Fuzzy proportional integral differential control of magnetorheological clutch torque based on bee colony algorithm optimization

Abstract

As an intelligent transmission device, the magnetorheological (MR) clutch cannot realize its accurate torque control because it is difficult to establish its accurate torque control mathematical model. This paper designs a squeeze shear MR clutch. In order to achieve accurate torque control of the MR clutch, this paper proposes a fuzzy proportional integral differential (PID) control strategy based on the optimization of the bee colony algorithm. Based on the mechanical transmission experiment platform of the MR clutch, the performance of the torque control of the MR clutch is experimentally studied by using the real-time operating system Phar Lap ETS built by LabVIEW real-time module, it is found that the fuzzy PID control strategy based on bee colony algorithm can not only improve the torque control accuracy of the MR clutch by 70% compared to traditional PID control strategies but also increase the response speed by more than 50%.

Keywords

magnetorheological clutch torque control fuzzy proportional integral differential bee colony algorithm

1. Introduction

Due to its unique advantages such as fast response, low friction loss, and adjustable transmission torque, magnetorheological (MR) clutch has received widespread attention in the field of intelligent transmission and braking research, and has broad prospects in industrial applications. However, as a typical time-varying nonlinear high order system, it is difficult to establish its accurate torque control mathematical model, which limits the application of modern control theory in the torque control system of MR clutch. Cobanoglu et al. (2003) adopted the ON-OFF closed-loop control strategy to ensure that the speed difference between the input and output shafts of the magnetorheological limited slip differential (LSD) clutch is within the preset range. Park et al. (2006) and Shamieh and Sedaghati (2018) designed a sliding mode controller to control the MR brake to achieve optimal wheel slip control. Xinhua et al. (2017) used the improved Drosophila Optimization Algorithm (IFOA) and proportional integral differential (PID) control strategy to improve the response characteristics of the traditional PID controller to the MR brake. Veronneau et al. (2019) combined the MR clutch with the low friction hydrostatic transmission system, a high-performance wearable mechanical arm is designed, and three force control methods, namely, open loop, force closed loop and pressure closed loop, are proposed to achieve better interactive force control effect. Russo and Terzo (2011a, 2011b) analyzed the influence of temperature and speed on the model parameters of MR brake, and adopted model reference adaptive control to achieve fast and accurate dynamic tracking of braking torque. Moghani and Kermani et al. (2020) and Nguyen and Choi et al. (2014) proposed a PID control strategy based on the MR clutch to achieve the speed and torque regulation output of the control system. Hwang et al. (2019) introduced a 6-DOF tactile master robot assisted surgery system driven by MR clutch and brake, established a tactile feedback control system based on PID controller, and realized the accurate tracking of robot end effector. Yadmellat and Kermani (2014) proposed an open-loop control model based on MR actuator. Wang et al. (2019) developed an MR brake and applied it to a data glove with power feedback, using an adaptive fuzzy PID control scheme to achieve force feedback tracking control. Adiputra et al. (2016) developed a passive control ankle foot orthosis (PICAFO) based on electromyographic (EMG) signals and ankle joint position signals, using a fuzzy logic controller to control the output torque of the MR brake, achieving the goal of preventing foot sagging after stroke. Li et al. (2015) proposed a closed-loop MR clutch input output relationship linearization control scheme based on field programmable gate array (FPGA) to solve the nonlinear hysteresis behavior between the input current and output torque of the MR clutch. Erol et al. (2012) proposed a new control scheme to eliminate hysteresis in magnetorheological brakes, which involves embedding a Hall sensor in the magnetic flux path and using a PID controller to directly control the magnetic induction intensity. Guo et al. (2020) proposed a fuzzy fractional order PID (OFFO-PID) optimization algorithm to achieve vibration isolation and vibration reduction control of precision platforms with MR elastomers (MRE) devices. Andrade et al. (2018) introduced a MR knee joint driver for artificial limbs, which achieved fast torque response through PI control algorithm. Song et al. (2016) proposed a tactile control robot assisted surgery system based on MR control technology, and achieved good torque tracking control performance through sliding mode control algorithm. Kikuchi et al. (2012) developed a virtual bicycle system based on MR brake. On this basis, considering the impact of speed on braking torque, he proposed a torque compensation algorithm based on speed feedback.

