Semi-active fuzzy control of a powerpack with magneto-rheological dampers at full operating conditions

Abstract

Powerpacks are commonly used as the power source in diesel multiple units (DMUs) due to their flexibility and economy. In order to enhance the ride comfort of DMUs at full operating conditions, it is a great challenge to design a multiple objectives semi-active control system to reduce the transmission force to the DMU, vibration intensity at start-stop conditions, and structural vibration in stable operating conditions. A fuzzy semi-active control system incorporating magneto-rheological (MR) dampers and vibration isolators with small stiffness coefficients is designed. Firstly, a rigid-flexible coupling powerpack model is established to reflect the rigid body and structural vibration characteristics. Next, an MR damper’s dynamic behavior at full operating conditions is investigated experimentally, direct and inverse models are established using a genetic algorithm backpropagation (GA-BP) neural network. Then, a variable universe hybrid fuzzy controller is designed for the multiple objectives requirements, including quick response during low-frequency start-stop conditions and effective suppression of structural vibration during high-frequency stable operating conditions. Finally, the vibration isolation performance of the powerpack is verified by simulation and experiments, demonstrating the effectiveness of the semi-active control system with MR dampers and the variable universe hybrid fuzzy controller at full operating conditions.

Keywords

powerpack vibration isolation system full operating conditions magneto-rheological dampers variable universe hybrid fuzzy control

1. Introduction

As the power source in DMUs, powerpacks have good economy and flexibility and they are widely used in high-speed railway branch lines (Wu et al., 2021; Song et al., 2023b). The powerpack is suspended below the DMU carriage with a passive double-layer vibration isolation system that reduces the excitation force from diesel generator sets (units) to the carriage (Chen et al., 2016). However, the lightweight design of the powerpack results in the transmission of structural vibration in a lower frequency range to the carriage, and decreases the ride comfort of the DMU (Li et al., 2022). Currently, powerpacks with passive vibration isolation systems could effectively attenuate resonances generated by rigid body vibrations (<20 Hz) under low-frequency start-stop conditions, but they fail to suppress the transmission of high-frequency structural vibration (>20 Hz) due to fixed stiffness and damping coefficients (Deng et al., 2020). To address the problem, this research takes advantage of MR dampers, which offer adjustable damping force and a wide range of control forces (Makowski and Knap, 2013; Biju and Shunmugam, 2017). And a semi-active vibration isolation system at full operating conditions should be redesigned to exhibit quick response behavior to reduce rigid body vibration during low-frequency start-stop conditions, as well as reduce the transmission of structural vibration during high-frequency steady-state operating conditions. Therefore, the controller strategy and the model accuracy of the actuator (MR damper) are the two key issues to ensure the performance of the powerpack with a control system.

In the current research, the controller strategy is related to the model accuracy of controlled objects. Lumped mass models are widely used in nonlinear controllers based on the Lyapunov stability theory, such as the sliding mode control (Dutta et al., 2016; Dong et al., 2017), controllers based on the optimal theory, such as the model predictive control (Mai et al., 2020), the clipped linear-quadratic optimal controller (Brezas et al., 2015; Mohebbi et al., 2017), due to their merits of a simplified controller design and improved control response speed. However, lumped mass models may produce interference between controlled modals and non-controlled modals, even causing a system damage, known as “control spillover” (Jia and Shan, 2018). Robust controllers and H∞ controllers are developed to mitigate “control spillover” by reducing their dependence on the model accuracy of controlled objects, making it particularly suitable for systems with uncertain parameters (Zong et al., 2013). These model-based controller designs invariably bring the challenge of balancing the model accuracy and computation cost of controllers. The powerpack with numerous structural vibration modals at all operating conditions makes “control spillover” prevalent, thereby it is necessary to design a controller which is unrelated to the model accuracy of the controlled object. The fuzzy controller determines the output using only observational signals, which can avoid the complexity associated with models (Eltantawie, 2012; Zhu et al., 2022). Nevertheless, the fixed universes in fuzzy controllers make it difficult to ensure a balance between the control accuracy and response speed. Therefore, further research on fuzzy controllers needs to be conducted to improve the quick response at start-stop conditions and control accuracy at steady-state conditions to meet the control requirements of the powerpack at full operating conditions.

Developing an accurate MR damper model is another crucial issue in a semi-active control system. The mechanical behavior models of MR dampers in current research are categorized into parametric and nonparametric models. Parametric models describe the relationship between the output damping force and parameters through specific equations, such as the Bingham plasticity model (Choi et al., 2016; Fang et al., 2018) the Bouc–Wen hysteresis model (Zong et al., 2012), or the Dahl model (Wei et al., 2019) are usually used as direct models for MR dampers to predict the output damping force in a semi-active simulation analysis. Nonparametric models employ data-driven intelligent algorithms to build MR dampers models, avoiding the computational cost of solving complex dynamic equations, which are widely used in inverse models’ establishment of MR dampers (Gedik et al., 2022; Lv et al., 2022). These researches mainly exploit the low-frequency performance of MR dampers without considering high-frequency structural vibrations behaviors of the controlled objects. However, a recent study shows that the compressibility of the MR fluid in high-frequency reciprocating motion cannot be negligible using a complex parametric model (Xu et al., 2020). For the vibration control of the powerpack with MR dampers at full operating conditions, it is still necessary to complement the high-frequency dynamic characteristics of MR dampers and establish corresponding direct and inverse models for a control system.

