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Edited by: Shuaishuai Sun, Tohoku University, Japan

Reviewed by: Yang Yu, University of Technology Sydney, Australia; Yancheng Li, University of Technology Sydney, Australia

This article was submitted to Smart Materials, a section of the journal Frontiers in Materials

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

This paper aims to improve control performance for a magnetorheological damper (MRD)-based semi-active seat suspension system. The vibration of the suspension is isolated by controlling the stiffness of the MRD using a proportion integration differentiation (PID) controller. A new intelligent method for optimizing the PID parameters is proposed in this work. This new method appropriately incorporates particle swarm optimization (PSO) into the PID-parameter searching processing of an improved fruit fly optimization algorithm (IFOA). Thus, the PSO-IFOA method possesses better optimization ability than IFOA and is able to find a globally optimal PID-parameter set. The performance of the PID controller optimized by the proposed PSO-IFOA for attenuating the vibration of the MRD suspension was evaluated using a numerical model and an experimental platform. The results of both simulation and experimental analysis demonstrate that the proposed PSO-IFOA is able to optimize the PID parameters for controlling the MRD semi-active seat suspension. The control performance of the PSO-IFOA-based PID is superior to that of individual PSO-, FOA-, or IFOA-based methods.

Engineers often work in a high vibration environment, which seriously affects their health (Maikala and Bhambhani,

Proportion integration differentiation (PID) controllers have been widely used in industrial contexts because of their advantageous characteristics of having a simple structure, strong robustness, high cost-benefit ratio, and high reliability (Kuntanapreeda,

The rest of this paper is organized as follows. In section Literature Review, a literature review is performed. In section Proposed Method, the basic theories of PID parameter optimization and FOA are presented, the PSO-IFOA is proposed. In section Vibration Control Performance, Simulation and experimental tests are carried out to evaluate the PSO-IFOA method. Conclusions and future work are summarized in section Conclusions and Future Work.

The most recent publications relevant to this paper have mainly been concerned with two research streams: PID parameter optimization and FOA. In this section, we try to summarize the relevant literature.

The parameter adjustment of a traditional PID mainly relies on working experience. In Xu (

In recent years, many researchers have started to focus on the FOA. In Yu et al. (

Many PID parameter optimization approaches have been proposed in the above literature and have been applied in recent decades, but these also have some shortcomings. Firstly, PID controllers designed by different intelligent algorithms have diverse control effects on the same system. Secondly, conventional PID controllers have a worse control effect than PID controllers designed with an intelligent algorithm. Thirdly, due to the large non-linearily and hysteresis of semi-active seat suspension, it is necessary to design a control system with a faster response, more accurate control, and less overshoot to address these problems. Lastly, FOA has great advantages in terms of iteration rate and encoding efficiency but still has the potential to fall into a local optimum.

Therefore, a PSO-IFOA is proposed to adjust the parameters for the PID controller of an MRD-based semi-active seat suspension. The velocity formula of PSO is utilized to redefine the flight distance and direction of IFOA to reduce the possibility of blind search of individual fruit flies. The convergence precision of IFOA can be enhanced, and local optima can be avoided. Both a simulation model and an experimental system of the MRD-based semi-active seat suspension are established to evaluate the effectiveness and correctness of the proposed PSO-IFOA-PID method.

FOA is a global intelligent optimization algorithm that is established by simulating the foraging behavior of the fruit fly. The FOA can be implemented via the following steps (Liu et al.,

Step 1: Determine the population amount (_{max}), flying distance range (_{−axis}_{−axis}) of the fruit fly population.

Step 2: Calculate the random flight direction and distance to search for the food of the individual fruit fly.

Step 3: Calculate the distance between the individual fruit fly and the origin, and then calculate the flavor concentration parameter, which is the reciprocal of the distance.

Step 4: Substitute _{i} into the fitness function, calculate the value of the flavor concentration function _{i}, and find the best flavor concentration in the fruit fly population. In this paper, the minimum value is taken as the best flavor concentration.

Step 5: Obtain the best flavor value and the coordinates of (_{−axis}_{−axis}).

Step 6: When the smell concentration reaches the preset precision value or the iteration number reaches the maximal _{max}, the search stops. Otherwise, repeat Steps 2–5.

