Fuzzy algorithm-based active control method for vibration of a mechanical gear transmission system

3.1. Mathematical model of the floating raft active vibration isolation system

The floating raft active vibration isolation system is a kind of technical system used to reduce or inhibit floating rafts (such as marine floating platforms, ships, etc.) by external waves, wind and waves and other environmental factors, the system usually includes a variety of sensors, controllers and actuators, etc., through real-time monitoring of changes in the external environment to take the corresponding control strategy, and then regulate the dynamic characteristics of the system to improve its stability and comfort. The floating raft active vibration isolation system consists of two main components: a mechanical device and an electronic control device. Specifically, it includes an excitation motor, a motor support plate, an electromagnetic actuator, a rubber vibration isolator, a floating raft, and an inner cylinder [12]. The excitation motor is primarily used to model the vibration signal of the ship’s power equipment. The electronic control device of the system comprises a power amplifier, a low-pass filter, a conditioning amplifier, and other internal components. The data acquisition instrument in the electronic control device for input signal acquisition, and can also assume the function of signal generator. Fig. 1 shows the test apparatus for the active vibration isolation system on the floating raft.

Fig. 1Test apparatus for floating rafts with a system for active vibration isolation

In Fig. 1, 1-1, 1-2, 1-3, 1-4 are four excitation motors, 2-1, 2-2, 2-3, 2-4 are four motor support plates, 3-1, 3-2, 3-3, 3-4 are four electromagnetic actuators, 4-1, 4-2, 4-3, 4-4 are the lower rubber vibration isolators, the upper vibration isolators, 4 is the floating raft, 5 is the foundation, 6-1, 6-2, 6-3, 64 are the four accelerometers. The active vibration isolation technique used by the floating raft is a nonlinear and solid coupling mechanism. It’s not a good idea to present a mechanism analysis because a few aim criteria such as its design and parameters are not satisfactory. The control channel’s information Mathematical models can be built using excitation data and outcome response data using the black-box system identification approach. According to the type of information and result data, the least-square approach, least to calculate, in the time-domain and frequency-domain, the mean square estimation and gradient estimation procedures are used for system identification [13]. The models used can be either non-parametric or parametric, depending on the model articulation:

where $e\left(t\right)$ is white noise signal; by means of Z-transform it can be written as:

where $A\left(z-1\right)=1+a_{1}z-1+\cdots +a_{n}z-n$ and $B\left(z-1\right)=b_1+b_{2}z-1+\cdots +b_{m}z-m+1$; $Z-1$ is lagoperator; $d$ is delay; $m$ and $n$ are order. The output content of the floating raft active isolation system system includes collected information and data. To gather this information and data, the system’s output is analyzed. The input signal is subject to background noise with a frequency range of 0-80 Hz and a voltage of 1.5 V. Before being sent to the electromagnetic actuator via a power amplifier, the background noise from the signal source is filtered using a low-pass channel [14]. To distinguish the model, use information and result data. The initial step is to choose reaction data that for processing that falls within the frequency range of 3-80 Hz. Data with a coherency of less than 0.95 should be excluded.

Fig. 2Gear transmission system with a built-in piezoelectric actuator: 1: motor, 2: gear box, 3: active control structure, 4: magnetic powder brake, and 5: base

Fig. 2 shows the three-part separation of the system identification technique used in the vibration isolation system for a floating raft. The identification model’s health and stability should be examined, and its frequency response should be compared to the experimental model’s frequency response. It is necessary to note the difference between the primary operating frequency and the secondary working frequency [15]. Then, to test the stability according to post zero, models for identification should be chosen based on high welfare and low request numbers diagrams. Subsequently, the study used system identification to establish a mathematical model of the floating raft vibration isolation system. This required experimental processing of input and output data that corresponded to the system’s dynamic characteristics. The least squares method was used for identification. The input signal for system identification is required to be the data that can stimulate the modal characteristics of the system. Its noise signal is a random signal, and the main frequency range of the vibration signal of the internal power equipment is about 10-50 Hz. Fig. 3 shows the identification content of the vibration isolation device of the floating raft diagram.

