Active vibration control method based on output feedback LQR optimization strategy

Abstract

The invention discloses a vibration active control method based on an output feedback LQR optimization strategy. The method comprises the following steps: constructing a system state space model and an output feedback controller of a large buoyant raft system for vibration source signals and vibration output; based on the system state space model, calculating through an LQR optimization strategy to obtain a state feedback gain matrix; and according to the state feedback gain matrix, the control gain of an output feedback controller is calculated through an LQR optimization strategy, and the large buoyant raft system is controlled through the output feedback controller with the control gain substituted so as to achieve vibration reduction control of the large buoyant raft system. According to the technical scheme, a more effective vibration reduction control effect can be provided.

Description

Technical Field

[0001] The present invention belongs to the technical field of active vibration reduction of large-scale structural vibration systems, and in particular relates to an active vibration control method based on an output feedback LQR optimization strategy. Background Art

[0002] Large floating raft systems are usually composed of floating rafts, supporting structures, vibration isolation devices, etc., and are designed to provide a stable platform on the water to support the operation of various equipment or structures. Its main functions include reducing the impact of water waves on structures, improving structural stability, reducing structural fatigue damage, and effectively isolating vibration and noise. With the significant increase in vibration reduction requirements, the vibration control problem currently applied to large floating raft systems is not very effective due to the existing control methods. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a vibration active control method based on output feedback LQR optimization strategy, which can provide a more effective vibration reduction control effect to solve the problem that the existing vibration active control method in the above-mentioned prior art is insufficient.

[0004] To achieve the above object, the present invention provides a vibration active control method based on output feedback LQR optimization strategy, comprising:

[0005] Construct a system state space model and output feedback controller for the vibration source signal and vibration output of a large floating raft system; Based on the system state space model, the state feedback gain matrix is ​​calculated through the LQR optimization strategy;

[0006] According to the state feedback gain matrix, the control gain of the output feedback controller is calculated by the LQR optimization strategy, and the large floating raft system is controlled by the output feedback controller into which the control gain is substituted to achieve vibration reduction control of the large floating raft system.

[0007] Optionally, the system state space model is:

[0008]

[0009] in, is the state vector, corresponding to the action signals of several vibration sources of the large floating raft system, through the state variables in the system state space model Using calculus, we can calculate is the control signal, is the output vector, corresponding to the vibration signals of several supporting positions of the large floating raft system, is the state matrix, is the input matrix, is the output matrix, To directly transfer the matrix, t represents the time.

[0010] Optionally, the output feedback controller is:

[0011]

[0012] in, is the control signal, To control the gain, is the output signal.

[0013] Optionally, the process of calculating and obtaining the state feedback gain matrix includes:

[0014] The state feedback gain matrix is ​​obtained by calculating the Riccati equation and the auxiliary equation using the LQR algorithm, where the Riccati equation and the auxiliary equation are respectively:

[0015]

[0016]

[0017] Among them, P is the solution of the Riccati equation, A is the state matrix, B is the input matrix, Q and R represent different weight matrices, Q is a positive semidefinite matrix, R is a positive definite matrix, and K is the state feedback gain matrix.

[0018] Optionally, the process of calculating and obtaining the control gain includes:

[0019]

[0020] Among them, x is the state vector, u is the control signal, y is the output vector, C * is the generalized inverse matrix of the output matrix, D is the direct transfer matrix, K is the state feedback gain matrix, K p To control the gain.

[0021] Optionally, control of large floating raft systems includes:

[0022] An output feedback controller with control gain substituted into it is set in the control system. The control system collects vibration signals of several supporting positions through sensors and generates control signals. According to the control signals, the actuators in the large floating raft system are controlled to generate force acting on the large floating raft system to achieve vibration reduction.

[0023] Optionally, the system state space model is derived and constructed by a finite element model.

[0024] Optionally, the sensor is a vibration acceleration sensor.