The traditional PID controller is widely used in many industrial fields because of its simple structure and easy design. Its control parameters are fixed in the whole control process, and can maintain good global control performance for some linear systems. However, it is difficult to achieve the desired control performance in the presence of unknown nonlinearity, time delay, disturbance, and system parameter changes. The fuzzy logic control does not need the mathematical model of the controlled object, but simulates the thinking process of human operators through language rules. These rules reflect human experience or knowledge of how to control dynamic systems. In addition, the fuzzy control is nonlinear and adaptive, and robust under the influence of parameter changes and load disturbances. Zhao et al. (2022) designed a fuzzy adaptive proportional integral differential (PID) control algorithm to optimize the overshoot of speed and torque, fuel consumption and exhaust emissions of the traditional PID control strategy in the process of working condition switching of an extended range electric vehicle. Fotuhi and Bingul (2021) proposed the fuzzy logic torque controller with nonlinear friction compensation (NLFC) is used to improve the deteriorating trajectory tracking performance caused by these nonlinear elements in rotary series elastic actuator (RSEA) systems of humanoid robots. The hybrid force and position control base on fuzzy proportional-integral-derivative (PID) is proposed to improve the quality of robotic automatic grinding aviation blades by Zhang et al. (2020).

The design process of fuzzy control generally involves four parts: fuzzification, knowledge base, fuzzy reasoning, and clearness. However, these parts usually depend on the experience of the designer, which results in that the actual effect of fuzzy control is greatly affected by human factors, and it is difficult to achieve the optimal control effect. Therefore, this article takes the torque control system of MR clutch in shear mode as the research object and proposes a robust and practical control strategy to achieve torque control of MR clutch. In order to avoid the influence of human factors in fuzzy control as much as possible, fuzzy control knowledge bases such as bee colony algorithm are used to optimize the proportion factor and membership function.

This paper designs a new type of squeeze shear MR clutch and a fuzzy PID controller for torque control of MR clutch. Based on the MR clutch transmission experimental platform, a fuzzy PID control strategy optimized by bee colony algorithm is proposed. The real-time operating system Phar Lap ETS constructed by LabVIEW real-time module is used to experimentally study the torque control performance of MR clutch. Through experiments, compared with traditional PID control strategies, the control strategy designed in this paper can significantly improve the accuracy of torque control and shorten the response time. For the torque control of MR clutch, this paper provides a new method for the contradiction between fast and overshoot caused by the inability to adjust traditional PID control parameters in real-time, and also provides a new approach for its subsequent research.

2. Magnetorheological clutch

MR clutch is widely used in torque control devices because of its excellent performance. It usually works in shear mode, and realizes the flexible connection between driving and driven parts through external magnetic field. In this paper, a squeeze shear MR clutch structure with double gap and single coil is designed, as shown in Figure 1. The whole structure is composed of active rotor, driven rotor, housing, driving mechanism, and sealing device. The active rotor is composed of left and right drive discs and magnetic isolation rings, and is fixedly connected with the drive shaft. The magnetic separator ring is used to reduce the magnetic flux leakage in the radial direction, separate the drive disk from the driven disk, and form a working gap of a certain thickness. There is a dynamic seal between the right drive plate and the driven shaft, which can effectively prevent the leakage of MR fluid. The drive plate is designed to be thicker to install the magnetic field sensor, and the wire of the magnetic field sensor can be connected to the external conductive slip ring through the shaft hole of the drive shaft. The driving mechanism is composed of oil cylinder, pressure plate, ball spline, fastening sleeve and tapered roller bearing. The magnetic flow path of the MR fluid is composed of a magnetic shell, a driving disk and a driven disk. The structure can work in a single shear mode, and the current flowing into the excitation coil is converted into a magnetic field that can excite the rheological characteristics of the MR fluid, so that the MR fluid in the working gap can produce a controllable shear yield stress and finally generate a controllable torque between the master and slave moving shafts. To further improve the torque capacity of the MR clutch, the MR clutch can be controlled to work in the extrusion shear composite mode. The electro-hydraulic servo system controls the hydraulic extrusion mechanism to drive the pressure plate and the intermediate drive plate to move axially. With the help of the extrusion strengthening effect, the soft magnetic particles that have been arranged into magnetic chains under the magnetic field can be transformed into a strong chain structure with high strength, a stronger shear yield stress is obtained, resulting in greater transmission torque. Through the dual input control of the current of the excitation coil and the displacement of the electro-hydraulic system, higher transmission performance, and control performance can be obtained.