In summary, a semi-active control system with MR dampers at full operating conditions is required to carry out the following tasks: (1) Designing a hybrid fuzzy controller for various control objectives to reduce the transmission of both rigid body and structural vibration at full operating conditions. (2) Conducting experiments on MR dampers at full operating conditions and developing accurate direct and inverse models covering a broad range of frequencies. So this research begins by analyzing the powerpack's rigid body and structural vibrations characteristics. Subsequently, an experimental investigation is conducted to assess the dynamic performance of an MR damper at full operating conditions. Then, a variable universe hybrid fuzzy controller is developed for the multiple objectives control requirements. Finally, the semi-active vibration isolation system's performance is verified through simulation and experiments at full operating conditions.

2. Modeling of the powerpack

The powerpack is suspended under the DMU carriage through a double-layer vibration isolation system, which comprises a primary vibration isolation system and a secondary vibration isolation system. The primary vibration isolation system supports a unit and a radiator on the frame with 5 primary vibration isolators, 2 MR dampers, and 4 radiator vibration isolators. A secondary vibration isolation system connects the frame and the carriage with 4 secondary vibration isolators, as shown in Figure 1(a). The powerpack features a straight-six diesel engine, with the 3.0 and 6.0 harmonics serving as the main excitation frequencies. At the highest speed condition of 1400 r/min, the 6.0 harmonic excitation force frequency is 140 Hz. The overall frame features a cavity structure, the installation positions of the secondary vibration isolators are reinforced by four cast steel end posts. The lightweight design will decrease the elastic modal frequencies of the frame, which generates structural vibration at full operating conditions, deteriorating its vibration isolation performance (Rao, 2017). Then, according to the ISO standard (ISO7626-2, 2015), the bench modal test of the frame is conducted by the unmeasured force method, and 13 measuring points are selected, as demonstrated in Figure 1(b). The test results of the elastic vibration modal of the frame structure are shown in Table 1.

Table 1.

Structural vibration of the frame.

Order	Mode	Simulated frequency (Hz)	Measured frequency (Hz)	Error (%)
1	Torsion	20.11	20.8	3.31
2	Rhombus	34.94	34.9	0.11
3	Transverse bending	61.38	61.1	0.46
4	Frame transverse beam torsion	67.67	66.5	0.26
5	Rhombus+Torsion	72.87	73.24	0.5
6	Single side bending of transverse beam	107.00	106.26	0.7
7	Vertical bending of transverse beam	109.85	111.94	1.86
8	The middle beam bent up and down	131.19	133.79	1.94

However, it is challenging to model the flexible frame accurately using directly multi-body dynamics simulation method due to its complex solid characteristics and the different materials involved in each part. As a result, a co-design of the FEM is adopted. Firstly, a geometric model is created in SOLIDWORKS based on solid features and geometric parameters. HYPERMESH is used for meshing, using shell 181 elements for the frame plates, solid185 elements for the end columns, contact elements at the contact surface of the shell and solid elements for the transmission of the force and displacement. Mass21 element simulates the mass and rotational inertia of the fuel and water tanks, a rigid element connects the center of mass of the auxiliary equipments to their relative position. The multi-material meshing and modeling issue is resolved by the upper flow. Then, the natural frequencies and corresponding vibration modes are computed in ANSYS. The ANSYS-ADAMS interface is used to generate a flexible body modal neutral file. The maximum error between the simulated frequencies and the measured values of the frame model is 3.31%, as demonstrated in Table 1, showing that the frame model could reflect its high-frequency structural vibration characteristics.

As the elastic modal frequencies are much higher than their operating frequencies, the unit, radiator, and other equipments are regarded as rigid body vibration models. These rigid body models are connected to the flexible frame through vibration isolators and MR dampers. Then, the rigid-flexible coupling dynamics model is established in ADAMS, as shown in Figure 1(a).

3. Modeling of the magneto-rheological damper considering high-frequency characteristics

The primary task of this section is to investigate experimentally the dynamic behavior of a MR damper at full operating conditions. The experimental design takes into account the full operating characteristics of the powerpack, including the large vibration amplitude at low frequencies and the small vibration amplitude at high frequencies. Then, based on the test data, the direct and inverse models are developed for a semi-active control system.

