 0.010g. The controller no longer uses the original measurements, but instead packages the displacement, velocity, and acceleration after this "Kalman + frequency domain" dual purification into a new feedback vector, which is directly sent to the multi-axis cooperative controller. Because high-frequency spikes and random electromagnetic disturbances are weakened in advance, the coupling amplitude calculated by the cooperative algorithm no longer produces false alarms; the model prediction optimization can also converge quickly on a smoother error curve.

[0110] In this embodiment, a double-layer noise suppression barrier is constructed using Kalman-frequency domain composite filtering pipeline technology. As a result, the filtering module effectively improves the anti-interference capability of multi-axis collaborative control against random disturbances and measurement noise, enabling the corbel formwork to maintain a more stable low vibration state during the continuous casting stage.

[0111] Figure 7 This is a schematic diagram of a multi-degree-of-freedom vibration reduction control system for a corbel formwork subjected to random disturbances, provided in an embodiment of this disclosure. The system includes the following modules:

[0112] Status acquisition module: used to acquire displacement, velocity and acceleration information of lifting rod, horizontal moving rod and tilting shaft, and simultaneously acquire the amplitude of external vibration disturbances acting on the trolley structure.

[0113] In this embodiment, the status acquisition module uses a set of sensors triggered by a unified clock to capture the internal movements and external disturbances of the corbel template trolley in real time.

[0114] Mechanical modeling module: used to establish or update a multi-degree-of-freedom mechanical model for the trolley.

[0115] In this embodiment, the mechanical modeling module first imports the three-dimensional geometric information of the corbel formwork trolley and the material properties of each component from the project BIM system, such as the moment of inertia of the H-beam main beam, the mass distribution of the hydraulic cylinder piston rod, and the friction characteristics of the ball screw pair. Subsequently, the module calls the embedded finite element preprocessor to automatically extract the concentrated mass, stiffness, and rotational inertia of each member and each joint, and constructs an initial multi-degree-of-freedom Lagrange dynamic model.

[0116] After the trolley is put into operation, the mechanical modeling module enters the online adaptive phase: it periodically inputs the real-time displacement, velocity, and driving torque provided by the state acquisition module into the initial model, comparing the error between the model's predicted acceleration and the sensor-measured values. The module has a built-in recursive least squares estimation algorithm that uses the error history of the past few seconds to automatically correct the friction coefficient and coupling torque parameters of each joint; at the same time, it adjusts the additional inertial effects caused by changes in hydraulic oil viscosity through feedback from the temperature sensor. After dozens of consecutive sampling cycles, the mechanical modeling module maintains a high degree of consistency between the model's parameters and the actual dynamic performance of the trolley.

[0117] Vibration assessment module: used to calculate the coupled vibration amplitude of each degree of freedom under the current disturbance and compare it with the preset vibration threshold.

[0118] In this embodiment, the vibration assessment module does not simply read model output or sensor data, but organically integrates the two to extract the true coupled vibration amplitude. Specifically, at the end of each control cycle, the module first calls the online-updated multi-degree-of-freedom mechanical model, inputs the driving torque sequence for this cycle, and simulates the theoretical displacement response of each degree of freedom under conditions without external disturbance. Subsequently, it performs point-by-point difference between the theoretical response and the measured displacement signal provided by the state acquisition module to obtain the coupled residual sequence of the three execution chains. The module applies Hilbert transform to these three sets of residuals respectively, extracts their instantaneous amplitude envelope, and calculates the peak-to-peak value within a sliding window of 50ms in length and 5ms in step. This peak-to-peak value is the coupled vibration amplitude of each degree of freedom under the current disturbance. Finally, the module compares the calculated three peak-to-peak values ​​with the vibration threshold (e.g., 0.20 mm) set in the system parameters beforehand. If the coupling amplitude of any degree of freedom exceeds the threshold, the module immediately sends a "vibration over-limit" signal to the control quantity generation module, along with the specific amplitude, to drive a stronger subsequent vibration suppression action. Otherwise, normal monitoring is maintained, thereby ensuring that the controller always responds accurately based on the actual coupled vibration level.

[0119] Control quantity generation module: Based on the evaluation results of the vibration evaluation module, it is used to determine a set of coordinated control quantities for reducing the amplitude of the coupled vibration.