Because the flight distance of an individual fruit fly in FOA is within a fixed interval and the search direction is blind, the probability of individual fruit fly falls into a local optimum greatly increases. In order to enhance the capacity of global and local search, the

The position of particles in PSO is affected by the current speed, memory, and optimal location of the population. The search direction of an individual fruit fly could be guided by PSO. The velocity equation of PSO can be used to replace the random flight distance of FOA to improve the search capability; this is described as follows:

where _{x}_{1}, _{x}_{2}, _{y}_{1}, and _{y}_{2} are the learning factors; the random constants _{1} and _{2} are within [0, 1]; _{x}_{i} and _{y}_{i} are the flying speed of an individual fruit fly along the X and Y directions. The increase of the inertia weight can enhance the global search capability but decrease the local search capability and vice versa. Therefore, in order to achieve a good trade-off between global and local search capabilities, the inertia weight

where _{1} = 100, _{2} = 16, _{3} = 1, _{4} = 0.2, _{1}, _{2}, and _{3} are used to control the change rate of the inertial weight and the upper limit of the control parameters, and _{4} is used to control the upper and lower limits of the inertia weight. In this method, when the gap between the individual and the global optimum positions is large, the calculated inertia weight is large, which increases the individual's global search capability. Meanwhile, when the gap between the individual and the global optimum positions is small, the calculated inertia weight is small, which can accelerate toward the optimal point. _{1}-_{4} can meet our requirements in the calculation. The flowchart of the proposed PSO-IFOA is illustrated in

The change rule of inertia weight with iteration number.

Flowchart of PSO-IFOA.

In order to verify the search capability of the PSO-IFOA, four tests were conducted using four popular functions (i.e., Ackely, Rastrigin, Schewell, and Matyas) (Xu et al.,

The optimal solution of the four test functions.

FOA | 0.0421 | 0.0357 | −0.00175 | 3.54e-06 |

PSO | 6.68e-08 | 0.0368 | −0.000782 | 7.44e-13 |

IFOA | 0.00241 | 0.00112 | −0.0000741 | 9.80e-09 |

PSO-IFOA | 2.22e-15 | 7.11e-15 | −1.70e-20 | 8.06e-21 |

Convergence curves of the test functions.

As can be seen in

The feasibility of PSO-IFOA for optimizing PID parameters was investigated using a numerical model of a semi-active seat suspension system. Modeling of the semi-active seat suspension system mainly included two aspects, which were human body dynamics modeling and seat dynamics modeling. The research in this paper is mainly concerned with the vibration absorption performance of semi-active seat suspension, which is the vibration attenuation transmitted from a cab to a human body. In this situation, the human body can be considered to a mass block without considering its internal vibration characteristics. In the actual seat suspension, the cushion also possesses vibration damping performance due to its characteristics of stiffness and damping. Therefore, the vibration damping characteristics of the cushion should be considered in establishing the semi-active seat suspension model. A shear suspension structure was adopted in this research due to its good lubrication at the turning structure, and the friction resistance at the rotating structure was then ignored. In order to simplify the calculation process, a 2-DOF semi-active seat suspension model was established. The human body was simplified as a mass block with equivalent mass of _{1}, the cushion was simplified as a spring and a damper, with a massless elastic coefficient and a damping coefficient of _{1} and _{1}, respectively. The suspension was regarded as a subsystem with equivalent mass of _{2}, equivalent stiffness of _{2}, and variable damping coefficient of _{2}. The kinematics equation was established according to the 2-DOF semi-active seat suspension model, as shown in Equation (12).

where _{2} is the displacement response of the top plate of the seat suspension, and _{1} is the displacement response of the human body; ẋ_{1} and ẍ_{1} are the first and second derivatives of _{1}, ẋ_{2}, and ẍ_{2} are the first and second derivatives of _{2}, and _{1} = 19,496 N/m, _{2} = 150,261 N/m, _{1} = 2,165 Ns/m, _{2} = 1,600 Ns/m, _{1} = 18 kg, _{2} = 70 kg.

The kinematic Equation (12) was transformed in Laplace transform, and the transfer function of human displacement response _{1} and vibration excitation

The parameters of the PSO-IFOA, IFOA, PSO, and FOA were set as: _{max} = 100, (_{−axis}, _{−axis})∈ (0, 5), _{1} = 0.999, ω_{2} = 0.001, ω_{3} = 2.0, and ω_{4} = 100.

In the simulation, a step command signal was input into the control system. The simulation time was 0.4 s. The convergence curves of the comprehensive performance index function

Control performance evaluation indicators of the controllers.

