Performance Analysis of Electro-Hydraulic Thrust System of TBM Based on Fuzzy PID Controller

Abstract

The tunnel boring machine (TBM) is widely used in tunnel construction projects. The thrust system plays a crucial role to drive the machine ahead and support gripper shoes stably while tunneling. More and more attention has been paid to the pressure and velocity regulation efficiency as the TBM advances in complex rock conditions to ensure the stabilization of the tunneling process. A thrust hydraulic control system, assembled with a proportional pressure reducing valve, is established with system operating parameters. The mathematical model of the thrust electro-hydraulic system is revealed. To improve the control characteristics of the thrust system, a self-tuning fuzzy PID controller is introduced in the pressure and velocity regulation procedures. After that, tests on a Φ2.5 m scaled TBM test rig are carried out. The test results show that the thrust system adopting the fuzzy PID controller results in less oscillation and a smoother regulation process. It takes less time to reach the target goal of pressure regulation with less vibration during the pressure regenerating periods, and both systems of conventional PID controller and fuzzy PID controller are qualified in velocity regulation movements. The proposed control methods show better benefits in reduction of vibrations and shorter time of regulation to stable conditions, which extends the machine’s life and affects the acceleration of the tunneling process.

1. Introduction

With the rapid development of big cities and the sustaining expansion of transport systems, demands of underground space exploration and utilization have been reasonably growing [1,2,3]. A tunnel boring machine (short for TBM) is a rock crushing machine, with continuous operation of slagging and supporting integrated. It is developed from shield tunneling technology [4,5,6,7]. The modern shield machine is integrated with mechanical, electrical, hydraulic, sensing and information technology, with functions of cutting soil, transporting soil ballast, assembled tunnel lining, measuring, orientation and rectification. More and more tunnels are employed to accommodate transportation systems, electricity and communication constructions at present, which leads to an extensive application of TBM in subway, railway, highway, municipal and hydroelectric tunnel projects [8,9,10,11,12,13,14,15,16]. TBM, with its characteristics of safe, inexpensive and highly efficient, plays a significant role in promoting the country’s modernization and urbanization.

A typical mainframe mechanical structure of hard rock TBM consists of cutterhead system, support system, propel cylinders and gripper shoes, as shown in Figure 1. The thrust system is a key part of TBM. The actuators of TBM are adopted by hydraulic cylinders due to their high power/mass ratio, fast response, and high stiffness [17,18]. The thrust system accomplishes the task of driving the machine ahead and supporting gripper shoes stably while tunneling and rectifies the attitude of TBM at the same time, which ensures the TBM to march along the expected path. At present, the thrust control is majorly relied on by machine drivers, whose experience is the conclusive element for the tunneling project.

Many studies focused on automation control in tunnel engineering projects have been carried out. Yang et al. [19] explored a numerical method predicting the mechanical behavior of the operating railway bridge and culvert based on the practice of large diameter slurry balance shield for boring North Huancheng Road underground expressway tunnel in Hangzhou. Hou et al. [20] designed a new propulsion system for a shield tunneling machine based on compliance characteristics. A new shield thrust system was designed by means of the compliance characteristics comparison. Results showed that the compliance index of the new shield thrust system increased by 25% compared to that of existing one. Venkaiah et al. [21] proposed a proportional valve-controlled semi-rotary electrohydraulic actuator for horizontal axis wind turbine pitch movement by feedforward fractional-order feedback controller. The proposed controller response has been compared with existing data of a 1.5 MW wind turbine. Feedforward fractional-order proportional–integral–derivative controller with adaptive teaching–learning based optimization algorithm was developed for wind turbine control application. The proposed controller performance has been found better compare to the existing result. Huang et al. [22] analyzed the force of an open TBM gripping-thrusting-regripping mechanism, which can be used either to estimate the thrust forces of the cylinders required to resist against the tunneling loads, or to predict the tunneling loads using the measured thrust forces of these cylinders. Achieving the thrust force by controlling the hydraulic cylinders was not studied in their work. Nogales et al. [23] developed a parametric analysis related with the TBM-thrust effects on FRC segments, using a nonlinear 3D FEM. There were still observed lacks and gaps related to the optimum reinforcement design (FRC strength class and/or amount of traditional steel bar reinforcement). Li et al. [24] studied a tunneling parameter prediction method for TBM construction control parameters and load parameters based on the support vector regression (SVR). Mandal et al. [25] designed an optimized model-free controller to achieve good tracking of the output position of the piston by a rugged electrohydraulic system. By coupling a model-free fuzzy controller with a feedforward controller with all the parameters estimated by a real-coded genetic algorithm, excellent responses with good disturbance rejection capability and energy efficiency have been achieved.