[0120] In this embodiment, after receiving the "vibration exceeding limits" signal and the three-degree-of-freedom coupled amplitude from the vibration assessment module, the control quantity generation module immediately initiates the coordinated control quantity solution process:

[0121] First, the module reads the absolute position and available remaining stroke of each actuator, as well as the remaining output torque of the hydraulic cylinders and servo motors, from the real-time mechanics model. Simultaneously, it obtains the latest three-degree-of-freedom vibration damping responsibility allocation ratio from the collaborative weighting unit.

[0122] Then, the module inputs these three pieces of information, including travel limits, torque limits, and cooperative weights, along with the online updated multi-degree-of-freedom dynamics model, into the real-time quadratic programming solver.

[0123] Control execution and closed-loop update module: used to simultaneously output the obtained control quantities to the lifting rod, the traverse rod and the tilting axis to drive the coordinated movement of each degree of freedom to suppress vibration.

[0124] In this embodiment, the control execution and closed-loop update module undertakes the dual tasks of synchronously distributing the calculated control increment to the three execution chains and quickly reading back the new state after the action is completed to start the next control cycle.

[0125] First, the module receives a control frame output from the control generation module. This frame contains incremental commands, timestamps, and safety verification information for the lifting rod, traverse rod, and tilting axis. The control execution and closed-loop update module packages the three sets of commands into a single EtherCAT message and broadcasts it to the hydraulic proportional valve controller, ball screw servo drive, and tilting cylinder valve assembly within the same 1μs time window. Since all execution units are locked to a common compensated clock, this message is parsed simultaneously by all three terminals within 100μs, enabling the three degrees of freedom to start almost at the same time: the lifting cylinder moves smoothly up and down according to the pulse width modulation curve, the traverse rod quickly tracks the new target under the position loop, and the tilting cylinder rotates precisely at a fine-tuning rate.

[0126] After the command is issued, the module automatically triggers the status acquisition subroutine with a fixed delay period of 5ms. It reads the latest measurements from the displacement, velocity, and acceleration sensors of each actuator, as well as the accelerometer of the main beam of the trolley, and performs CRC integrity verification. After converting the data into a new status vector, the module pushes the vector back to the status acquisition module's buffer queue. Next, the control execution and closed-loop update module checks the vibration recovery status of the current cycle: if the peak-to-peak amplitude of any degree of freedom is still higher than the threshold, the control quantity generation process is forcibly repeated in the next 20ms control cycle; otherwise, it normally enters the next cycle of steps S100 to S500. Through this closed-loop mode of "synchronous output—delayed readback—rapid limit judgment—cyclic update," continuous coordinated vibration suppression of the three degrees of freedom (lifting, lateral movement, and tilting) is achieved in complex random disturbance environments, ensuring that the vibration of the corbel template trolley is always stably maintained within the preset threshold.

[0127] Furthermore, the multi-degree-of-freedom vibration reduction control system for the corbel template oriented to random disturbance disclosed in this embodiment also includes a state observation module set in the feedback loop of each degree of freedom of the lifting rod, the transverse rod and the flipping axis, which is used by the observer to estimate the unmeasured coupled vibration state and instantaneous coupled torque of each degree of freedom based on the real-time displacement, velocity and acceleration signals.

[0128] The correction module is used to write the synchronous action ratio of each degree of freedom into the coordination matrix based on the coupled vibration state output by the observation module, and generate a coordination correction factor that is dynamically updated over time.

[0129] The correction module is also used to apply the collaborative correction factor to the control quantity generation stage, so that the lifting rod, the lateral rod, and the tilting axis are output synchronously according to the correction ratio under the same time reference, further reducing the coupled vibration amplitude between the multiple degrees of freedom of the corbel template.

[0130] Furthermore, the multi-degree-of-freedom vibration reduction control system for corbel templates oriented to random disturbances disclosed in this embodiment also includes a disturbance observation module, which is used to estimate the external random disturbance force or disturbance torque acting on the lifting rod, the lateral rod and the tilting shaft, and generate a compensation amount based on the estimation result; the compensation amount and the coordinated control amount output by the multi-axis collaborative control are superimposed to jointly drive the actuators of each degree of freedom to counteract the coupled vibration influence of external random disturbances on the corbel template.