3. Fuzzy proportional integral differential control based on bee colony algorithm optimization

Figure 2 shows the basic structure of the fuzzy PID control system based on bee colony algorithm designed in this paper, which is mainly composed of three parts, namely, bee colony algorithm optimization, fuzzy logic, and PID controller. It can be seen that in the actual control process, the fuzzy controller adjusts the values of the three control parameters K_p, K_i, and K_d of the PID control in real time according to the error and the error change rate through the corresponding control rules to ensure the rapidity and stability of the system. Through the analysis of error e and error change rate e_c (de/dt), appropriate membership function is set, e and e_c are quantified into the universe of discourse, fuzzy control rules are designed according to actual requirements, fuzzy values of K_p, K_i, and K_d are calculated according to the rules, and then the change adjustment of PID parameters is obtained through fuzzification, and the self-tuning PID parameters can be obtained by adding with the initial PID parameters to improve the robustness and stability of the system. In addition, the fuzzy PID algorithm needs to set initial parameters, including K_e, K_ec, membership function and the initial value of PID parameters, etc. These parameters determine the effect and efficiency of the fuzzy PID. Therefore, the bee colony algorithm is used to optimize and iterate the system parameters to obtain the optimal parameters that conform to the fitness function.

3.1. Proportional integral differential controller design

The PID algorithm is based on the principle of error negative feedback, that is, the feedback is used to detect the deviation signal, and the deviation signal is used to control the controlled quantity. The controller itself is the superposition of proportion, integral and differential. Its functional block diagram is shown in Figure 3. Equation (1) is the ideal formula of PID controller under continuous system

u (t) = K c (e + \frac{1}{T_{i}} \int e (t) d t + T_{d} \frac{d e (t)}{d t})

(1)

where u(t) is the output of the controller; e(t) is the deviation between the set value and the feedback value; Kc is the amplification coefficient of the controller; Ti is the integral time constant of the controller; Td is the differential time constant of the controller. In this paper, the digital control system based on computer is adopted, and its principle is sampling control. Equation (2) is the positional PID control formula adopted in this paper

u (k) = K c (e (k) + \frac{T_{k}}{T_{i}} \sum e (k) + T_{d} \frac{e (k) - e (k - 1)}{T_{k}})

(2)

where u(t) is the output of the controller at a sampling time; e(t) is the deviation between the set value and the feedback value at a sampling time; T_k is the sampling time interval of the controller, which is 0.01 s in this paper.

Ziegler Nichols (ZN) parameter tuning method is the most basic engineering tuning method of PID controller, which is widely used in industrial control. This method tests the key information of the system through step response experiment and constant amplitude oscillation experiment, and is used for PID parameter tuning (ZN-PID). It has a strong ability of anti-load interference. Table 1 shows a critical proportionality method. The setting rule is: set the system as a closed loop system with pure proportional control, and put the gain K_c at a smaller value to put the closed loop system into operation; Then K_c gradually increases until

K c^{'}

, the system appears constant amplitude oscillation, and the system is in a critical stable state,

K c^{'}

is the critical gain, and its critical oscillation period

T^{'}

is measured. Finally, the PID parameters are initially set by the formula in the table, and on this basis, the satisfactory PID parameters can be obtained by fine tuning.

Table 1.

Parameter setting table of critical scale method.