In Fig. 3, the recognition process of the system consists of three main parts, the first part is to collect the data from the input and output of the system. Next, a low-pass filter with a sampling frequency of 750 Hz is used to process the white noise signal. The second part is to screen the frequency response data with coherence less than 0.95 with the help of the recognition model. Finally, the MATLAB recognition toolbox is used to process the remaining data. In the third part the fit of the discriminative model is checked. The study identifies the discrete transfer functions G11, G12, G21 and G22 between links 6-1 and 6-2 of power amplifiers 1 and 2. G11 and G12 discrete transfer capabilities between There are G21 and G22 discrete transfer capacities between a 1# amplifier and a sensor 6-1, 6-2, the following are the mathematical articulations of discrete transfer work:

Fig. 3An identification of a vibration isolation device for a floating raft diagram

In the floating raft system on a boat, multiple types of gear are typically in operation simultaneously. To replicate the conditions created by a range of devices and reflect the real environment, dual-frequency sinusoidal impulses of 25 and 45 Hz are utilized. Furthermore, during the run-time, the floating raft system will be interrupted therefore background noise is used in the simulation to handle random signal blockages to lead a MATLAB/Simu link. The discrete transfer work matrix GM is employed in a dual-channel fuzzy control simulation. To simulate the active vibration isolation system of the floating raft, a 2D fuzzy controller is used as the basic structural unit. Considering that multiple controllers will generate coupling in the control process, they need to be processed with linear iteration to suppress the error signal. Fig. 4 shows the schematic diagram of the two-channel fuzzy control simulation.

Fig. 4Diagram of dual-channel fuzzy control simulation

In the simulation framework in Fig. 4, FLC1 and FLC22 are conventional fuzzy controllers, E1 (the value of 6-1 accelerometer in power amplifier No. 1) and E2 (the value of 6-2 accelerometer in power amplifier No. 2), and GM is the matrix model consisting of four discrete transfer functions.

3.2. Optimization and improvement of fuzzy controller design based on GA algorithm

The error and blunder ratio (variation) of a two-dimensional fuzzy controller’s information variables are always selected to match the dynamic features of the managed system. The outcome variables of the item are also considered. This article uses a Mamdani-type structural model with dual-input and single-output, with acceleration and its fluctuation as data sources [16]. The fuzzy domains for the fuzzy states are PB (positive huge), PS (positive small), ZO (zero), NS (negative small), and NB (negative large). The fuzzy domains of E, EC, and U are set to [3, 3], with the fuzzy states PB, PS, ZO, NS, and NB, respectively, Ke and Kec as the quantitative acceleration and acceleration variation variables, and Ku as the scaling factor.

Fig. 5Membership function curve of E, EC, and U

Quantization factor and scaling factor are important elements for realizing the transformation between the fuzzy domain and matter theory. Providing a proportional scaling to the input and output variables is essential for regulating the control system. Factors that are too large or too small will affect the response speed, transition time, and steady-state accuracy of the system. Therefore, when setting the factors for the fuzzy control system, it is not sufficient to rely solely on the converted theoretical values. It is necessary to design certain control rules to reduce the dispersion effect of the system. Therefore, the study of optimizing fuzzy control using genetic algorithms involves two parts: applying the genetic algorithm directly to the fuzzy controller and using the genetic algorithm to process the operating state of the floating raft vibration isolation system to obtain the optimal quantization, scaling factor, and control rule parameters. The optimal parameter value is then assigned to the fuzzy controller. The fuzzy controller’s brains are fuzzy rule uses language to depict the relationship between fuzzy data and the outcome. In this article, the acceleration measurements of the floating raft vibration isolation system are utilized to determine the size of the vibration transmitted to the base [17]. The hazy control principles are then constructed based on the four acceleration change scenarios:

1) When the acceleration value is positive, and the acceleration fluctuation is small grows, more negative power is required.

2) When the acceleration value is positive, and the acceleration value is positive variance reduces, the amount of negative power required decreases.

3) Less positive power is required if the acceleration variance grows as the acceleration value decreases.

4) More positive power is required if the acceleration value is negative, and the variation in acceleration is decreasing.

The quantization and scaling factors’ function is to bridge the gap between the fuzzy and physical worlds domains, i.e., to grow or decrease the information and outcome variables by a given scale. In the control system, this transformation serves as a regulatory function. The system’s reaction speed, overshoot, transition time, and steady-state accuracy are all impaired when the quantization factors and scale factors are too big or too small. During the time period of setting quantization and scaling factors for the control system, the theoretical value that changes from the ratio of fuzzy domain to physical domain cannot produce significant control effects. It takes time to Fig. the quantization and scaling factors by trial and error [18]. The fuzzy controller receives the The blunder derivative e and the error $e\left(t\right)$. The fuzzy logic is used to adjust the proportional coefficient $K_p$, the integral coefficient $K_i$, and the differential coefficient $K_d$ as guidelines derivation.

As a result, the controller’s result is:

Fuzzification, fuzzy surmising, and defuzzification are the three primary aspects of the fuzzy controller’s operation. Fuzzification is the method involved with changing transforming real-world values into semantic variables. The domain of the fuzzy set is defined as the error rate of change and the variation range of the acceleration blunder $e\left(t\right)$. Its fuzzy set includes NB, NS, ZE, PS, and PB. Participation work can address a variety of issues the fuzzy set. They deal with negative huge, negative tiny, zero, positive small, and positive large.

