A real-time hybrid test H-infinity robust control design method based on particle swarm optimization

Abstract

The application discloses a particle swarm optimization real-time hybrid test H∞ robust control design method, which comprises the following steps: establishing a controlled object model; constructing a generalized controlled object containing a target loop and a weighting function based on the controlled object model, and determining an H ∞ robust control target; constructing a fitness function containing a time delay index and an amplitude error index; obtaining an optimized control parameter; substituting the optimized control parameter into the generalized controlled object to obtain an H ∞ robust controller; the H ∞ robust controller generates an actuator control quantity, so that the actuator implements real-time loading on the test substructure according to a corresponding instruction displacement, and returns a measured displacement and a feedback force of the test substructure to the numerical substructure for next integral step calculation. The application is suitable for single-actuator and multi-actuator real-time hybrid simulation tests including nonlinear components as test substructures.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural testing and disaster prevention and mitigation engineering technology, and in particular to an H∞ robust control design and optimization method for actuator displacement tracking control in real-time hybrid simulation tests. Background Technology

[0002] Real-time hybrid simulation testing is a structural dynamic testing method that combines numerical calculation with physical loading. This method typically divides the overall structure into a numerical substructure and a test substructure. The numerical substructure is solved in real time by a computer, while the test substructure is loaded in real time by actuators. The measured displacements and feedback forces are then fed back to the numerical substructure, thereby simulating the dynamic response of the overall structure.

[0003] In real-time hybrid simulation experiments, actuators need to accurately track the commanded displacement calculated by the numerical substructure. However, due to the dynamic characteristics, measurement noise, parameter perturbations, and high-frequency unmodeled dynamics of hydraulic servo actuators and their control systems, the actual measured displacement usually exhibits time lag and amplitude errors relative to the commanded displacement. This error gradually accumulates during real-time integration, affecting experimental accuracy and, in severe cases, leading to system instability.

[0004] Existing actuator control methods mainly include PID control, inverse compensation, adaptive inverse compensation, and windowed frequency domain evaluation index compensation. These methods can improve displacement tracking performance to some extent, but they still have the following shortcomings: First, PID control parameters depend on the dynamic characteristics of the experimental substructure, and control accuracy tends to decrease when the substructure enters the nonlinear stage; second, inverse compensation and adaptive compensation methods are sensitive to the accuracy of time delay estimation, and are prone to undercompensation or overcompensation; third, traditional H... ∞ Although the control has good robustness, the selection of the target loop or weighting function depends on human experience and requires repeated trial and error, resulting in low design efficiency.

[0005] Therefore, it is necessary to propose a method that combines frequency domain evaluation metrics and particle swarm optimization to evaluate H. ∞ A method for automatically optimizing the design of robust controllers is proposed to reduce time delay errors and amplitude errors in real-time hybrid simulation tests, thereby improving actuator tracking accuracy and test system robustness. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to address the problems of time delay error, amplitude error, reliance on manual experience for parameter tuning, and insufficient adaptability to nonlinear experimental substructures in existing real-time hybrid simulation experiments by providing a particle swarm optimization-based robust control design method for real-time hybrid experiments.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A robust control design method for real-time hybrid experiments using particle swarm optimization, applied to a real-time hybrid simulation experimental system including a numerical substructure, an experimental substructure, actuators, displacement and feedback force measurement units, and a real-time control unit, includes the following steps:

[0009] S1, acquire the command displacement, measured displacement and feedback force data of the actuator acting on the test substructure, and establish a controlled object model;

[0010] S2, based on the controlled object model, construct a generalized controlled object containing the target loop and a weighting function, and determine H related to tracking performance, disturbance suppression, measurement noise attenuation, and robust stability. ∞ Robust target control;

[0011] S3, based on the frequency domain relationship between the commanded displacement and the measured displacement, construct a fitness function that includes time delay index and amplitude error index;