^{*} |
|||||
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σ/% | 42.33 | 14.65 | 7.95 | 0 | 0 |

_{s}/s |
0.113 | 0.094 | 0.098 | 0.078 | 0.052 |

_{r}/s |
0.028 | 0.032 | 0.046 | 0.091 | 0.062 |

_{s} is the adjustment time

In order to evaluate the effectiveness of the PSO-IFOA-optimized PID controller, an MRD-based semi-active seat suspension system was established using Matlab/Simulink. The MRD damping effect was considered in this model. The displacement and acceleration responses of the human body were measured under different excitations such as collision and harmonic and random vibrations that were imposed on the seat model. The vibration control performances of the FOA-PID, PSO-PID, IFOA-PID, and PSO-IFOA-PID methods are shown in

Acceleration and displacement responses under collision vibration.

The displacement and acceleration responses of the human body in the condition of collision vibration are shown in

The displacement and acceleration responses of the human body in the condition of harmonic vibration are shown in

Acceleration and displacement responses under harmonic vibration.

Acceleration response characteristics under random vibration.

RMS (m/s^{2}) |
0.4112 | 0.3057 | 0.2441 | 0.1799 | 0.1634 |

PTP (mm) | 3.9362 | 3.5095 | 3.1193 | 2.5494 | 2.2162 |

VDV (m/s^{1.75}) |
1.5356 | 1.3156 | 1.1165 | 0.9928 | 0.9225 |

The design principle of MRD is that the curing degree of magnetorheological fluid (MRF) is controlled in real time by changing the magnetic field intensity at the damping channel so as to achieve the purpose of controllable damping force. The structure of the MRD is shown in

Structural diagram of MRD. One to twenty-two are the piston rod, end cover, pressing plate, nut-M5, washer, screw-M5, guide holder, seal ring, O-ring (41.2 × 3.55A), cylinder block, piston, coil, spring washer, nut-M12, O-ring (38.7 × 3.55G), floating piston, screw-M5, nut-M5, sealing washer, joint, working space 1, and working space 2, respectively.

In order to make the design of MRD more reasonable, the key sizes of the MRD are optimized by the genetic multi-objective optimization algorithm, which possesses better accuracy in achieving multi-objective optimization. The implementation of the optimization processes can be achieved through the following steps.

Step 1: Define the damping force equation and the adjustable multiple calculation model of the MRD, which is as follows:

where _{η} is the non-adjustable viscous damping force, _{τ} is the adjusted coulomb damping force, η, τ, and v are the dynamic viscosity, shear yield stress, and flow velocity of MRF, respectively. _{p}, D, and h indicate the effective length, effective area of the inner ring, inner diameter, and clearance thickness of the damped channel, respectively.

Step 2: Establish the mathematical model of the optimized objective function, which as follows:

where m and n are the weighting coefficients, and the sum of

Step 3: Set the optimization variables and the corresponding value range. These are shown in Equations (17) and (18).

where

Photograph of the developed MRD.

The MRF for this experiment is MRF-250, purchased from Zhang Dongnan intelligent materials studio. It is comprised of soft magnetic carbonyl iron particles (average diameter: 8 μm, density: 7.86 g/cm^{3}; Beijing DK Nano Technology Co., Ltd.), dimethyl silicone oil (viscosity: 100 cSt at 25°C, density: 0.965 g/cm^{3}; Shin-Etsu, Japan), sodium dodecylbenzenesulfonate, oleic acid (purity 90%), graphite, and diatomite powder. The zero-field viscosity, saturation yield stress, and working temperature of MRF-250 are 242.5 mPa•s, 55.25 kPa, and −40 to 150°C, respectively.

Vibration experiments were performed on the semi-active seat suspension with MRD to evaluate the actual control performance of the proposed control method. The experimental system consists of a 6-DOF vibration table (model 6ZYD, rated load: 500 kg, frequency: 50 Hz, maximum displacement and acceleration: ±400 mm and 50 m/s^{2}), a semi-active seat suspension with MRD, two acceleration sensors (model CT1005L, sensitivity: 50 mv/g, frequency range: 0.5–800 Hz, measuring range: 0–100 g, maximum impedance and linearity: 100 Ω and 1%), a constant current adapter (model CT5204, maximum frequency, output amplitude, accuracy, and noise: 0.31 KHz, 10 VP, 1.5%, and 1 mVrms), a data acquisition card (model PCI8735, measuring range: 0–10 V, accuracy: 0.0001, non-linearity: ±1 LSB, sampling rate: 500 KHz), a programmable current source (model DP811A, voltage range: 0–40 V, current range: 0–5 A, maximum response speed: 50 μs, resolution: 1/0.5 mV), and a digital signal processor (model TMS320F28335). The main performance parameters of the digital signal processor are shown in

Main technical indicators of the TMS320F28335 development board.