Among the above research, the influence factor of thrust force and velocity were studied intensively. The control methods of a thrust system to achieve accurate target values were hardly mentioned. Therefore, this paper presents a novel electro-hydraulic thrust control system. To verify the control effects, a self-tuning fuzzy PID controller is conducted in the thrust system, in contrast to a conventional PID controller. A Φ2.5 m scaled TBM test rig is designed and assembled to simulate TBM under engineering projects. The thrust system with the adopted fuzzy PID controller shows less oscillation and a smoother regulation process, with less impact for the mechanical parts of TBM.

2. Description of Thrust Hydraulic Control System

In consideration of complex rock environments, the regulation of pressure and speed is a key part during the whole tunneling process. A proportional pressure reducing valve is adopted in the thrust hydraulic control system to achieve smooth and stepless regulation effects. The thrust hydraulic control system is majorly made up of a pump, proportional pressure reducing valve, safe valve, propel cylinder, and oil pipe, as shown in Figure 2.

By adjusting the electric current through the coils of the proportional pressure reducing valve, the working pressure of propel cylinders can be regulated to adapt to different surrounding rock conditions, especially when a TBM moves across two rock layers. The thrust pressure must be set higher to resist bigger thrust resistance force when marching in Ⅰ and Ⅱ rock layers, which desires slower cylinder movements. Oppositely, lower thrust pressure and bigger cylinder velocity are set when advancing in Ⅲ and Ⅳ rock layers to achieve high efficiency and good economic benefits. The save valve is settled to prevent thrust systems from unexpected damage in extreme circumstance, which is closed when the machine is working in a normal process. When thrust is applied, the cylinder piston rod moves forward, the pressure and displacement of which are measured by a pressure sensor and displacement sensor in real time. With the control closed-loop, the pressure and speed of the system can be obtained with anticipated efficiency.

To give a glimpse of the variation process of thrust pressure and velocity in tunnel engineering, a set of engineering data is introduced here. The data come from a water diversion project in the Jilin province of China. To classify the surrounding rock conditions, the hydropower classification method (HC method) is employed, by which the surrounding rock were classified into five classes from class I to class V. In this classification, class I represents the hardest and most complete class and class V represents the weakest and most broken class, as shown in

Table 1. Qualitative descriptions of rock classes with HC method.

Class	Qualitative Description
I	The hardest and most complete
II	Hard and complete
III	Relatively hard and complete
IV	Relatively weak and broken
V	The weakest and most broken

.

During the whole engineering project, the machine tunnels through several rock layers, including 191 m, 4125.7 m, 1822.5 m and 552 m of Class II, III, IV and V rock layers, according to the geological anterior detection. Figure 3 and Figure 4 show the changing process of pressure and velocity of the thrust hydraulic control system. A good TBM should be equipped with a thrust hydraulic system adaptable to different rock layers and external sudden load.

3. Mathematical Modeling

In the tunneling process, the output flow of the proportional pressure reducing valve can be revealed as:

$${\mathrm{q}}_1={\mathrm{K}}_{\mathrm{q}}{\mathrm{x}}_{\mathrm{v}}-{\mathrm{K}}_{\mathrm{c}}{\mathrm{p}}_{\mathrm{L}}$$

(1)

where q₁ is the flow rate (m³/s), K_q is the valve flow gain (m²/s), x_v is the spool displacement (m), K_c is the valve flow-pressure coefficient (Pa⁻¹⋅m³/s), and p_L is the load pressure (Pa).