[0012] S4, using the target loop parameters and weighted function parameters as particle positions, perform offline particle swarm iteration optimization, with the goal of minimizing the fitness function value, to obtain the optimized control parameters;

[0013] S5, Substitute the optimized control parameters into the generalized controlled object to obtain H. ∞ Robust controller;

[0014] S6, during the real-time hybrid simulation test, the numerical substructure calculates the current integral step displacement based on the external excitation and the feedback force of the previous integral step, and inputs the calculated displacement and the measured displacement into the H. ∞ Robust controller, by the H ∞ The robust controller generates actuator control quantities, enabling the actuator to apply real-time loading to the test substructure according to the corresponding command displacement, and returns the measured displacement and feedback force of the test substructure to the numerical substructure for the next integration step calculation.

[0015] Furthermore, the controlled object model is obtained through system identification methods or first-principles modeling methods, and the controlled object model is one of the following: continuous-time transfer function model, discrete-time transfer function model, state-space model, single-input single-output model, or multiple-input multiple-output model.

[0016] Furthermore, the time delay index and amplitude error index are obtained from frequency domain evaluation indices. The frequency domain evaluation indices are calculated based on the frequency domain components of the command displacement, the frequency domain components of the measured displacement, and the frequency domain energy weight of the command displacement; wherein, the amplitude error index is used to characterize the amplitude deviation of the measured displacement relative to the command displacement, and the time delay index is used to characterize the phase lag or phase lead of the measured displacement relative to the command displacement.

[0017] Furthermore, the fitness function includes a time delay penalty term, an amplitude error penalty term, and a controller output constraint term. When the peak value of the controller output exceeds a preset multiple of the peak value of the command displacement, the controller output constraint term increases the fitness function value to limit the actuator control quantity and suppress the excitation of high-frequency unmodeled dynamics of the actuator.

[0018] Furthermore, the target loop adopts a second-order loop forming structure, and the target loop parameters include low-frequency gain, first corner frequency and second corner frequency; the particle swarm iterative optimization includes: initializing particle position and particle velocity, updating particle velocity according to individual optimal position and swarm optimal position, updating particle position according to the updated particle velocity, and outputting the target loop parameters and / or weighted function parameters that optimize the fitness function value after the iteration termination condition is met.

[0019] Furthermore, in the particle swarm iteration optimization, the particle positions are represented by a logarithmic scale to represent the target loop parameters; the first turn frequency, the second turn frequency, and the low-frequency gain are respectively set within a preset search interval to form an open-loop frequency characteristic with high gain in the low-frequency band, a predetermined attenuation slope in the mid-frequency band, and a roll-off in the high-frequency band.

[0020] Furthermore, in the H ∞ The robust controller is also equipped with an outer loop compensation module, which includes a low-pass filter and an outer loop gain compensation unit. The cutoff frequency of the low-pass filter is adjusted according to the time delay index, and the outer loop gain compensation unit is adjusted according to the amplitude error index to compensate for the phase error and amplitude error of the actuator response.

[0021] The beneficial effects of this invention are:

[0022] 1. This invention applies the particle swarm optimization algorithm to H ∞ Optimization of the target loop or weighting function parameters of a robust controller can reduce the traditional H ∞ The reliance on manual experience for parameter tuning in controller design improves controller design efficiency.

[0023] 2. This invention uses the time delay index and amplitude error index in the frequency domain evaluation index as optimization targets, so that the controller design is directly oriented towards the actuator tracking error in real-time hybrid simulation test, which can effectively improve the synchronization performance between command displacement and measured displacement.

[0024] 3. This invention uses H ∞ Robust control methods can maintain good robust stability and tracking performance when the controlled object has parameter perturbations, measurement noise, and high-frequency unmodeled dynamics.

[0025] 4. The particle swarm optimization process of this invention is completed offline before the experiment, and only the solved H is called during the real-time experiment. ∞ The robust controller does not increase the burden of real-time integral calculations and meets the real-time computation requirements of real-time hybrid simulation experiments.