3.1. Experimental design

The MR damper (as shown in Figure 2) in the literature (Xu et al., 2022) provides a controllable damping force and offers the theoretical and simulation support to suppress the resonance peaks of the powerpack. Further testing is needed to obtain the mechanical behavior of the MR damper at full operating conditions.

The test system is shown in Figure 2. The MR damper is tested in an MTS850 servo-hydraulic test system. The current of the MR damper is controlled by the programmable power supply (N67744 B). The MTS Damper Software controls test displacement and frequency through the servo system, and also records displacement and force signals from sensors on the damper. The damper test conditions are selected by considering the vibration isolation requirements of the powerpack at full operating conditions. Under the 0–2 A current, the adjustable damping force range of this damper is about 8 times at 2 mm at low-frequency start-stop conditions and 3 times at 0.1 mm at high-frequency steady-state conditions of the powerpack. The test conditions are divided into Stage 1 (<50 Hz) and Stage 2 (50–140 Hz) at 0, 0.5, 1.5, 2 A test electric currents, and the test displacement for the two stages are 2 mm and 0.1 mm, respectively. These test results provide the foundational data to establish both direct and inverse models of the MR damper under full operating conditions.

3.2. Direct model and inverse model of magneto-rheological damper

In the nonparametric model for the MR damper, the BP neural network can approximate any continuous function in a closed interval using a single hidden layer, and can be used to model complex nonlinear systems (Girosi and Poggio, 1990). A genetic algorithm (GA) is utilized to optimize the initial weights of the BP neural network, which addresses the issue of non-convergence caused by improper initial values and improves the model accuracy effectively. The key parameters of GA include a population size of 80, a maximum number of iterations of 100, a crossover probability of 0.8, a variation probability of 0.1. The nonparametric modeling process is depicted in Figure 3.

The direct and inverse models for the MR damper are divided into 4 nonparametric models, depending on the different dynamical characteristics of MR dampers in low (Stage 1 < 50 Hz) and high frequencies (Stage 2 > 50 Hz) (Xu et al., 2022). The number of neurons in the hidden layer is determined by the grid search method, the network parameters are shown in Figure 3.

The direct model predicts the output damping force f_k at the current k moment according to the displacement s_k, velocity v_k, electric current I_k of the MR damper at the current k moment and the displacement s_k-1, velocity v_k-1, electric current I_k-1, damping force f_k-1 at the k-1 moment. Similarly, the inverse model is used to predict the electric current I_k at the current k moment with a nonparametric model.

The training and test sets are selected based on the operating conditions of the powerpack. According to the rigid body vibration modal frequency of 4 Hz and the highest operating condition excitation frequency of 140 Hz, the training set of stage 1 uses the 4 Hz experimental data as the test set, while in stage 2, the 140 Hz experimental data is set to the test set, and the remaining data as the training set.

The prediction damping performance of the direct model is shown in Figures 4 and 5. It presents visually that the predicted values from the GA-BP neural network are close to the measured values in different current case. The RMS error values for the five input currents are provided in Table 2, with the maximum error value of 13.86 N, indicating a high level of identification accuracy of the direct GA-BP direct model.

Table 2.

The RMS error of the models.

Models		Current (A)
Models		0	0.5	1	1.5	2
Direct model (N)	4 Hz	2.52	13.86	11.53	12.56	11.71
Direct model (N)	140 Hz	1.23	1.12	1.25	1.53	2.07
Inverse model (mA)	4 Hz	0.04	0.05	0.1	0.19	0.31
Inverse model (mA)	140 Hz	0.14	0.17	0.08	0.03	0.03

The inverse model of the MR damper exhibits excellent prediction accuracy and slight error, as shown in Figure 6 and Table 2. The predicted currents match closely the measured values, with a maximum RMS error of 0.31 mA, which verifies the reliability and effectiveness of the inverse damper model.

4. Improved fuzzy controller design

The fuzzy controller does not depend on a specific mathematical model, avoiding the complexity brought about by the controlled object. It is necessary to improve the constant input and output universes of the fuzzy controller to raise the control accuracy and response speed in order to meet the vibration control requirements of the powerpack at full operating conditions. Based on the improved fuzzy controller, a hybrid fuzzy controller is designed to provide multi-objective control rules at full operating conditions, which can control the damping force of the MR damper in order to reduce quickly the vibration intensity of the unit, improving the ride comfort of the DMU by reducing the transmission of structural vibration to the carriage.

4.1. Variable universe fuzzy controller design

Variable universe fuzzy controllers allow for a real-time adjustment of the universes according to the error. A contracting-expanding factor σ is introduced to transform an input range of [−E₁, E₁] to [−σE₁, σE₁]. When σ > 0, the universe expands, improving the response speed. When σ < 0, the universe contracts, increasing the control accuracy. The constant number of fuzzy control rules ensures small calculation cost and less response time. The real-time change of the universes improves the control accuracy and robustness of the system.