By Newton’s laws of motion, we can find the dynamics equation of the spool as:

$${\mathrm{k}}_{\mathrm{i}}\mathrm{i}-{\mathrm{k}}_1{\mathrm{x}}_{\mathrm{v}}={\mathrm{m}}_1\frac{{\mathrm{d}}^2{\mathrm{x}}_{\mathrm{v}}}{{\mathrm{dt}}^2}+{\mathrm{D}}_1\frac{{\mathrm{dx}}_{\mathrm{v}}}{\mathrm{dt}}$$

(2)

where k_i is the current force gain (N/A), i is the output current of solenoid (A), k₁ is the stiffness of spring (N/m), m₁ is the mass of the spool (kg), and D₁ is the coefficient of viscous friction (N⋅s/m).

The current characteristic equation of the proportional solenoid coil can be written as:

$$\mathrm{u}=\mathrm{L}\frac{\mathrm{di}}{\mathrm{dt}}+\mathrm{iR}+{\mathrm{K}}_{\mathrm{v}}\frac{{\mathrm{dx}}_{\mathrm{v}}}{\mathrm{dt}}$$

(3)

where u denotes the output voltage of the solenoid coil (V), L is the inductance (H), R is the resistances of coils and amplifier (Ω), and K_v is the coefficient of velocity back electromotive force induced by armature displacement (V⋅s/m).

In view of the oil flow through the orifice of the throttle between the spool and circle, the flow rate of the pressure reducing valve can be also presented as:

$${\mathrm{q}}_1={\mathsf{\alpha }\mathsf{\pi }\mathrm{x}}_{\mathrm{v}}\mathrm{d}\sqrt{\frac{2\left({\mathrm{p}}_{\mathrm{P}}-{\mathrm{p}}_{\mathrm{L}}\right)}{\mathsf{\rho }}}$$

(4)

where α denotes the flow rate coefficient, d is the diameter of the spool (m), p_P is the pump pressure (Pa), and ρ is the oil density (kg/m³).

The flow equation of the cylinder is conducted as:

$${\mathrm{q}}_{\mathrm{L}}=\mathrm{A}\frac{\mathrm{dx}}{\mathrm{dt}}+{\mathrm{C}}_{\mathrm{tc}}{\mathrm{p}}_{\mathrm{L}}+\frac{\mathrm{V}}{\mathrm{E}}\frac{{\mathrm{dp}}_{\mathrm{L}}}{\mathrm{dt}}$$

(5)

where q_L is the cylinder flow (load flow) (m³/s), A is the effective working area (m²), x is the displacement of cylinder (m), C_tc is the coefficient of leakage (Pa⁻¹⋅m³/s), V is the total actuating volume (m³), and E is the effective bulk modulus (Pa).

The dynamics equation of the cylinder is carried out as:

$${\mathrm{Ap}}_{\mathrm{L}}=\mathrm{M}\frac{{\mathrm{d}}^2\mathrm{x}}{\mathrm{dt}}+{\mathrm{B}}_{\mathrm{v}}\frac{\mathrm{dx}}{\mathrm{dt}}+\mathrm{Kx}+{\mathrm{F}}_{\mathrm{L}}$$

(6)

where M is the total mass of the moving parts (kg), B_v is the viscous damping coefficient (N⋅s/m), K is the stiffness of the load (N/m), and F_L is the load force (N).

4. Electro-Hydraulic Control System Design

4.1. Control Strategy

The working pressure and velocity of the thrust system should be regulated to adapt to different rock layers and mixed load to balance safety and efficiency. The thrust system should attain the control parameters of the thrust speed on one hand and perform pressure regulation to maintain the face stability on the other hand. To achieve a preferable performance in the pressure and speed control system, which comprises controllers, amplifiers, valves, cylinders and sensors, a proper controller is needed to improve the system control characteristic.

Pressure regulation is under the control of the proportional pressure reducing valve. The signal of the working pressure of the propel cylinders detected by pressure sensors is delivered back to the control units, which constitutes the closed-loop control system, as shown in Figure 5.

Similar to the thrust pressure control, the velocity control is carried out by the proportional pressure reducing valve. The displacement of cylinders is detected by displacement sensors, whose signal will be fed back to the control units after that. Then, the displacement signal will be differentiated to velocity signal to accomplish the closed-loop control, as illustrated in Figure 6.