Control law	$K c$	$T_{i}$	$T_{d}$
PI	0.45 $K c^{'}$	0.833 $T^{'}$	0
PID	0.6 $K c^{'}$	0.5 $T^{'}$	0.125 $T^{'}$
Final parameters	0.2	0.18	0.024

3.2. Design of fuzzy proportional integral differential controller

The torque error e and the torque error change rate e_c (de/dt) are taken as the input variables of the fuzzy controller, and the three parameter changes of the PID control are designed as the output variables $Δ$ K_p, $Δ$ K_i, and $Δ$ K_d of the fuzzy control, the fuzzy controller is designed as a two input three output form. The universe of torque error e and torque error change rate e_c is [−6, 6], and the universe of output variable adjusting PID control parameters $Δ$ K_p, $Δ$ K_i, and $Δ$ K_d is [−1, 1]. The continuous quantities within the set range are divided into seven different segments, and each segment corresponds to a fuzzy subset, which can simplify the fuzzy process of the control system. The two inputs and three outputs are divided into {PB, PM, PS, ZO, NS, NM, NB} 7 semantic values, representing positive big, positive middle, positive small, zero, negative small, negative middle, and negative big, respectively. To facilitate calculation, trigonometric functions are selected for input and output membership functions, as shown in Figures 4 and 5. PID parameters can be updated through the following equation (3).

K_{p} = K_{p 0} + Δ K_{p}, K_{i} = K_{i 0} + Δ K_{i}, K_{d} = K_{d 0} + Δ K_{d}

(3)

where K_p, K_i, and K_d are the adjusted PID parameters, and K_p0, K_i0, and K_d0 are the initial PID parameter values.

The principle of PID parameter tuning is as follows: since K_p can speed up the control process, at the beginning of the control process, in order to reduce the rise time and make the control process faster, K_p should be larger. In the middle stage of the control process, considering the system stability and control accuracy, it is necessary to adjust the K_p value to the middle value. In the last cycle, in order to reduce the steady-state error, the K_p value should be taken as a smaller value. K_d can restrain the overshoot and force error of the control system. Therefore, when the variation of force error is large, K_d should also be large. When the variation of force error is small, K_d shall be taken as the smaller value. K_i can improve the steady-state accuracy of the control system, but it will slow down the control process. Therefore, K_i should be smaller at the beginning to improve the response speed of the control system. In the medium term, in order to maintain the stability of the control system, K_i should be adjusted to the intermediate value. In the last stage, K_i should be larger in order to reduce the steady-state error and improve the control accuracy, but K_i is relatively small compared to K_p and K_d.

The core of fuzzy control design is to establish an appropriate fuzzy rule table based on the technical knowledge and experience of engineering designers. For the torque control of the MR clutch under the action of a single current studied in this paper, the rule base of control system optimization for the three parameters $Δ$ K_p, $Δ$ K_i and $Δ$ K_d are shown in Tables 2 and 3. The specific fuzzy rules are designed as follows:

(1) When e or e_c is smaller or equal to 0, K_p takes a larger value, K_i takes a larger value, and K_d takes a medium value;

(2) When e or e_c is large, K_p is larger, K_i is zero, and K_d is smaller;

(3) When e or e_c is medium, K_p is small, K_i is moderate, and K_d is moderate.

Table 2.

Fuzzy rules for the calculation of the $Δ K_{d}$ .

$Δ K_{d}$		e
$Δ K_{d}$		NB	NM	NS	ZO	PS	PM	PB
e _c	NB	PS	NS	NB	NB	NB	NM	PS
	NM	PS	NS	NB	NM	NM	NM	PS
	NS	ZO	NS	NM	NM	NM	PS	ZO
	ZO	ZO	NS	NS	ZO	NS	NS	ZO
	PS	ZO	ZO	PM	PS	PM	ZO	ZO
	PM	PB	NM	PS	PS	PS	PB	PB
	PB	PB	PM	PM	PM	PS	PS	PB

Table 3.

Fuzzy rules for the calculation of the $Δ K_{p}$ and $Δ K_{i}$ .