[0026] 5. This invention compensates for residual phase error and amplitude error by using a low-pass filter and an outer loop gain compensation unit, thereby further improving the actuator displacement tracking accuracy. It is suitable for real-time mixed simulation tests of single actuators and multiple actuators. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the technical process of the method of the present invention.

[0028] Figure 2 This is a schematic diagram of a real-time hybrid simulation test system exemplified in the specific implementation method of the present invention. Detailed Implementation

[0029] The present invention will be further described below with reference to specific embodiments. These embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0030] like Figure 1 and Figure 2 As shown, this invention provides a robust control design method for real-time hybrid experiments using particle swarm optimization, applicable to a real-time hybrid simulation experimental system. The real-time hybrid simulation experimental system includes a numerical substructure, an experimental substructure, actuators, displacement and feedback force measurement units, and a real-time control unit.

[0031] The numerical substructure is used to calculate the displacement of the current integration step based on external excitation, structural parameters, and the feedback force of the previous integration step; the experimental substructure is used to generate an actual dynamic response under the loading action of the actuator; the actuator is used to convert the control quantity into a real-time loading displacement of the experimental substructure; the displacement and feedback force measurement unit is used to collect the measured displacement and feedback force of the experimental substructure; and the real-time control unit is used to perform numerical integration, H... ∞ Robust control, particle swarm optimization parameter calling, and outer loop compensation.

[0032] In one embodiment, the test substructure may be a damper, seismic isolation bearing, energy dissipation connector, or other nonlinear structural component. The numerical substructure may be a numerical model of a layered shear structure, a numerical model of a frame structure, or a numerical model of a bridge structure. The actuator may be a single actuator or multiple actuators.

[0033] The method of the present invention includes the following steps.

[0034] S1, acquire the commanded displacement, measured displacement, and feedback force data during the process of the actuator acting on the test substructure, and establish a controlled object model. Specifically, before the experiment, a controlled object consisting of the actuator and the test substructure is modeled. The controlled object model is used to describe the dynamic relationship between the commanded displacement input and the measured displacement output. The controlled object model can be obtained through system identification methods or through first-principles modeling methods.

[0035] In one implementation, a frequency sweep loading method is used to acquire the commanded displacement and measured displacement of the actuator, and a transfer function model is established using a system identification method. The controlled object model can be one of a continuous-time transfer function model, a discrete-time transfer function model, a state-space model, a single-input single-output model, or a multiple-input multiple-output model. For example, the controlled object model can be represented as:

[0036]

[0037] in, Let be the controlled object model, and s be the Laplace operator. This expression is only one specific embodiment and does not constitute a limitation on the form of the controlled object model.

[0038] S2, based on the controlled object model, construct a generalized controlled object containing the target loop and / or weighting function, and determine H related to tracking performance, disturbance suppression, measurement noise attenuation, and robust stability. ∞ Robust control objective. Specifically, let the controlled object model be... H ∞ Robust controller is Then the open-loop transfer function of the system is:

[0039]

[0040] System sensitivity function Complementary sensitivity function They are respectively:

[0041]

[0042]

[0043] Where I is the identity matrix. The sensitivity function... The complementary sensitivity function is used to characterize the tracking error and disturbance suppression capability of the system. Used to characterize the tracking performance of the system and to measure the impact of noise on the system output.

[0044] In one implementation, a loop shaping method is used to design the target loop, so that the system has a higher gain in the low-frequency band to improve the actuator's ability to track commanded displacement, and a lower gain in the high-frequency band to reduce the impact of measurement noise and high-frequency unmodeled dynamics on system stability.

[0045] Furthermore, the target loop adopts a second-order loop forming structure:

[0046]

[0047] in, For the target loop, For low-frequency gain, The first transition frequency, This is the second transition frequency. (Adjustment is needed.) , and This enables the target circuit to form an open-loop frequency characteristic with high gain in the low-frequency band, a predetermined attenuation slope in the mid-frequency band, and roll-off in the high-frequency band.