The contracting-expanding factor σ(x) of the variable universe must satisfy duality, zero-preserving, monotonicity, coordination, and normality. In this study, a proportional function is used to describe the contracting-expanding factor. That is

σ (x) = {(\frac{| x |}{E})}^{τ} + ε

(1)

where x represents the input variable, E represents the boundary value of the initial universe, τ∈(0,1) is the adjustment parameter, ε is a positive number that could be infinitely small. When x > E, the universe expands to fasten the control dynamic process and decrease the response time. When x < E, the system trends to the desired value, the universe contracts to improve the control resolution and reduce the error.

The performance of the improved controller is verified by the water tank level control in Matlab Simulink (Matlab, 2021), as shown in Figure 7. The rise time reflects the response speed of the system, which represents the time when the system reaches 90% of the desired value for the first time. The desired value of the water level is 60 mm. To achieve this goal, the rise time of the case using the fuzzy controller is 8.40 s, while the rise time with the variable universe fuzzy controller is decreased to 3.47 s, which improves the response speed by 58.69%. In addition, the control error indicates the control accuracy, which is 2.12 mm for the case using the fuzzy controller, 0.35 mm for the variable universe fuzzy controller. The example demonstrates that the variable universe fuzzy controller significantly improves the response speed and control accuracy, and could be applied to vibration isolation of the powerpack system, which requires quick response at start-stop conditions and high control accuracy at steady-state conditions.

4.2. Hybrid variable universe fuzzy controller design

The variable universe fuzzy controller improves the response speed and control accuracy in Section 4.1, this section combines the advantages of skyhook control and groundhook control to design the hybrid fuzzy controllers to meet the control requirements of the powerpack vibration isolation at full operating conditions.

The controller employs MR dampers to produce control force in the vertical direction to improve vibration isolation performance since the vertical transmission force has the most significant impact on the ride comfort of the DMU. The vibration isolation performance is evaluated by the vibration intensity of the unit at low-frequency start-stop conditions and the transmission force (force transmission rate) at high-frequency steady-state conditions.

The controller design takes into account the dynamic response characteristics of the double-layer vibration isolation system of the powerpack. The vibration velocity v₁ of the unit reflects directly its vibration severity, the vibration velocity v₂ of the frame reflects the dynamic reaction force transmitted to DMU. The controller takes v₁ and v₂ as input variables and the damping control force f as the output variable. The fuzzy universe is set to [−6, 6], the fuzzy controller input and output variables are divided into seven fuzzy subsets, NB, NM, NS, ZE, PS, PM, PB, which represent “negative large”, “negative medium,” “negative small,” “zero,” “positive small,” “positive middle,” and “positive large,” respectively. The membership function of each input and output fuzzy subset is constructed from a Gaussian function. The contraction and expansion of the universe of the argument are achieved in the control process by the contracting-expanding factor σ(x) described in Section 4.1. Finally, the variable universe fuzzy controller is designed for the isolation vibration of the powerpack.

The variable universe fuzzy controller combined with the skyhook control rules to determine the output damping force of the MR damper at the low-frequency start-stop conditions, which aims to reduce the vibration intensity of the unit. The direction of the damping force is determined by the relative speed direction of the unit and the frame; the output damping force could be changed by adjusting the input current value. It assumes that the vibration speed v₁ is positive in the upward direction, the relative speed v₁-v₂ is positive in the separated direction. The rules are

(1) When v₁ > 0 & v₁-v₂ ≥ 0, the unit experiences a downward damping force, which is in the same direction as the ideal skyhook damping force, then the variable universe fuzzy controller could adjust the damping force f = c_sv₁ to suppress the vibration, where, c denotes the damping coefficient of the MR damper, ascertained experimentally in Section 2.2, c_max represents the maximum damping coefficient of the MR damper.

(2) When v₁ > 0 & v₁-v₂ ≤ 0, the unit experiences an upward damping force, which is opposite to the ideal skyhook damping force. In such a situation, the application of damping force may aggravate the vibration, thus the force exerted by the MR damper should be minimized, f = 0 is the ideal state.

f = {\begin{cases} - c v_{1} \\ - c_{\max} v_{1} \\ 0 \end{cases} \begin{array}{l} v_{1} (v_{1} - v_{2}) \geq 0, f \leq f_{\max} \\ v_{1} (v_{1} - v_{2}) \geq 0, f > f_{\max} \\ v_{1} (v_{1} - v_{2}) < 0 \end{array}

(2)

Based on the above rules, a set of skyhook-fuzzy control rules presented in Table 3 is developed to minimize the vibration velocity of the unit.

Table 3.

Hybrid fuzzy control rules.