[0025] Compared with the prior art, the present invention has the following advantages and technical effects:

[0026] The present invention proposes a vibration active control method based on output feedback LQR optimization strategy. Based on traditional output feedback, LQR optimization strategy is introduced to easily form closed-loop optimal control, so that the controller can more accurately match the system model, thereby providing a more effective vibration reduction control effect. At the same time, because the dimension of the output is much smaller than the state space dimension of the controlled system, the advantages of this control method are simple structure and low control energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0028] Figure 1 A schematic diagram of a vibration control experiment according to an embodiment of the present invention;

[0029] Figure 2 A schematic diagram of an output feedback controller design according to an embodiment of the present invention;

[0030] Figure 3 A schematic diagram of the arrangement position of sensors in a large floating raft system according to an embodiment of the present invention;

[0031] Figure 4 This is a schematic diagram of comparison of test data before and after control of an embodiment of the present invention;

[0032] Figure 5 This is a schematic diagram showing the comparison before and after the control of sensor No. 3 in an embodiment of the present invention;

[0033] Figure 6 This is a schematic diagram showing the comparison before and after control of sensor No. 6 in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0035] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0036] The present invention proposes an active vibration control method based on an output feedback LQR optimization strategy. In the technical solution of the present invention, the LQR (linear quadratic regulator) optimization strategy based on output feedback shows significant advantages in the active vibration control of large floating raft systems. Compared with traditional PID control, LQR is particularly outstanding in processing multi-input multi-output (MIMO) systems, and can simultaneously consider multiple state variables and control inputs to ensure the overall performance optimization of the system. Secondly, the LQR optimization strategy has good robustness. By selecting appropriate weight matrices Q and R, LQR can balance control energy and system state errors, while maintaining system stability and minimizing control costs. In addition, LQR is based on rigorous mathematical theory and optimization algorithms, and the design process is standardized and systematized, avoiding a large number of parameter adjustments and trial and error processes in traditional control methods, making the design and implementation more efficient and reliable. Therefore, the present invention aims to explore new ideas and methods based on the output feedback LQR optimization strategy to meet the challenges in the vibration control of large floating raft systems and provide new theoretical and methodological support for the development and practice of the field of structural engineering.

[0037] The technical solution of the present invention specifically includes: firstly, according to the structural dynamics equation of the large floating raft system, a mathematical model is constructed to derive its system state space model. Then, in the output feedback control, the LQR optimization strategy is introduced to obtain the control parameter K adapted to the system. p , and then actively control the system vibration.

[0038] Step 1: Establish a system state space model and carry out optimal control based on the system state space model, where the system state space model is:

[0039] (1)

[0040] in, is the state vector, through the state variables in the system state space model The calculus calculations show that the signals corresponding to the multiple vibration sources of the floating raft are: is the control signal, is the output vector, corresponding to the vibration output signals of multiple supporting positions of the floating raft, is the state matrix, derived through the finite element model, is the input matrix, determined by the position of the controller, is the output matrix, determined by the sensor position, It is a direct transfer matrix determined by the position of the sensor and the actuator. The above parameters can also be calculated by measuring the state vector and the output vector, where t represents the time, and the corresponding (t) in the parameter represents the parameter at the corresponding time t.

[0041] The output feedback controller is introduced as:

[0042] (2)

[0043] in, is the control signal, To control the gain, is the output signal.

[0044] In large floating raft systems, all state variables are not always measurable, or due to the limited number of sensors, all states cannot be measured in real time. The output feedback controller only uses the output signal of the large floating raft system for control and does not need to directly access all state variables of the system. Therefore, the output feedback controller is introduced and combined with the LQR optimization strategy. In the case of limited sensors, the control gain can be quickly and accurately obtained. .

[0045] Step 2: Introduce the LQR optimization strategy to solve the state feedback gain matrix .