[0048] S3. Based on the frequency domain relationship between the commanded displacement and the measured displacement, a fitness function including a time delay index and an amplitude error index is constructed. Specifically, the commanded displacement and the measured displacement are frequency domain transformed, and a frequency domain evaluation index is calculated based on their frequency domain components and the frequency domain energy weight of the commanded displacement. The frequency domain evaluation index is used to decompose the actuator tracking error into a time delay index and an amplitude error index.

[0049] The amplitude error index characterizes the amplitude deviation of the measured displacement relative to the commanded displacement; the time delay index characterizes the phase lag or phase lead of the measured displacement relative to the commanded displacement. In one embodiment, the fitness function can be expressed as:

[0050]

[0051] Where J is the fitness function value, d is the time delay index, and σ is the amplitude error index. For the target time delay, Let Q be the target amplitude error, and let Q be the controller output constraint term. Take 1ms, The value is set to 1%. When the peak value of the controller output exceeds a preset multiple of the peak value of the commanded displacement, the controller output constraint term Q increases the fitness function value to prevent this set of parameters from being selected as the optimal parameters. The preset multiple can be 3 times, or it can be adjusted according to the actuator loading capacity and test safety requirements.

[0052] S4, using the target loop parameters and / or weighted function parameters as particle positions, perform offline particle swarm optimization to obtain optimized control parameters with the goal of minimizing the fitness function value.

[0053] Specifically, the low-frequency gain in the target circuit First turning frequency Second transition frequency As parameters to be optimized, each particle represents a set of possible target loop parameters.

[0054] In one implementation, the particle position is represented using a logarithmic scale, and the parameter search range is set as follows: ∈[10 -1 10 1 ];

[0055] ∈[10 1 10 3 ];20lg( )∈[10,100].

[0056] Particle swarm optimization includes the following process:

[0057] First, initialize the particle position and particle velocity within the preset search range;

[0058] Secondly, a generalized controlled object is constructed based on the target loop parameters corresponding to each particle, and the corresponding H∞ robust controller is solved.

[0059] Next, the time delay index and amplitude error index are calculated based on the commanded displacement and measured displacement, and the quality of the particle is evaluated by the fitness function;

[0060] Then, the particle velocity and particle position are updated based on the individual optimal position and the group optimal position;

[0061] Finally, when the preset number of iterations is reached or the fitness function value meets the convergence condition, the target loop parameters and / or weighted function parameters corresponding to the optimal particle are output.

[0062] In one implementation, particle velocity and particle position are updated according to the following formula:

[0063]

[0064]

[0065] in, Let be the velocity of the i-th particle in the t-th iteration. Let ω be the position of the i-th particle in the t-th iteration, and ω be the inertia coefficient. and As a learning factor, and A random number between 0 and 1 Let be the optimal position for the i-th particle. The optimal position for the population. The number of particles is set to 50, and the learning factor is... and All values ​​are set to 1.5, and the inertia coefficient ω is set to 1. The above parameters are only one preferred implementation and do not constitute a limitation on the parameters of the particle swarm optimization algorithm.

[0066] In one implementation, the target loop, after optimization using the particle swarm optimization algorithm, can be represented as:

[0067]

[0068] This target loop is used for subsequent H. ∞ Solving for a robust controller.

[0069] S5, Substitute the optimized control parameters into the generalized controlled object to obtain H. ∞ Robust controller.

[0070] Specifically, the optimized control parameters obtained in step S4 are substituted into the target loop and the weighting function to construct a generalized controlled object, which is then transformed into a standard H. ∞ Control problem. By solving H ∞ The control problem aims to obtain H, which enables the closed-loop system to meet the requirements of robust stability and tracking performance. ∞ Robust controller.

[0071] In one implementation, the H ∞ The robust controller can be a continuous-time controller or a discrete-time controller formed by discretization. Preferably, if the real-time control unit operates with a fixed sampling period, then the continuous-time H... ∞ The robust controller is discretized and deployed in the real-time control unit.