As an intelligent control method, fuzzy control is robust to nonlinear, time-varying and hysteretic systems, and is therefore suitable for active control of complex floating raft systems. However, the parameter selection and design of fuzzy controllers usually depend on the experience of experts, which is difficult to adapt to the actual situation of the controlled object and lead to the optimal control effect. Moreover, fuzzy controllers are not immune to problems such as steady state error, stability and adaptability, so the study proposes to optimize the fuzzy controller with the help of genetic algorithm. Genetic algorithm, as an algorithm based on Darwin’s natural selection mechanism and the evolutionary theory of genetics, has the characteristics of good global optimization ability, implied parallelism, high robustness and self-adaptability. And the genetic algorithm is used for the parameter optimization of fuzzy controller in the floating raft active vibration isolation system, which can effectively improve the dynamic characteristics of the controller and achieve better vibration isolation effect. By using GA, the quantization factors, scale factors, and control rules are all improved simultaneously in this article. The fuzzy controller based on GA is made up of two main parts: the fuzzy controller and the fuzzy controller which controls the controlled item directly and has dynamically changing. The GA optimization method obtains parameters for the floating raft active vibration isolation system based on its operating status. The parameters include Ke, Kec, and Ku, as well as control rules. The method uses a genetic algorithm for optimization. The parameters are then inputted into the fuzzy controller [19]. In this diagram, a fuzzy controller based on the GA is shown schematically.

Fig. 6Schematic the image shows a fuzzy controller based on a genetic algorithm in this diagram

When using genetic algorithms to optimize fuzzy controllers, it is necessary to encode quantity factors, proportion factors, and control rules. Then it is necessary to determine the fitness function, chromosome selection, crossover, and mutation until the optimal population is obtained. Then the individuals in the optimal population are the optimal solution for the optimized quantity, proportional factor, and control rules of the fuzzy controller.

3.3. Simulation Design of Active Damping System for Floating Raft

In Fig. 7, a fuzzy control system with two inputs and two yields is demonstrated. Blunder signals, E1, E2, and E3, are voltage signals that correlate to the low-pass channel’s acceleration signal, as seen in Fig. 15. The separated 1# acceleration signal from the moulding is denoted by E1, the sifted 2# acceleration signal is denoted by E2, and the sifted 3# acceleration signal is denoted by E3. The A/D port of CLP1103, the dSPACE1103 system’s wiring panel, is connected to the channel yield port based on the planned controller, the DS1103 control board calculates the control amount. Because acceleration is one of the contributions for fuzzy controllers.

Fig. 7Two-input two-output fuzzy control system

Gear manufacturing errors, the cross section of gear drives can be affected by external loads, coincident collisions, and other factors. The addition of A control force close to the source of excitation can significantly reduce the quantity of excitation of excitation lattice excitation.

The piezoelectric actuator is a mechanical energy Electrical energy is converted into mechanical energy using a converter, employing the piezoelectric effect of opposing piezoelectric ceramics. Its features include high control accuracy and quick reaction time. It is commonly Position compensation, active vibration control, and precision positioning are all examples of applications.

Where $q_{0}q$ indicates the actual distance between the two items during the crash, and represents the initial distance between them and $q_{0}q$ represents the impact deformation. When $q{q}_0$ is true, two pieces There was no collision, and the crash force was zero. The two components were affected whenever $q{q}_0$.

According to the Hertz contact hypothesis, the gear crash solidness coefficient is 0:

$R$ is the curvature radius relative:

where $R_1$ and $R_2$ are the equivalent radii of the two lattice gears’ contact sites individually, the relative radius of curvature $R$ equals:

Because the two Steel gear sets have a Poisson’s ratio of 0.27, and the Young’s modulus of the gear material is $E_1=E_2=$2.07e11 Pa. The results the impact solidness coefficient KH for high-velocity gear may be calculated: KH = 5.27e5 N mm^3/2. The impact solidness coefficient of the low-speed gear is KL = 5.54e5 N mm^3/2. The spring is in charge of controlling the power change during the impact. The damper absorbs only a small portion of the overall crash energy.

AFPID controller is a controller with three outputs and ($e\left(t\right)$ and $e\left(t\right)$) are two inputs ($K_p$, $K_i$, and $K_d$). The acceleration of vibrations is incorrect. The following three components are included in the planning and construction of a multistage gear train vibration active control test platform’s active control structure, control system, and signal acquisition and handling system [20].