$Δ K_{p}$ / $Δ K_{p}$		e
$Δ K_{p}$ / $Δ K_{p}$		NB	NM	NS	ZO	PS	PM	PB
e _c	NB	PB/NB	PB/NB	PM/NM	PM/NM	PS/NS	ZO/ZO	ZO/ZO
	NM	PB/NB	PB/NB	PM/NM	PS/NS	PS/NS	ZO/ZO	ZO/NS
	NS	PM/NB	PM/NM	PS/NM	PS/NS	PS/NM	NS/PS	NS/PS
	ZO	PM/NB	PM/NM	PS/NS	ZO/ZO	NS/PS	NM/PM	NM/PM
	PS	PS/NM	PS/NS	PS/PM	NS/PS	NS/PM	NM/PM	NM/PB
	PM	PS/ZO	ZO/ZO	NS/PS	NM/PS	NM/PM	NM/PB	NB/PB
	PB	ZO/ZO	ZO/ZO	NM/PS	NM/PM	NM/PM	NB/PB	NB/PB

3.3. Optimization of bee colony algorithm

Fuzzy method can provide a simple strategy to maintain the classical PID structure through soft switching of controller gain. No matter what architecture is used, fuzzy has the advantages of adaptability to control nonlinear processes, flexibility in implementation, and no strict mathematical model. But the design parameters of fuzzy controller are determined by tracking error method or the experience of designers, and this process is often faced with a lot of trial and error process. In order to obtain better performance to solve the optimization problem, this paper uses the bee colony algorithm to optimize the control rules and initial parameters in the fuzzy control. Bee colony algorithm is a very simple and robust random optimization algorithm based on population. It simulates the foraging behavior of bees, and refers to bees using a variety of mechanisms, such as waggle dance, to best locate food sources and find new food. According to the research of Karaboga and Akay (2009) and Du et al. (2022), it was found that compared to genetic, particle swarm optimization, and differential evolution algorithms, bee colony algorithm is better than or similar to that of these algorithms although it uses less control parameters. The bee colony algorithm produces the candidate solution from its parent by a simple operation based on taking the difference of randomly determined parts of the parent and a randomly chosen solution from the population. This process increases the convergence speed of search into a local minimum. The bee colony algorithm model includes: honey source (possible solution in solution space), leading bee and waiting bee. The waiting bee is divided into reconnaissance bee and observation bee. The honeybee colony searches for the honey source as follows:

(1) Lead bees to find honey sources and share information through dance movements. The quality of honey sources is proportional to the range of movements;

(2) High quality honey source attracts more observation bees to collect honey near it. If higher quality honey source is found, observation bees will be leading bees;

(3) If the leading bee fails to find a higher quality honey source after Lt searches near it, it will give up the honey source and convert it into a reconnaissance bee, and then randomly generate a new honey source. Through the transformation of the roles of the three bees, they work together to search for high-quality honey sources.

Among them, leading bees can maintain the excellence of solution; Observing bees can improve the convergence rate; The reconnaissance bee can effectively make the algorithm jump out of the local optimal solution. The basic steps of the bee colony algorithm are:

Step 1

Algorithm initialization, that is, determine the dimension d and range of the solution space, set the total number of bees n, in which the leading bees and waiting bees each account for n/2, the final iteration number Nc and the maximum local search number Lt of honey source.

Step 2

Let all bees be scouts and randomly generate n solution vectors in the solution space according to Formula (4), calculate the fitness of each solution, and let the top n/2 bees be the initial leader bees

X_{i}^{j} = X_{\min}^{j} + r a n d \times (X_{\max}^{j} - X_{\min}^{j})

(4)

where i = 1, 2, …, n, j = 1, 2, …, d, rand are random numbers between [0, 1]. And are upper and lower limits of values, respectively.

Step 3

At the beginning of the search phase, each leading bee uses equation (5) to search for a better honey source in its neighborhood. When the adaptability of the new honey source is higher, the greedy selection mechanism is used to replace the old honey source with the new one. Where, φ is a random number of [−1, 1], l ∈ {1, 2,..., n/2}, and l ≠ i

V_{i}^{j} = X_{i}^{j} + φ (X_{i}^{j} - X_{l}^{j})

(5)

Step 4

The observation bee selects a leading bee according to the adaptability of the honey source, and uses the greedy selection mechanism to search for new honey sources in its neighborhood. The selection probability Ps is given by equation (6)

P_{s} = \frac{f i t n e s s_{i}}{\sum_{i = 1}^{n / 2} f i t n e s s_{i}}

(6)

where fitness is the fitness function.