4.2. Design of Fuzzy PID Controller

In this work, we first employ a conventional PID controller to the thrust system. Then, a fuzzy PID controller is adopted in the control loop. The controller is customized for the thrust system, which requires appropriate modification of the fuzzy PID controller [26,27,28]. Many scholars have studied fuzzy control in various aspects and algorithms [29,30]. Castillo et al. [31] presented a comparative analysis of Type-1 and Type-2 fuzzy controllers to drive an omnidirectional mobile robot in line-following tasks using line detection images. Mohammadzadeh et al. [32] proposed a novel robust and asymptotically stable controller to synchronize uncertain fractional order chaotic systems. Its design is based on the linear matrix inequality (LMI) technique.

In conventional PID controller design, the parameters of the controller can be conducted as below:

$$\mathrm{u}\left(\mathrm{k}\right)=\mathrm{u}\left(\mathrm{k}-1\right)+\mathsf{\Delta }\mathrm{u}\left(\mathrm{k}\right)$$

(7)

$$\mathsf{\Delta }\mathrm{u}\left(\mathrm{k}\right)={\mathrm{K}}_{\mathrm{p}}\cdot \left(\mathrm{e}\left(\mathrm{k}\right)-\mathrm{e}\left(\mathrm{k}-1\right)\right)+{\mathrm{K}}_{\mathrm{i}}\cdot \mathrm{e}\left(\mathrm{k}\right)+{\mathrm{K}}_{\mathrm{d}}\cdot \left(\mathrm{e}\left(\mathrm{k}\right)-2\mathrm{e}\left(\mathrm{k}-1\right)+\mathrm{e}\left(\mathrm{k}-2\right)\right)$$

(8)

where u(k) denotes the value of the control subject, e(k) is the error between u(k) and the desired value, and K_P, K_i and K_d denote the proportional, integral and derivative coefficient, respectively.

As for the fuzzy PID controller, self-tuning fuzzy PID is most widely used in electro-hydraulic systems. The controller takes error (defined as e) and change rate of error (defined as ec) as its input. In order to enhance the control characteristics, the self-tuning fuzzy PID controller can adjust its parameters adaptively to meet the system requirement when e and ec changes in real time. The structure of the self-tuning fuzzy controller is shown in Figure 7.

In a sampling period, the deviation between desired value and the practical value e and its change rate ec are settled as inputs, while the outputs are the change rate of PID controller parameters, which are Δk_P, Δk_i and Δk_d.

4.3. Definition of Domain and Membership

The domain of the fuzzy PID controller must be formatted uniformly, combining with the real thrust control system. In this work, we adopted general relative domain. The input domain of e is {−3, 3} and domain of ec is {−3, 3}. As for the output domain, after several attempts, the domain is ascertained as {−0.3 0.3} of Δk_P, {−0.03 0.03} of Δk_i and {−0.02 0.02} of Δk_d. The fuzzy subsets of variables are defined as {NB, NM, NS, ZO, PS, PM, PB}, which represents negative big, negative middle, negative small, zero, positive small, positive middle, and positive big, respectively. The membership functions of input variables and surface viewer of the PID controller parameters are shown in Figure 8 and Figure 9, respectively.

4.4. Fuzzy Control Rules

According to engineering experience and technical attempts, fuzzy rules are drawn as

Table 2. Fuzzy control rules.

e	ec
	NB	NM	NS	ZO	PS	PM	PB
NB	PB/NB/PS	PB/NB/NM	PM/NM/NB	PM/NM/NB	PS/NS/NB	ZO/NS/NM	ZO/ZO/PS
NM	PB/NB/PS	PM/NM/NM	PM/NM/NB	PS/NS/NM	PS/NS/NM	ZO/ZO/NS	NS/PS/ZO
NS	PM/NM/ZO	PM/NM/NS	PS/NS/NM	PS/NS/NM	ZO/ZO/NS	NS/PS/NS	NS/PS/ZO
ZO	PM/NM/ZO	PS/NS/NS	PS/NS/NS	ZO/ZO/NS	NS/PS/NS	NS/PS/NS	NM/PM/ZO
PS	PS/NS/ZO	PS/NS/ZO	ZO/ZO/ZO	NS/PS/ZO	NS/PS/ZO	NM/PM/ZO	NM/PM/ZO
PM	PS/NS/PB	ZO/ZO/NS	NS/PS/PS	NS/PS/PS	NM/PM/PS	NM/PM/PS	NB/PB/PB
PB	ZO/ZO/PB	NS/PS/PM	NS/PS/PM	NM/PM/PM	NM/PM/PM	NB/PB/PS	NB/PB/PB