[0072] S6, During the real-time hybrid simulation test, the numerical substructure calculates the current integral step displacement based on the external excitation and the feedback force of the previous integral step, and inputs the calculated displacement and the measured displacement into the H. ∞ Robust controller, by the H ∞The robust controller generates actuator control quantities, enabling the actuator to apply real-time loading to the test substructure according to the corresponding command displacement, and returns the measured displacement and feedback force of the test substructure to the numerical substructure for the next integration step calculation.

[0073] Specifically, within each integration step, the numerical substructure first calculates the current integration step displacement based on the external excitation and the feedback force from the previous integration step; then, the real-time control unit inputs the calculated displacement and the measured displacement into H. ∞ Robust controller; subsequently, H ∞ The robust controller outputs a control quantity to the actuator, which then applies a load to the test substructure based on this control quantity. Finally, the displacement and feedback force measurement unit collects and measures the displacement and feedback force, and returns them to the numerical substructure for the next integration step calculation. This process is repeated continuously until the real-time hybrid simulation test ends.

[0074] In one implementation, the H ∞ An external outer-loop compensation module is also provided on the robust controller. This outer-loop compensation module includes a low-pass filter and an outer-loop gain compensation unit. The low-pass filter is used to suppress high-frequency components in the controller output, and its transfer function can be expressed as:

[0075]

[0076] in, This is the cutoff frequency of the low-pass filter. The cutoff frequency of the low-pass filter is adjusted according to the time delay index to compensate for the phase error of the actuator response. The outer loop gain compensation unit is used to compensate for the amplitude error. If the amplitude index obtained from the frequency domain evaluation index is A, then the outer loop gain can be taken as 1 / A to reduce the amplitude deviation of the measured displacement relative to the commanded displacement.

[0077] In one specific embodiment, the real-time hybrid simulation test system employs a single actuator. The numerical substructure is a single-degree-of-freedom layered shear structure numerical model with a mass of 50t, a damping ratio of 0.05, and natural frequencies ranging from 1Hz to 5Hz. The test substructure is a self-resetting viscous damper. The external excitation uses seismic wave input with a sampling frequency of 1024Hz. The actuator displacement limit is set to ±28mm, and the velocity limit is set to 300mm / s.

[0078] Before the experiment, a controlled object model was established through frequency sweep loading and system identification. Then, a generalized controlled object was constructed based on this model, and the target loop parameters were optimized offline using the particle swarm optimization algorithm. H was obtained. ∞ After implementing the robust controller, it was deployed into the real-time control unit. During the experiment, the numerical substructure and H... ∞The robust controller, actuator, test substructure, and displacement and feedback force measurement unit operate cyclically according to step S6 to achieve real-time loading control of the self-resetting viscous damper.

[0079] In another specific embodiment, the real-time hybrid simulation test system adopts a dual-actuator configuration. The numerical substructure is a numerical model of a two-degree-of-freedom layered shear structure or a two-layer frame structure. The test substructure includes two dampers, and the two actuators correspond to the inter-layer displacement loading of the first and second layers, respectively. For the dual-actuator system, the controlled object model can be represented as a multi-input multi-output transfer function matrix; when the coupling between the two actuators is weak, a diagonally dominant model can also be used for controller design. The time delay index and amplitude error index of each actuator can be calculated separately, and the corresponding low-pass filter cutoff frequency and outer loop gain can be adjusted accordingly.

[0080] Through the above embodiments, the present invention can complete H before the experiment. ∞ Offline optimization of robust controller parameters allows for direct invocation of the optimized controller during real-time testing, avoiding increased real-time integral calculation burden. Simultaneously, this invention reduces time delay and amplitude errors in actuator displacement tracking, improving the synchronization performance and robust stability of real-time hybrid simulation experiments.