Step 5

If a better honey source is not found after Lt times of searching around the position of a leading bee, the leading bee will be converted into a reconnaissance bee, and equation (4) will be used again for initialization.

Step 6

If the algorithm cycles N_C times, stop calculating and output the optimal fitness and the optimized parameter values, otherwise turn to Step 2.

The design parameters of the fuzzy controller have a great impact on the performance of the controller. In order to achieve better control effect, the objective function in the form of weighting of each performance index is used when the initial parameters are optimized by the bee colony, as shown in equation (7)

J_{1} = \int_{0}^{\infty} (w_{1} | e (t) | + w_{2} u^{2} (t)) d t + w_{3} \cdot t_{r} + w_{4} \cdot σ_{s}

(7)

where w₁, w₂, w₃, and w₄ are the weight values of each indicator, e(t) are the errors, t_r are the rise time, and σ_s are the overshoots.

Set the number of bee colonies to 30, the maximum number of iterations to 50 and the maximum number of honey source mining times to 50, after 30 runs of the bee colony algorithm, the standard deviation values are noted as 0.0623. According to the research by Konar and Bagis (2016), this result is satisfactory.

4. Experiments and results

4.1. Establishment of experimental platform

In order to verify the influence and robustness of fuzzy PID controller based on bee colony algorithm optimization on torque control of MR clutch, a real-time torque control system based on MR clutch is built, as shown in Figures 6 and 7. The whole experimental system consists of a mechanical transmission platform and a measurement and control system with LabVIEW as the core. The laptop is used as the upper computer for instruction input and measurement display of human-computer interaction interface, and the lower computer is a desktop computer (Phar Lap ETS) equipped with LabVIEW RT real-time operating system, which is used to receive the communication instructions of the upper computer and run the control algorithm in real time. At the same time, Phar Lap ETS has also installed a multi-function data acquisition card of PCI-6229 from NI Company, which can collect signals of MR clutch torque and MR fluid temperature, and output corresponding voltage signals according to the control algorithm to control the voltage and current output of the voltage source. In addition, Phar Lap ETS can also communicate with the programmable power supply of frequency converter and magnetic powder brake through RS485 serial port and RS232 serial port to load power and load.

In addition, LabVIEW and Simulink are mixed programmed to realize mutual communication and complementary advantages. In the process of mixed programming to develop virtual instruments and control systems, LabVIEW designs user graphical interfaces to be responsible for data acquisition, hardware control, operation control, and network communication; Simulink provides various operation and control algorithms for LabVIEW to call.

According to Table 1, the closed loop torque response curve and control voltage curve of the MR clutch corresponding to the PID controller are shown in Figure 8. It can be seen from Figure 8 that the adjustment time is about 1.6s, there is no steady-state static error, and the PID controller shows strong repeatability and stability for the same set torque value.

Figure 9 shows the torque control effect of the MR clutch under the step signal under the fuzzy PID control algorithm based on the bee colony algorithm optimization. It can be seen from Figure 9 that the step response curve can quickly track the change of step input signal in real time at any set value, and there is no error and overshoot in the whole process. For different set torque, the fuzzy PID control algorithm shows good control effect, which shows that it has good robustness.

4.2. Comparison between fuzzy proportional integral differential control and proportional integral differential control

Figure 10 shows the comparison of control effect between traditional PID and fuzzy PID. It is obvious from Figure 10 that PID control has obvious overshoot and oscillation, while fuzzy PID algorithm can restrain overshoot and reach the set value quickly. This is because compared with PID, fuzzy PID can optimize the initial value of the controller by using the bee colony algorithm, and can use fuzzy logic to adjust the three parameters of PID online in real time, so that when the error is large, it can increase the proportion coefficient to achieve rapid rise, while when the error is small, it can increase the integral coefficient to reduce overshoot and achieve steady state error. It can be seen from the error distribution diagram that the fuzzy PID control strategy based on the bee colony algorithm optimization can achieve better torque control effect for the MR clutch compared with the traditional PID control strategy, which not only has higher control accuracy but also has shorter response time.