shows. The rules are identical whether the control variable is the pressure of the pressure reducing valve or the velocity of the cylinder, while the outputs of the fuzzy control system are completely diverse.

5. Experimental Results and Analysis

5.1. Test Rig

In this project, a test rig of TBM is built up to simulate the real machine. Figure 10 shows the test rig, which contains the mechanical structure, hydraulic pump-valve station and electrical cabinets. The Φ2.5 m scaled TBM test rig consists of four dominating systems: cutterhead system, support and gripper system, thrust system and load simulation system. The load simulation system simulates thrust and torque load while tunneling by shell structure with hydraulic cylinders and motors. The thrust system consists of four propel cylinders with two on the right of the vertical axis and two on the left. The whole tunneling process including advancing, supporting and shifting to the next step can be achieved proportionally to tunnel engineering with TBM conveniently.

Table 3. Main parameters of the thrust electro-hydraulic system of the Φ2.5 m scaled TBM test rig.

Parameter	Value	Unit
Rod diameter of propel cylinder	180	mm
Inside bore diameter of propel cylinder	125	mm
Stroke of propel cylinder	530	mm
Control pressure of pressure reducing valve	0–310	bar
Max. flow rate of pressure reducing valve	40	L/min
Max. output current of solenoid of pressure reducing valve	800	mA
Setting pressure of safe valve	320	bar
Max. thrust force (4 cylinders in total)	2000	kN

shows the main parameters of the thrust electro-hydraulic system of the Φ2.5 m scaled TBM test rig.

To sample and transmit analogical and digital I/O variables, industry PLC is adopted as the lower machine, while the host computer is a personal computer (PC) with Wincc based human–computer interface. The host computer and lower machine communicate with each other via industry internet. In addition, the OPC server is led-in so as to exploit the advantage of Simulink interface in Matlab software in control and signal analysis. The algorithm of the fuzzy PID controller is shown in Figure 11.

5.2. Test Results

The thrust pressure regulation tests are carried out on the Φ2.5 m scaled TBM test rig. Figure 12 shows the geological conditions of a water diversion project, as mentioned in Section 2, in the Jilin province of China. Different sections in different colors represent the rock layers in the project. The darker the section depicts, the harder the surrounding rock circumstance is. The TBM hydraulic systems suffers intensive load impact, especially when the machine crosses disparate rock layers.

As shown in Figure 3, the thrust system varies from 80 bar to 140 bar in the whole section. In order to check out overshot value and response speed of the thrust control system, the differential pressure of pressure regulation should be in a reasonable range. Taking account of engineering conditions and control subject, we choose the pressure variation from 90 bar to 100 bar as the pressure increasing interval and 100 bar to 95 bar as the pressure declining interval.

The test cycle is set at 160 s, while thrust pressure goes up from 90 bar to 100 bar at the time of 50 s and thrust pressure decrease from 100 bar to 95 bar at the time of 120 s. The initial pressure accumulating process is built up by hydraulic oil flowing into the whole thrust system through oil pipes, hydraulic cylinders and propel cylinders, while the pressure of the thrust system increases from 0 bar to 90 bar. In this study, we focus on the pressure regulation behaviors when the thrust pressure goes up and decreases.