Rules			v₁-v₂
Rules			NB	NM	NS	ZE	PS	PM	PB
Skyhook-fuzzy control rules at start-stop conditions	v ₁	NB	PB	PB	PB	PM	ZE	ZE	ZE
		NM	PB	PB	PM	PS	ZE	ZE	ZE
		NS	PB	PM	PS	PS	ZE	ZE	ZE
		ZE	PM	PM	PS	ZE	NS	NM	NM
		PS	ZE	ZE	ZE	NS	NS	NM	NB
		PM	ZE	ZE	ZE	NS	NM	NB	NB
		PB	ZE	ZE	ZE	NM	NB	NB	NB
Groundhook-fuzzy control rules at steady-state operating conditions	v ₂	NB	ZE	ZE	ZE	PM	PB	PB	PB
		NM	ZE	ZE	ZE	PS	PM	PB	PB
		NS	ZE	ZE	ZE	PS	PS	PM	PB
		ZE	NM	NM	NS	ZE	PS	PM	PM
		PS	NB	NM	NS	NS	ZE	ZE	ZE
		PM	NB	NB	NM	NS	ZE	ZE	ZE
		PB	NB	NB	NB	NM	ZE	ZE	ZE

Similar to the skyhook-fuzzy controller, the variable universe fuzzy controller combined with the groundhook control rules to determine the output damping force of the MR damper at the high-frequency steady-state conditions, which aims to reduce the transmission force to the DMU. The controller should follow the rules:

(1) When v₂ > 0 & v₁-v₂ ≥ 0, the frame experiences to a downward damping force, which is the same as the ideal damping force of the groundhook, the damping force f = cv₂ could be adjusted by the variable universe fuzzy controller to suppress the vibration of the frame.

(2) When v₂ > 0 & v₁-v₂ ≤ 0, the frame experiences an upward damping force, which is opposite to the ideal damping force of the groundhook. In such a situation, the application of damping force on the frame would aggravate the vibration of the frame. Hence, the force provided by the MR damper should be minimized, and f = 0 is the ideal state.

f = {\begin{cases} - c v_{2} \\ - c_{\max} v_{2} \\ 0 \end{cases} \begin{array}{l} v_{2} (v_{1} - v_{2}) \geq 0, f \leq f_{\max} \\ v_{2} (v_{1} - v_{2}) \geq 0, f > f_{\max} \\ v_{2} (v_{1} - v_{2}) < 0 \end{array}

(3)

The groundhook-fuzzy control rules are presented in Table 3, each rule is the same weight, the area center of gravity method is employed for the defuzzification. Therefore the designed hybrid variable universe fuzzy controllers can meet the control requirements of the powerpack vibration isolation at full operating conditions.

5. Performance analysis of the semi-active control system

In this section, the vibration isolation performance of the semi-active control system with MR dampers and hybrid variable universe fuzzy controllers is verified at full operating conditions of the powerpack by simulation and experiment respectively. In the simulation analysis, the vibration isolation performance is verified by the rigid-flexible coupling model under the sweep frequency case. In the experiment, the vibration isolation performance is tested at start-stop and steady-state operating conditions respectively.

5.1. Simulation Analysis

The vibration isolation performance of the semi-active control system is verified by using co-simulation in ADAMS-SIMULINK. The rigid-flexible coupling model in Section 2 is applied the excitation forces and the vibration response and rotation speed are monitored in ADAMS. Excitation forces acting on the model include the overturning moment generated by the diesel engine, the reciprocating inertia force generated by the manufacturing errors, the centrifugal inertia force at the generator mass center position. The rotation speed and the vibration velocity on the powerpack are monitored. Then the operating conditions and vibration data are transmitted to the hybrid fuzzy controller as input in SIMULINK. In SIMULINK, the controller selects skyhook-fuzzy and groundhook-fuzzy strategy for start-stop and steady-state operating conditions, and determines the desired output damping force. The output current is then determined by the inverse model of the MR damper, and the actual output damping force acting on the powerpack is obtained using the direct model. The flowchart is shown in Figure 8.

Measurement points are selected following the ISO standards (ISO5348, 2021; ISO8528-9, 2017). 9 vertical vibration velocity measurement points are on the unit, 7 vertical vibration velocity measurement points are on the frame.

Two vibration isolation cases are proposed. Case 1 is passive, using rubber isolators with the original design stiffness for both the primary and secondary vibration isolation systems. Case 2 is semi-active, using MR dampers and spring isolators for the primary vibration isolation system and rubber isolators for the secondary vibration isolation system. The spring isolator stiffness is 0.25 times that of the rubber isolator.