Figure 11 shows the transient performance comparison between PID algorithm and fuzzy PID algorithm for torque control of MR clutch under step input. It can be seen from Figure 11 that when PID algorithm is applied, the transition process of the closed-loop system shows obvious oscillation, the maximum output overshoot is 16.7%, the rise time of the system is about 0.23 s, and the adjustment time is about 1.68 s. However, when the fuzzy PID algorithm is applied, there is no overshoot in the transition process of the closed-loop system. Its rise time is about 0.42 s, which is slightly greater than the rise time of the PID algorithm, but its adjustment time is 0.82 s, which is far less than the adjustment time of the PID algorithm. Table 4 compares the specific parameters of the torque response of the MR damper under two control strategies.

Table 4.

Comparison of control quality between PID algorithm and Fuzzy PID algorithm.

	PID algorithm	Fuzzy PID algorithm
Rise time $t_{r}$	0.23 s	0.42 s
Maximum overshoot $M_{p}$	16.7%	0%
Adjust time $t_{s}$	1.68 s	0.82 s
Number of oscillations	4	0

5. Discussion

The bee colony algorithm used in this paper has the difficulty of local optimization due to the imbalance between global search and local search. Some strategies have been used to develop variants of artificial bee colony (ABC) algorithm to further improve performance; but the improved ABC algorithm has a large computational load and is not suitable for high-dimensional optimization problems. Different selection mechanisms and initial population determination methods are used to improve the ability of the ABC algorithm. For jumping out of the local optimal, ant colony algorithm can be used to avoid convergence to the local optimal solution.

Based on the powerful properties of the ABC algorithm, using it can solve many combinatorial optimization problems. Especially for combinatorial optimization problems with relatively few studies, new and effective research can be conducted; for complex nonlinear systems, combining PID control with fuzzy control and adaptive control to achieve high synchronization control accuracy is also a part of our future work.

6. Summary

(1) A new type of squeeze shear MR clutch is designed, and based on the MR clutch transmission experimental platform, the performance of the torque control of the MR clutch is experimentally studied using the real-time operating system Phar Lap ETS built by LabVIEW real-time module.

(2) A digital PID controller is designed for torque control of MR clutch with single current input. Three parameters of the PID controller are adjusted by Ziegler Nichols parameter tuning method, and the closed-loop control quality with fast and no steady-state error is obtained, which lays a foundation for the performance comparison of the fuzzy PID controller.

(3) Aiming at the contradiction between rapidity and overshoot caused by the traditional PID control parameters cannot be adjusted in real time, a fuzzy PID control strategy based on bee colony algorithm optimization is designed. Through experiments, compared with the traditional PID control strategy, the control strategy designed in this paper can improve the accuracy of the torque control of the MR clutch by more than 70%, and reduce the response time by more than 50%.

Footnotes

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 research was supported by the National Key Research and Development Program of China (No. 2022YFB3403003) and the National Natural Science Foundation of China (No. 52074272 and No. 51575512) and the Postgraduate Research Practice Innovation Program of Jiangsu Province (No. KYCX23_2678).

ORCID iDs

Xiao Wang

Fei Chen

References

Adiputra

Ubaidillah

Mazlan

, et al. (2016) Fuzzy logic control for ankle foot orthoses equipped with MR brake. Jurnal Teknologi 78(11): 25–32.

Andrade

Filho

Vimieiro

CBS

, et al. (2018) Optimal design and torque control of an active MR prosthetic knee. Smart Materials and Structures 27(10): 1–28.

Cobanoglu

Gordaninejad

Evrensel

, et al. (2003) Time Response of a Controllable Multiplate MR Fluid Limited Slip Differential Clutch. In: Proceedings of Spie the International Society for Optical Engineering, San Diego, CA, March 02–06, 2003, pp. 514–523. Spie-Int Soc Optical Engineering.

Cui

Liu

, et al. (2022) Reformative artificial bee colony algorithm based PID controller for radar servo system. Electronic Research Archive 30(2): 2941–2963.