[0046] In the LQR optimization strategy, i.e., the LQR algorithm, a quadratic performance index is used to measure the dynamic performance of the control system, i.e., the integral representation of the quadratic function of the state variable x(t) and the control variable u(t) is used as the performance index of the optimal control of the control system. The formula of the quadratic performance index J is:

[0047] (3)

[0048] Among them, Q and R represent different weight matrices, is a positive semidefinite matrix, is a positive definite matrix. The first term of the integrand corresponding to the quadratic performance index Represents the error in the entire process of large floating raft system vibration reduction The size of The positive semidefiniteness of determines the non-negativity of this term. The second term of the integrand Represents the consumption of vibration reduction control power, and its integral represents the consumption of control energy in the whole vibration reduction process. The positive definiteness of determines that this term is always positive. Therefore, by minimizing the quadratic performance index, we can obtain the optimal controller that uses less control energy to obtain a smaller error.

[0049] In the LQR optimization strategy, the linear state feedback controller used is:

[0050] (4)

[0051] Among them, x represents the state, and the state feedback gain matrix It can be calculated by LQR algorithm:

[0052] (5)

[0053] (6)

[0054] Where P is the solution of the Riccati equation and is the state feedback gain matrix Auxiliary parameters for calculation, is the state matrix, is the input matrix, is a positive semidefinite matrix, which represents the weight of the vibration reduction effect in the optimization objective. is a positive definite matrix, representing the weight of vibration reduction power consumption.

[0055] Step 3: Based on the LQR optimization strategy, further solve the control gain K in the output feedback p .

[0056] The output control quantity of the P (proportional) control with output feedback is:

[0057] (7)

[0058] Where y is the output of the system, and the control gain K p The improved LQR algorithm is used to calculate:

[0059] Since the state x cannot be fully measured, according to the output y,

[0060] (8)

[0061] in, is the state vector, is the control signal, is the output vector, yes The generalized inverse matrix of To directly transfer the matrix, is the state feedback gain matrix, is a unit matrix.

[0062] The obtained control gain K p Applied to the output feedback controller, the output of the system is collected in real time through the output feedback controller to generate the value of the control signal to control the electromagnetic actuator to achieve an effective vibration reduction effect. At the same time, because the dimension of the output is much smaller than the state space dimension of the controlled system, the advantages of this control method are simple structure and low control energy consumption.

[0063] The working process of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0064] like Figure 2 As shown, step 1: construct a mathematical model of the controlled object according to the given formula, in preparation for introducing the active vibration control of the large floating raft system based on the output feedback LQR optimization strategy.

[0065] Step 2: Solve the feedback gain matrix K.

[0066] According to the proportion of vibration reduction effect and power consumption in the optimization target, the weight matrix is ​​selected through manual experience setting and , calculate the following formula:

[0067] (9)

[0068] (10)

[0069] Step 3: Further solve the control gain in the output feedback .

[0070] (11)

[0071] in yes The generalized inverse matrix of .

[0072] Example: The large floating raft controlled system studied in this project is a multi-input multi-output system, that is, multiple vibration sources act on the floating raft system to form multiple input signals, and multiple supporting positions of the floating raft serve as multiple vibration outputs. The state space model of the system is derived based on the finite element model, and the vibration active control method based on the output feedback LQR optimization strategy proposed in this invention is used to solve the state feedback gain matrix according to the LQR optimization strategy. , and further solve the control gain , complete the design of the controller and introduce it into this example system to carry out active control tests of the raft system.

[0073] like Figure 1 As shown, first connect the actuator to the control system, and connect the sensor to the control system. According to the control strategy and feedback gain parameters, debug the control system, and control the control system through the output feedback controller. The control system calculates the data collected by the sensor to obtain the actuator control signal, drives the actuator to generate actuating force, and acts on the raft system to achieve the function of vibration reduction. The control system mainly includes a feedback signal conditioning module, a DSP control cabinet, a control signal conditioning module and a power amplifier, which are used in turn for signal conditioning of the feedback signal (vibration source signal), setting the above controller to generate the control signal, signal conditioning of the control signal, and signal amplification.

[0074] The node (286, UZ) is selected as the actuator layout position. The vibration suppression effect of linear output feedback control is analyzed by monitoring the acceleration of each point. According to the actual installation of the raft system, the 7 sensors are arranged at the nodes of the raft as shown in Table 1:

[0075] Table 1

[0076]

[0077] Specific location such as Figure 3 shown.