Frequency sweep analysis from 0 Hz to 140 Hz is conducted on the model according to the excitation force characteristics of the powerpack. Under low-frequency conditions, the exciting frequency of the internal combustion engine stimulates the occurrence of rigid body vibration modals. The reduced equivalent stiffness of the system at low frequencies causes more severe vibration responses, leading to the presence of peak amplitudes at low frequencies of the powerpack. Figure 9(a) shows the vibration velocities of the unit and the frame, Figure 9(b) displays the transmission rates. The stiffness coefficients of the spring isolators in Case 2 are 0.25 times those of the passive rubber isolators in Case 1. These reduction values in stiffness are much greater than the additional stiffness introduced by the MR dampers. The overall reduction value in the stiffness coefficients of the primary isolators decreases the natural frequencies of the rigid body vibration modals, decreasing the resonance peak amplitude of the unit and frame’s vibration response. In addition, the reaction force acting on the frame is reduced simultaneously, resulting in a decrease in the structural vibration modal frequencies.

Moreover, the semi-active control system suppresses effectively the vibration velocities of the unit and frame at low-frequency start-stop conditions. Compared with the rubber passive vibration isolation system (Case 1), the hybrid fuzzy control (Case 2) reduces the maximum vertical vibration velocity of the unit, the maximum vertical vibration velocity of the frame, the maximum force transmission rate by 40.77%, 76.44% and 41.92% respectively. It could be analyzed from the vibration isolation theory (Rao, 2017) that Case 2 provides a lower stiffness coefficient, which can reduce the modal frequencies of rigid body vibration and increase the peak vibration amplitude, bringing about the deteriorated low-frequency isolation vibration performance of the powerpack. However, the designed semi-active control system can suppress effectively the first vibration peak, as the hybrid fuzzy controller is capable of controlling vibration amplitude at low frequencies. These results highlight the effectiveness of the semi-active control system in reducing the vibration magnitude of the unit and frame at start-stop conditions.

The steady-state conditions at higher frequencies can cause varying degrees of vibration peaks to occur on the powerpack, signifying the excitement of structural vibration modals of the frame and an increased transmission force to the DMU. As illustrated in Figure 9, Case 2 exhibits lower vibration velocity and force transmission rate than Case 1, indicating a superior vibration isolation performance at the steady-state conditions.

The co-simulation results present that Case 2 using the hybrid fuzzy controller and MR dampers significantly improve the isolation performance at full operating conditions of the powerpack.

5.2. Experimental verification

A double-layer vibration isolation system test bench is designed based on the powerpack of the DMU (Song et al., 2023a), as shown in Figure 10(a). The bench mainly considers the rigid body and structural vibration characteristics of the powerpack, although these frequency values are not exactly the same. The system consists of an internal combustion engine (4100Q) and an electric motor (SIEMENS YPL200) (which together represent the unit) mounted on a flat plate, which is connected to the frame by three primary vibration isolators, the frame is connected to the foundation (ground) by four secondary vibration isolators. The main components and position parameters match those of the reference powerpack. The internal combustion engine generates reciprocating inertia force and overturning moment, the motor produces centrifugal inertia force by an eccentric mass block on a rotating disk. The motor drives the internal combustion engine and applies exciting force by the SIEMENS VFD-B motor drive control system. The semi-active control system includes acceleration sensors (CZLYB-1H), a magnetoelectric pulse sensor (J14530) to monitor the engine state, a dynamic signal test and analysis system (DH5922N) to process data in real time, a programmable power supply (N67744B) to control the output of MR dampers.

The unit is equipped with 3 measurement points, and the frame is fitted with 4 measurement points at each of its four secondary vibration isolator locations, following the ISO standards (ISO8528-9, 2017; ISO5348, 2021). Figure 10(b) depicts the arrangement of the measurement points.

The vibration isolation performance of the powerpack at full operating conditions is verified by experiments, including start-stop operating conditions and steady-state operating conditions. And 2 experimental cases are the same as the simulation. The unit is accelerated from 0 r/min to 900 r/min and then decelerates to 0 r/min to simulate the start and stop conditions. The excitation-induced mechanism of rigid body vibration is consistent during both the startup and shutdown conditions of the powerpack. As the startup process often undergoes rapidly, the longer duration of the shutdown process can better represent the rigid body vibration isolation effects. Therefore, the vibration responses during the shutdown process are used to analyze the vibration isolation performance of the double-layer vibration isolation system. Under steady-state conditions, eight different operating speeds are selected, including 900 r/min, 1020 r/min, 1140 r/min, 1230 r/min, 1320 r/min, 1470 r/min, 1680 r/min and 1800 r/min. Since the unit adopts a 4-cylinder engine, its harmonic frequencies of 2.0 and 4.0 are the main harmonic frequencies, and the corresponding frequency range is from 30 Hz to 120 Hz.

The time-domain signal of vibration speed during the shutdown process is depicted in Figure 11. The different isolation system designs in Case 1 and Case 2 lead to the difference in natural frequencies, resulting in the inconsistency in peak values of vibration response signals. This research focuses on reducing the overall vibration level by controlling the peak values of the maximum vibration velocity for the powerpack. For Case 1, the results show that the unit resonates between 2 to 4 s, and the maximum vibration velocity is 13.92 mm/s. For Case 2, no significant resonance is observed, with a maximum vibration velocity of 9.62 mm/s, representing a 21.72% reduction in velocity amplitude. These observations indicate that the semi-active control system is effective in reducing low-frequency rigid body vibration and the vibration intensity of the unit, and can improve the vibration isolation performance at start-stop conditions of the powerpack.