[0131] In this embodiment, the disturbance observation module and the multi-axis cooperative controller work in parallel to counteract coupled vibrations caused by external random disturbances within the same control cycle. Specifically, after the cooperative controller calculates the ideal control torque for the next moment, the disturbance observation module immediately calls the online-updated multi-degree-of-freedom mechanical model. Based on the difference between "ideal torque → model-predicted acceleration" and "measured acceleration," the module inversely derives the actual external disturbance torques acting on each degree of freedom. The module takes the opposite of these disturbance torques as compensation amounts and vector-superimposes them with the torque commands of the cooperative controller. By seamlessly superimposing the real-time estimation of external disturbance torques with the cooperative control quantities, this embodiment significantly improves the anti-disturbance performance and vibration suppression efficiency of the corbel template trolley in complex random vibration environments.

[0132] On the other hand, this disclosure also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform a multi-degree-of-freedom vibration reduction control method for a corbel template oriented to random disturbances provided by the methods described above.

[0133] It should be understood that the above embodiments are only used to illustrate the technical solutions of this disclosure, and not to limit them; although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure.

Claims

1. A multi-degree-of-freedom vibration reduction control method for corbel formwork trolleys accommodating random disturbances, applied to a corbel formwork trolley with lifting rods, lateral movement rods, and a tilting shaft, characterized in that... include: Status acquisition steps: Acquire the displacement, velocity and acceleration information of the lifting rod, the horizontal moving rod and the tilting shaft, and simultaneously acquire the amplitude of external vibration disturbances acting on the trolley structure; Mechanical modeling steps: Based on the connection method of the trolley rods, joint friction characteristics, component inertial parameters, and joint coupling torque parameters, establish or update a multi-degree-of-freedom mechanical model for the trolley; Vibration assessment steps: Input the real-time status of the state acquisition step into the multi-degree-of-freedom mechanical model, calculate the coupled vibration amplitude of each degree of freedom under the current external vibration disturbance, and conduct vibration assessment under the stroke and torque limitations of the actuator. Control quantity generation step: Based on the vibration assessment results, a set of coordinated control quantities for reducing the amplitude of the coupled vibration is determined using a multi-axis cooperative control algorithm; Control execution and closed-loop update steps: Simultaneously output the coordinated control quantities obtained in the control quantity generation step to the lifting rod, the horizontal moving rod and the flipping axis to drive the coordinated action of each degree of freedom to suppress vibration, so that the vibration amplitude of the corbel template trolley is kept within the preset vibration threshold, and the state acquisition step is restarted.

2. The method for multi-degree-of-freedom vibration reduction control of a corbel template oriented towards random disturbances according to claim 1, characterized in that, The multi-axis cooperative control algorithm includes a multi-axis cooperative algorithm based on model predictive control, specifically: The lifting rod, the lateral rod, and the tilting axis are mapped to a common virtual reference axis, and the cooperative weight vector is calculated based on the real-time load and coupling torque of each degree of freedom. The cooperative weight vector is introduced into the objective function of the model predictive control so that the predicted displacement error of each degree of freedom and the control increment simultaneously obey cooperative constraints. The optimal set of control quantities that satisfy the travel, torque and coordination constraints is obtained through rolling optimization, and the first moment control quantity in the set is output to drive the synchronous action of each degree of freedom.

3. The method for multi-degree-of-freedom vibration reduction control of a corbel template oriented towards random disturbances according to claim 1, characterized in that, The multi-axis cooperative control algorithm includes a state observer-based multi-axis cooperative algorithm, specifically: A state observer is set in the feedback loop of each degree of freedom of the lifting rod, the lateral rod and the tilting axis. The observer estimates the unmeasured coupled vibration state and instantaneous coupled torque of each degree of freedom based on the real-time displacement, velocity and acceleration signals. Based on the coupled vibration state output by the observer, the synchronous action ratio of each degree of freedom is written into the coordination matrix to generate a coordination correction factor that is dynamically updated over time. The collaborative correction factor is applied to the control quantity generation process, so that the lifting rod, the horizontal moving rod and the flipping axis are output synchronously according to the correction ratio under the same time reference, which further reduces the coupling vibration amplitude between multiple degrees of freedom of the corbel template.