[0078] According to the method provided by the present invention, the feedback parameter of the linear output feedback controller is calculated as K p =[-0.0371, 0.0988, -0.0583, 0.1800, 0.0890, 0.1277, 0.1821]. The feedback parameter K of the linear output feedback controller is p In the bench test, the sensor measures the vibration acceleration at 7 sensors. The test data before and after control is compared. Figure 4 shown.

[0079] The total vibration acceleration level (10-1000Hz) and the maximum drop value of the single-frequency vibration acceleration level at each sensor position are measured as follows:

[0080] Table 2

[0081]

[0082] Sensor 3 controls the front and rear contrast Figure 5 As shown, sensor 6 controls the front and rear contrast. Figure 6 As shown. From the above analysis, it can be seen that after linear output feedback control, the total vibration acceleration level (10-1000Hz) of the support position decreased by 4.38dB and 8.66dB. There are 4 obvious peaks in the single frequency point of the characteristic line spectrum at sensor No. 3, namely 51.20Hz, 151.04Hz, 450.56Hz and 136.41Hz. The vibration acceleration level at the 4 peaks has decreased, among which the value at 51.20Hz is 10.07dB. There are 8 obvious peaks in the single frequency point of the characteristic line spectrum at sensor No. 6, namely 51.20Hz, 151.04Hz, 199.68Hz, 550.40Hz, 599.04Hz, 650.24Hz, 698.88Hz and 750.08Hz. The vibration acceleration level at the 8 peaks has decreased, among which the value at 599.04Hz has decreased by 13.62dB.

[0083] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. The active vibration control method based on the output feedback LQR optimization strategy is characterized by: include: Construct the system state space model and output feedback controller for the vibration source signal and vibration output of the large floating raft system; Based on the system state space model, the state feedback gain matrix is ​​calculated through the LQR optimization strategy; According to the state feedback gain matrix, the control gain of the output feedback controller is calculated by the LQR optimization strategy, and the large floating raft system is controlled by the output feedback controller into which the control gain is substituted to achieve vibration reduction control of the large floating raft system.

2. The method according to claim 1, characterized in that: The system state space model is: in, is the state vector, corresponding to the action signals of several vibration sources of the large floating raft system, through the state variables in the system state space model Using calculus, we can calculate is the control signal, is the output vector, corresponding to the vibration signals of several supporting positions of the large floating raft system, is the state matrix, is the input matrix, is the output matrix, To directly transfer the matrix, t represents the time.

3. The method according to claim 1, characterized in that The output feedback controller is: in, is the control signal, To control the gain, is the output signal.

4. The method according to claim 1, characterized in that The calculation process of the state feedback gain matrix includes: The state feedback gain matrix is ​​obtained by calculating the Riccati equation and the auxiliary equation using the LQR algorithm, where the Riccati equation and the auxiliary equation are respectively: Among them, P is the solution of the Riccati equation, A is the state matrix, B is the input matrix, Q and R represent different weight matrices, Q is a positive semidefinite matrix, R is a positive definite matrix, and K is the state feedback gain matrix.

5. The method according to claim 1, characterized in that: The calculation process of the control gain includes: Among them, x is the state vector, u is the control signal, y is the output vector, C * is the generalized inverse matrix of the output matrix, D is the direct transfer matrix, K is the state feedback gain matrix, K p To control the gain.

6. The method according to claim 1, characterized in that Control of large floating raft systems includes: An output feedback controller with control gain substituted into it is set in the control system. The control system collects vibration signals of several supporting positions through sensors and generates control signals. According to the control signals, the actuators in the large floating raft system are controlled to generate force acting on the large floating raft system to achieve vibration reduction.

7. The method according to claim 1, characterized in that The system state space model is derived and constructed through the finite element model.

8. The method according to claim 6, characterized in that The sensor adopts a vibration acceleration sensor.

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