Master processor | TMS320F28335, dominant frequency: 150 KHz |

SRAM | 34 K × 16 bits in chip, 0 waiting; 512 K × 16 bits out of chip, 15 ns. |

FLASH | 256 K × 16 bits in chip, 36 ns; 512 K × 16 bits out of chip, 70 ns. |

ROM | BOOT ROM 8 K × 16 bits in chip; OPT ROM 1 K × 16 bits out of chip, 15 ns. |

A/D | 2 × 8 channels in chip; resolution: 12 bits; switching rate: 80 ns. |

HOST USB2.0 | One channel; full speed. |

CAN bus | One channel; maximum transmission rate: 1 Mbps. |

The 6-DOF vibration table consists of a foundation platform, a top platform, and six hydraulic cylinders, which can realize shock vibration, simple harmonic vibration, random vibration, and path spectrum reappearance. One acceleration sensor is used to measure the acceleration response of the human body, and another acceleration sensor is used to measure the excitation acceleration of the seat suspension. The constant current adapter is used to provide appropriate working voltage for the acceleration sensors, meanwhile, which can amplify the signal detected by the sensors and de-noise the measured signal. The data acquisition card is used to collect data and transmit the collected data to the controller and computer. The digital signal processor is the core of the whole control system and is employed as the controller for the semi-active seat suspension with MRD. Semi-active seat suspension with MRD is a kind of suspension system that uses MRF as a damping medium and is designed by using the rheological effect of MRF. The damping force of the suspension can be adjusted in real time according to the vibration state of the automobile cab. Compared to other suspension systems, semi-active seat suspension with MRD possesses the strengths of a simple structure, controllable performance, fast response, strong adaptability, and continuously adjustable damping force.

^{2}). The experiments verify the effectiveness and superiority of the purposed PSO-IFOA-PID control method.

Evaluation indices of the acceleration response.

RMS (m/s^{2}) |
0.7475 | 0.5474 | 0.4536 | 0.3242 | 0.2573 |

PTP (mm) | 6.0759 | 5.1708 | 4.8066 | 3.9023 | 3.1881 |

VDV (m/s^{1.75}) |
1.1574 | 0.9888 | 0.9048 | 0.7573 | 0.6637 |

This paper proposed a PSO-IFOA-PID control method to improve the control performance for an MRD based semi-active seat suspension system. In order to verify the feasibility and superiority of the PSO-IFOA-PID, the search and control parameter optimization ability of traditional PID, FOA-PID, PSO-PID, IFOA-PID, and PSO-IFOA-PID were compared. The results indicated that the PSO-IFOA-PID had better optimization accuracy, faster convergence speed, and higher convergence precision in solving four test functions. Meanwhile, the PSO-IFOA-PID exhibited the advantages of adjusting the control parameters with better convergence speed and precision, and a shorter adjustment time, without overshoot, and having better steady and dynamic response characteristics. Furthermore, example simulations and experiments using the traditional PID, FOA-PID, PSO-PID, IFOA-PID, and PSO-IFOA-PID were carried out, and the results of both the simulations and experiments indicated that PSO-IFOA-PID control was the most ideal method.

In future work, new intelligent algorithms should be researched to achieve better response characteristics for the control performance of the semi-active controller of MRD seat suspension. Moreover, the temperature of MRD rises when it has been working for a long time, which will increase the internal pressure of the cylinder and result in the leakage of MRF. This adversely affects the damping characteristics of MRD, so further study is needed on how to improve the damping characteristics by controlling the temperature, and relevant experiments will also need to be carried out.

The datasets generated for this study are available on request to the corresponding author.

NW, XL, and KW: conceptualization, methodology, and formal analysis. NW, KW, ZL, and HH: software. WL, NW, and TS-G: validation. NW, WL, and HH: investigation. XL and ZL: resource and data curation. NW and KW: writing–original draft preparation and visualization. HH, TS-G, and WL: writing–review and editing. XL: supervision and project administration.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors would like to thank the reviewers for their contributions to this paper.

The Supplementary Material for this article can be found online at:

Experimental system.