4. The method for multi-degree-of-freedom vibration reduction control of corbel templates oriented towards random disturbances according to claim 1, characterized in that, In the multi-axis collaborative control process executed using the aforementioned multi-axis collaborative control algorithm, a disturbance observer is embedded. The disturbance observer is used to estimate the external random disturbance force or disturbance torque acting on the lifting rod, the lateral rod, and the tilting axis, and to generate a compensation amount based on the estimation result. The compensation amount is superimposed with the coordinated control amount output by the multi-axis collaborative control to jointly drive the actuators of each degree of freedom, so as to counteract the coupled vibration effect of the external random disturbance on the corbel template.

5. A multi-degree-of-freedom vibration reduction control method for corbel templates oriented towards random disturbances according to any one of claims 1-4, characterized in that, A filtering module is set in the multi-axis collaborative control link executed by the multi-axis collaborative control algorithm. The filtering module is located between the real-time status signals of the lifting rod, the horizontal rod and the flipping axis and the collaborative controller. It is used to suppress noise and reduce high-frequency interference of the displacement, velocity and acceleration signals collected by each degree of freedom.

6. The method for multi-degree-of-freedom vibration reduction control of a corbel template oriented towards random disturbances according to claim 5, characterized in that, The filtering process of the filtering module is a signal processing step that combines Kalman filtering and frequency domain filtering, including: Kalman filtering is first performed on the displacement, velocity, and acceleration signals of each degree of freedom to obtain estimated state values ​​with measurement noise removed; The estimated state value is subjected to real-time frequency domain analysis, and frequency domain filtering is applied to suppress high-frequency components that exceed the preset frequency band threshold. The signal processed by Kalman filtering and frequency domain filtering is used as the feedback input of the multi-axis collaborative control loop to improve the anti-interference ability of multi-axis collaborative control against random disturbances and measurement noise.

7. A multi-degree-of-freedom vibration reduction control system for corbel formwork oriented towards random disturbances, comprising: Status acquisition module: used to acquire displacement, velocity and acceleration information of lifting rod, horizontal moving rod and tilting shaft, and simultaneously acquire the amplitude of external vibration disturbances acting on the trolley structure; Mechanical modeling module: used to establish or update a multi-degree-of-freedom mechanical model for the trolley; Vibration assessment module: used to calculate the coupled vibration amplitude of each degree of freedom under the current disturbance, and to perform vibration assessment under the conditions of stroke and torque limitations of the actuator; Control quantity generation module: used to determine a set of coordinated control quantities for reducing the amplitude of the coupled vibration based on the evaluation results of the vibration evaluation module; Control execution and closed-loop update module: used to simultaneously output the obtained control quantities to the lifting rod, the traverse rod and the tilting axis to drive the coordinated movement of each degree of freedom to suppress vibration.

8. A multi-degree-of-freedom vibration reduction control system for corbel formwork oriented towards random disturbances according to claim 7, characterized in that, The system also includes: The state observation module is used to observe real-time displacement, velocity and acceleration signals, and estimate the unmeasured coupled vibration state and instantaneous coupled torque of each degree of freedom; The correction module is used to write the synchronous action ratio of each degree of freedom into the coordination matrix based on the coupled vibration state output by the observation module, and generate a coordination correction factor that is dynamically updated over time. The correction module is also used to apply the collaborative correction factor to the control quantity generation stage, so that the lifting rod, the horizontal moving rod and the flipping axis are output synchronously according to the correction ratio under the same time reference, further reducing the coupling vibration amplitude between multiple degrees of freedom of the corbel template.

9. A multi-degree-of-freedom vibration reduction control system for corbel formwork oriented towards random disturbances according to claim 7, characterized in that, The system also includes a disturbance observation module, which is used to estimate the external random disturbance force or disturbance torque acting on the lifting rod, the lateral rod and the tilting axis, and generate a compensation amount based on the estimation result; the compensation amount and the coordinated control amount output by the multi-axis collaborative control are superimposed to jointly drive the actuators of each degree of freedom to counteract the coupled vibration effect of the external random disturbance on the corbel template.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-6.

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