The test results of pressure regulation are shown in several figures. Figure 13 and Figure 14 depict the pressure regulation process of the existing system, while Figure 15 and Figure 16 show the control behaviors of the thrust system under conventional PID control, and Figure 17 and Figure 18 show the control behaviors of the thrust system under fuzzy PID control respectively. Due to the nonlinearity, caused by bulk modulus of oil and hydraulic pipes, and uncertainty of coupling characteristics of pressure and flow rate in an electro-hydraulic system, the thrust pressure fluctuates when the control signal changes. Considering an acceptable pressure error of 0.5 bar, thrust pressure reaches the target value in 30 s (50 s to 80 s) and 29 s (120 s to 149 s) in existing system, 45 s (50 s to 95 s) and 24 s (120 s to 144 s) under conventional PID control, while it takes 16 s (50 s to 66 s) and 13 s (120 s to 133 s) under fuzzy PID control, as shown in Figure 14, Figure 16 and Figure 18. Comparison of differential pressure under 3 types of systems is drawn in Figure 19. More characteristics of the control effects of the three types of control systems are shown in

Table 4. Control effects of three type of control systems.

Characteristics		Existing System	PID Control	Fuzzy PID Control
Overshoot	0–90 bar	9.3 bar	2.3 bar	5.0 bar
	90–100 bar	10.1 bar	9.5 bar	6.8 bar
	100–95 bar	4.3 bar	3.3 bar	2.8 bar
Settling time	0–90 bar	42 s	38 s	7 s
	90–100 bar	30 s	45 s	16 s
	100–95 bar	29 s	24 s	13 s

. The thrust system suffers from greater oil fluctuation in the existing system and under conventional PID control, which means bigger force and torque impact on the mechanical and hydraulic components. In the meantime, it takes a shorter amount of time for thrust pressure regulation under fuzzy PID control.

The test of velocity regulation is conducted into two phases, referring to velocity variation in tunnel engineering as drawn in Figure 4: Phase 1, time 0–50 s, velocity 1.5 mm/s; and Phase 2, time 50–100 s, velocity 3 mm/s. The displacement of the cylinder during the velocity regulation process is shown in Figure 20. Both control methods can smoothly achieve the target velocity in the dimension of cylinder displacement.

For further observation of two control systems, we choose two vital phases of the test to explore their control effects. As Figure 21 depicts, at the beginning phase when the hydraulic oil is compressed to build system pressure, the system adopting fuzzy PID control shows smoother characteristics and a quicker response. Regarding the velocity variation phase, both control systems are qualified. Thanks to the stability of rock layers, the advancing velocity of TBM is not so large in tunneling engineering.

Figure 22 shows the velocity variation of cylinders in two control systems during the velocity regulation process. Velocity oscillation exists in both systems because of the nonlinearity of an electro-hydraulic system. Regarding the other aspect, mechanical vibration inevitably occurs due to the large inertia of the whole TBM during the rotation of the cutterhead, which brings oscillation in the tunneling process.

Based on above discussion, two control systems are more than sufficient to reach the velocity regulation needs. The system oscillation of velocity control is in reasonable variation range.

6. Conclusions

The proportional pressure reducing valve is widely adopted in thrust hydraulic control systems to achieve smooth and stepless effects in the pressure and velocity regulation process. By establishing the mathematical model, the characteristics of the thrust control system can be revealed convectively. In this study, a novel electro-hydraulic system is conducted in the tunneling process efficiently. Two control methods are proposed and compared on the test rig. Above all, the main conclusions are as follows:

(1)

The model of the electro-hydraulic thrust system operating under the varying conditions was built and verified.

(2)

The thrust system with the fuzzy PID controller is more efficient in pressure regulation operation, which reaches the target value from 16–45 s in ascending interval and 13–24 s in descending circumstances. The larger variation of pressure changes, the more time the fuzzy PID system reduces.

(3)

Both systems can qualify the velocity need of tunneling projects. The thrust system of the fuzzy PID controller shows smoother impact when the system generates pressure at the beginning phase. The conventional PID controller can undertake the velocity regulation task as long as the tunneling routine has been continuously executed.

Overall, this study indicates the fuzzy PID controller is available and efficient in tunneling engineering in theory and practice. Further research on this project is being conducted taking into account uncertain geological conditions and sudden load variation in the tunneling prediction arrangement. The control methods of attitude correction and trajectory rectification with support system and torque cylinders for TBM will be a promising challenge to study to improve efficiency of the tunneling projects.