The steady-state vibration velocities and reaction forces are used to represent the vibration isolation performance on high-frequency structural vibrations of the powerpack, as presented in Figure 12(a). Reaction forces represent the transmission force to the DMU carriage (ground). The reaction force, which is the vector sum of the elastic force and damping force, is directly related to the vibration displacement and velocity responses of the powerpack. The forced vibration response is periodic for the periodic excitation generated by the diesel engine (B, 1988), therefore, the reaction force signal is periodic, as shown in Figure 12(b). In Figure 12(a), Case 2 demonstrates that vibration velocities are reduced slightly and reaction forces are decreased significantly at steady-state conditions. At 1140 r/min, reaction forces exhibit a substantial increase, suggesting that the frame structural vibration is transmitted to the DMU carriage. In Case 2, the semi-active control system decreases the maximum vertical vibration velocity by 8.59% and reduces the reaction force by 40.13% compared to Case 1. Figure 12(b) shows the time-domain signal of the reaction force at a measuring point at 1140 r/min, revealing a reduction in the maximum value from 78.14 N in Case 1 to 47.50 N in Case 2, a decrease of 39.21%. These results highlight the effectiveness of the designed hybrid fuzzy controller in suppressing the transmission of high-frequency structural vibration at steady-state conditions for the powerpack.

According to the above experimental results, the semi-active vibration isolation system can reduce effectively the vibration intensity of the powerpack at start-stop conditions, high-frequency structural vibration, and transmission force at steady-state conditions.

6. Conclusions

This research developed a semi-active control system with MR dampers for a powerpack, which can suppress both rigid body vibrations at start-stop conditions and structural vibration at steady-state conditions. The following conclusions are obtained.

(1) The rigid-flexible coupling model of the powerpack is developed by a co-simulation method and verified by the modal experiments.

(2) The dynamics experiments of the MR damper at 2 Hz–140 Hz are designed considering the full operating conditions of the powerpack. The experimental data are used to establish both direct and inverse models of the MR damper through the GA-BP neural network. These models are capable of accurately capturing both the low-frequency and high-frequency characteristics of the MR damper.

(3) The speed and accuracy of the controller are enhanced by utilizing the variable universe. To ensure the vibration isolation performance of the powerpack at full operating conditions, a hybrid fuzzy controller is designed, which employs a skyhook-fuzzy control strategy to enhance anti-vibration performance at low-frequency start-stop conditions and a groundhook-fuzzy control strategy to reduce the transmission force at high-frequency steady-state operating conditions.

(4) The vibration isolation performance of the semi-active control system of the powerpack with the MR dampers and the hybrid variable universe fuzzy controller is verified at full operating conditions by simulation and experiment. The results demonstrate a significant reduction in the vibration intensity of the powerpack at start-stop conditions and the transmission force at steady-state conditions especially for structural vibration in high-frequency.

Footnotes

Author’s contribution

Song Shizhe: Modeling and programming; Experiment; Writing original draft; Hua Chunrong: Conceptualization; Paper revision and suggestions; Methodology; Project administration. Huang Yan and Dong Dawei: Supervision; Validation; Cai Dingzhong and Yan Bing: Experiment.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China [No. 51875482 and No. 52305134] and the Natural Science Foundation of Sichuan Province of China [No. 2022NSFSC0416].

ORCID iDs

Shizhe Song

Chunrong Hua

Yan Huang

References

Biju

Shunmugam

(2017) Development of a boring bar with magneto rheological fluid damping and assessment of its dynamic characteristics. Journal of Vibration and Control 24: 3094–3106.

Brezas

Smith

Hoult

(2015) A clipped-optimal control algorithm for semi-active vehicle suspensions: theory and experimental evaluation. Automatica 53: 188–194.

Chen

Dong

Yan

, et al. (2016) An analytical study on forced vibration of beams carrying a number of two degrees-of-freedom spring–damper–mass subsystems. Journal of Vibration and Acoustics 138: 061011.

Choi

S-B

Nam

M-H

Lee

B-K

(2016) Vibration control of a MR seat damper for commercial vehicles. Journal of Intelligent Material Systems and Structures 11: 936–944.

Deng

Yang

(2020) Optimal design and experimental evaluation of magneto-rheological mount applied to start/stop mode of vehicle powertrain. Journal of Intelligent Material Systems and Structures 31: 1126–1137.

Dong

Liao

(2017) Fuzzy sliding mode control based on hybrid Taguchi genetic algorithm for magneto-rheological suspension system. Proceedings of the Institution of Mechanical Engineers - Part D: Journal of Automobile Engineering 225: 735–746.