Erol

Gonenc

Senkal

, et al. (2012) Magnetic induction control with embedded sensor for elimination of hysteresis in MR brakes. Journal of Intelligent Material Systems and Structures 23(4): 427–440.

Fotuhi

Bingul

(2021) Fuzzy torque trajectory control of a rotary series elastic actuator with nonlinear friction compensation. ISA Transactions 115: 206–217.

Guo

Zhang

, et al. (2020) MR elastomer precision platform control using OFFO-PID algorithm. Advances in Materials ence and Engineering 2020: 1–9.

Hwang

Kang

Cha

, et al. (2019) A robot-assisted cutting surgery of human-like tissues using a haptic master operated by MR clutches and brakes. Smart Materials and Structures 28(6): 1–33.

Karaboga

Akay

(2009) A comparative study of artificial bee colony algorithm. Applied Mathematics and Computation 214: 108–132.

10.

Kikuchi

Kobayashi

Sugiyama

(2012) Torque Control of Virtual Bike with MR Fluid Brake and Sensory Evaluation for Difference Threshold of Pedal Resistance. In: IEEE Ras & Embs International Conference on Biomedical Robotics & Biomechatronics, Rome, Italy, Jun 24–27, 2012, pp. 1458–1463. IEEE.

11.

Konar

Bagis

(2016) Performance comparison of particle swarm optimization, differential evolution and artificial bee colony algorithms for fuzzy modelling of nonlinear systems. Elektronika Ir Elektrotechnika 22(5): 8–13.

12.

Yadmellat

Kermani

(2015) Linearized torque actuation using FPGA-controlled MR actuators. IEEE 20(2): 696–704.

13.

Moghani

Kermani

(2020) A lightweight MR actuator using hybrid magnetization. IEEE 25(1): 76–83.

14.

Nguyen

Choi

(2014) A new method for speed control of a DC motor using MR clutch. In: Active and Passive Smart Structures and Integrated Systems. San Diego, CA: Spie-Int Soc Optical Engineering.

15.

Park

Stoikov

Falcao da Luz

, et al. (2006) A performance evaluation of an automotive MR brake design with a sliding mode controller. Mechatronics 16(7): 405–416.

16.

Russo

Terzo

(2011a) Modelling, parameter identification, and control of a shear mode MR device. Proceedings - Institution of Mechanical Engineers 225(15): 549–562.

17.

Russo

Terzo

(2011b) Design of an adaptive control for a MR fluid brake with model parameters depending on temperature and speed. Smart Materials and Structures 20(11): 115003.

18.

Shamieh

Sedaghati

(2018) Development, optimization, and control of a novel MR brake with no zero-field viscous torque for automotive applications. In: Journal of Intelligent Material Systems and Structures. Madrid, Spain: Sage Publications Ltd.

19.

Song

B-K

J-S

Kim

, et al. (2016) Repulsive torque control of a robot-assisted surgery system using a MR haptic master. Proc IMechE Part I: Journal of Systems and Control Engineering 230(10): 1116–1125.

20.

Veronneau

Denis

Lebel

, et al. (2019) A Lightweight Force-Controllable Wearable Arm Based on MR-Hydrostatic Actuators. In: IEEE International Conference on Robotics and Automation (ICRA), Montreal, CA, May 20–24, 2019, pp. 4018–4024. IEEE.

21.

Wang

Pang

, et al. (2019) Development and control of an MR brake-based passive force feedback data glove. IEEE Access 7: 172477–172488.

22.

Xinhua

Yao

Jing

(2017) Parameters tuning approach for proportion integration differentiation controller of MR fluids brake based on improved fruit fly optimization algorithm. Symmetry 9(7): 109.

23.

Yadmellat

Kermani

(2014) Adaptive modeling of a MR clutch. IEEE ASME Transactions on Mechatronics 19(5): 1716–1723.

24.

Zhang

Jibin

, et al. (2020) Design and implementation of hybrid force/position control for robot automation grinding aviation blade based on fuzzy PID. International Journal of Advanced Manufacturing Technology 107(3): 1741–1754.

25.

Zhao

Lou

Zhang

(2022) Optimization and realization of the coordination control strategy for extended range electric vehicle. Machines 10(5): 297.