Claims

1. A robust control design method for real-time hybrid experiments using particle swarm optimization (PSO), characterized in that, Includes the following steps: S1, acquire the command displacement, measured displacement and feedback force data of the actuator acting on the test substructure, and establish the controlled object model; S2, based on the controlled object model, construct a generalized controlled object containing the target loop and a weighting function, and determine H related to tracking performance, disturbance suppression, measurement noise attenuation, and robust stability. ∞ Robust target control; S3, based on the frequency domain relationship between the commanded displacement and the measured displacement, construct a fitness function that includes time delay index and amplitude error index; S4, using the target loop parameters and weighted function parameters as particle positions, perform offline particle swarm iteration optimization, with the goal of minimizing the fitness function value, to obtain the optimized control parameters; S5, Substitute the optimized control parameters into the generalized controlled object to obtain H. ∞ Robust controller; S6, during the real-time hybrid simulation test, the numerical substructure calculates the current integral step displacement based on the external excitation and the feedback force of the previous integral step, and inputs the calculated displacement and the measured displacement into the H. ∞ Robust controller, by the H ∞ The robust controller generates actuator control quantities, enabling the actuator to apply real-time loading to the test substructure according to the corresponding command displacement, and returns the measured displacement and feedback force of the test substructure to the numerical substructure for the next integration step calculation.

2. The robust control design method for real-time hybrid experiments using particle swarm optimization according to claim 1, characterized in that, The controlled object model is obtained through system identification methods or first-principles modeling methods. The controlled object model is one of the following: continuous-time transfer function model, discrete-time transfer function model, state-space model, single-input single-output model, or multiple-input multiple-output model.

3. The robust control design method for real-time hybrid experiments using particle swarm optimization according to claim 2, characterized in that, The time delay index and amplitude error index are obtained from the frequency domain evaluation index, which is calculated based on the frequency domain components of the command displacement, the frequency domain components of the measured displacement, and the frequency domain energy weight of the command displacement. The amplitude error index is used to characterize the amplitude deviation of the measured displacement relative to the command displacement, and the time delay index is used to characterize the phase lag or phase lead of the measured displacement relative to the command displacement.

4. The robust control design method for real-time hybrid experiments using particle swarm optimization according to claim 3, characterized in that, The fitness function includes a time delay penalty term, an amplitude error penalty term, and a controller output constraint term. When the peak value of the controller output exceeds a preset multiple of the peak value of the command displacement, the controller output constraint term increases the fitness function value to limit the actuator control quantity and suppress the activation of high-frequency unmodeled dynamics of the actuator.

5. The robust control design method for real-time hybrid experiments using particle swarm optimization according to claim 4, characterized in that, The target loop adopts a second-order loop forming structure. The target loop parameters include low-frequency gain, first corner frequency and second corner frequency. The particle swarm iterative optimization includes: initializing particle position and particle velocity, updating particle velocity based on individual optimal position and swarm optimal position, updating particle position based on updated particle velocity, and outputting the target loop parameters and weighted function parameters that optimize the fitness function value after the iteration termination condition is met.

6. The robust control design method for real-time hybrid experiments using particle swarm optimization according to claim 5, characterized in that, In the particle swarm optimization, the particle positions are represented by a logarithmic scale to represent the target loop parameters; the first corner frequency, the second corner frequency, and the low-frequency gain are respectively set within a preset search interval to form an open-loop frequency characteristic with high gain in the low-frequency band, a predetermined attenuation slope in the mid-frequency band, and a roll-off in the high-frequency band.

7. The robust control design method for real-time hybrid experiments using particle swarm optimization according to claim 6, characterized in that, In the H ∞ The robust controller is also equipped with an outer loop compensation module, which includes a low-pass filter and an outer loop gain compensation unit. The cutoff frequency of the low-pass filter is adjusted according to the time delay index, and the outer loop gain compensation unit is adjusted according to the amplitude error index to compensate for the phase error and amplitude error of the actuator response.

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