Dutta

Choi

S-M

Choi

S-B

(2016) A new adaptive sliding mode control for Macpherson strut suspension system with magneto-rheological damper. Journal of Intelligent Material Systems and Structures 27: 2795–2809.

Eltantawie

(2012) Decentralized neuro-fuzzy control for half car with semi-active suspension system. International Journal of Automotive Technology 13: 423–431.

Fang

Zuo

Xia

(2018) Vibration transmission analysis of nonlinear floating raft isolation system with magneto-rheological damper. Journal of Low Frequency Noise, Vibration and Active Control 37: 700–710.

10.

Gedik

Kurt

Pala

, et al. (2022) An experimental and artificial neural network investigation on the laminar flow of magnetorheological fluids through circular pipes. Journal of Magnetism and Magnetic Materials 546: 168893.

11.

Girosi

Poggio

(1990) Networks and the best approximation property. Biological Cybernetics 63: 169–176.

12.

(1988) Internal Combustion Engine Fundamentals. New York: Mcgraw-hill.

13.

ISO5348 .(2021) Mechanical Vibration and Shock — Mechanical Mounting of Accelerometers. Geneva: International Organization for Standardization.

14.

ISO7626-2 (2015) Mechanical Vibration and Shock — Experimental Determination of Mechanical Mobility — Part 2: Measurements Using Single-point Translation Excitation with an Attached Vibration Exciter. Genève, Switzerland: International Organization for Standardization.

15.

ISO8528-9 (2017) Reciprocating Internal Combustion Engine Driven Alternating Current Generating Sets — Part 9: Measurement and Evaluation of Mechanical Vibrations. Genève: International Organization for Standardization.

16.

Jia

Shan

(2018) Optimal actuator placement for constrained gyroelastic beam considering control spillover. Journal of Guidance, Control, and Dynamics 41: 2073–2081.

17.

Liu

, et al. (2022) Vibration fatigue analysis of high-speed railway vehicle carbody under shaking condition. Vehicle System Dynamics 60: 1867–1887.

18.

Sun

(2022) Data-driven prediction-control system modeling for magnetorheological damping force. Journal of Intelligent Material Systems and Structures 34: 155–167.

19.

Mai

Yoon

D-S

Choi

S-B

, et al. (2020) Explicit model predictive control of semi-active suspension systems with magneto-rheological dampers subject to input constraints. Journal of Intelligent Material Systems and Structures 31: 1157–1170.

20.

Makowski

Knap

(2013) Reduction of wheel force variations with magnetorheological devices. Journal of Vibration and Control 20: 1552–1564.

21.

Matlab (2021) Simulink User’s Guide. Natick, Massachusetts: Mathworks Inc.

22.

Mohebbi

Dadkhah

Rasouli Dabbagh

(2017) A genetic algorithm–based design approach for smart base isolation systems. Journal of Intelligent Material Systems and Structures 29: 1315–1332.

23.

Rao

(2017) Mechanical Vibrations. 6th edition. Upper Saddle River: Pearson.

24.

Song

Dong

Huang

, et al. (2023a) Vibration energy decoupling method and application for flexible double-layer vibration isolation systems. Joural of Southwest Jiaotong University 58: 304–313.

25.

Song

Huang

Hua

, et al. (2023b) Transmission path and influencing factors of abnormal broadband noise and vibration of the generator induced by the driveline. Journal of Sound and Vibration 556: 117730.

26.

Wei

Zhao

, et al. (2019) A theoretical study on the train-induced vibrations of a semi-active magneto-rheological steel-spring floating slab track. Construction and Building Materials 204: 703–715.

27.

Liu

Ding

, et al. (2021) Vibration responses of rotor systems in diesel multiple units under dynamic spatial misalignments and base motions. Journal of Sound and Vibration 492: 115817.

28.

Dong

Huang

, et al. (2020) Physical modeling and experimental verification of magneto-rheological damper under medium and high frequency excitation. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235: 353–365.

29.

Dong

Huang

, et al. (2022) A comprehensive optimal design method for magnetorheological dampers utilized in DMU power package. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 236: 533–547.

30.

Zhu

Zhang

, et al. (2022) Delay-dependent sliding mode variable structure control of vehicle magneto-rheological semi-active suspension. IEEE Access 10: 51128–51141.

31.

Zong

L-H

Gong

X-L

Guo

C-Y

, et al. (2012) Inverse neuro-fuzzy MR damper model and its application in vibration control of vehicle suspension system. Vehicle System Dynamics 50: 1025–1041.

32.

Zong

L-H

Gong

X-L

Xuan

S-H

, et al. (2013) Semi-active H∞ control of high-speed railway vehicle suspension with magnetorheological dampers. Vehicle System Dynamics 51: 600–626.