J. Cent. South Univ. Technol. (2010) 17: 537−543 DOI: 10.1007/s11771−010−0519−z
Motion control of thrust system for shield tunneling machine YANG Hua-yong(杨华勇), SHI Hu(施虎), GONG Guo-fang(龚国芳) State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China © Central South University Press and Springer-Verlag Berlin Heidelberg 2010 Abstract: The thrust hydraulic system of the prototype shield machine with pressure and flow compound control scheme was introduced. The experimental system integrated with proportional valves for study was designed. Dynamics modeling of multi-cylinder thrust system and synchronous control design were accomplished. The simulation of the synchronization motion control system was completed in AMESim and Matlab/Simulink software environments. The experiment was conducted by means of master/slave PID with dead band compensating flow and conventional PID regulating pressure. The experimental results show that the proposed thrust hydraulic system and its control strategy can meet the requirements of tunneling in motion and posture control for the shield machine, keeping the non-synchronous error within ±3 mm. Key words: shield machine; thrust system; synchronous motion; co-simulation; PID control
1 Introduction Shield tunneling machine is a kind of modern construction equipment. Tunneling with shield machine is the most promising and competitive tunnel forming method characterized by quick and safe construction, high automation, and environment friendliness [1]. Driven by hydraulic power, thrust system is a key part of shield machine. It performs the tasks of driving shield ahead and controlling the pose of shield, which ensures that the shield can advance along the expected route. During excavating, the thrust hydraulic cylinders push shield forward while the cutter head at the front of shield rotates and cuts the earth to enter a chamber full of pressurized earth and support the excavating face [2−3]. To prevent the tunneling route from deviation, the attitude and posture of shield machine should be regulated through thrust control. This is achieved by controlling the force and speed of multi-cylinder actuators. Current research on shield thrust is mainly focused on the excavated face support and the tunneling simulation by FEA analysis [4−5]. As for multi-cylinder coordination control, to the best of our knowledge, it is rarely researched as a special subject, except for the lifting machines such as the hydraulic elevator [6−7]. These applications are characterized relatively fixed load and concern speed most. Thrust system is different because of varying load, so the thrust force and the speed must be considered simultaneously.
A major issue considered in this work was synchronous motion control of the thrust cylinders for straight line tunneling, which were affected by uneven load acting on the cutter under the complex and poor excavating conditions. Proper control strategy was applied and preferable results were obtained.
2 Thrust system 2.1 Prototype system Working under varying nonlinear loads, the shield tunneling machine has a high installed power. The advancement of the shield tracking the designed line is dependent on the thrust forces of the hydraulic cylinders. The shield sometimes deviates from the alignment during excavation due to the complicated geological conditions and other unpredictable factors. Furthermore, tunneling in the curved line is also a sophisticated task fully related to the thrust system. On the other hand, to make the cutting face stay in position, the thrust speed control is strongly needed. To deal with these problems, it is greatly desirable that the thrusting pressure and speed can achieve smooth and stepless regulation. For this purpose, the hydraulic system for prototype shield thrust works according to the proportional pressure and flow regulation principle, as shown in Fig.1. In the engineering applications, the thrust hydraulic cylinders installed in the circle direction of the shield are separated into some groups to implement simple controlling respectively, as shown in Fig.2. In each group, there exist a displacement sensor and a pressure sensor.
Foundation item: Project(50425518) supported by National Outstanding Youth Foundation of China; Project(2007CB714004) supported by National Basic Research Program of China Received date: 2009−05−30; Accepted date: 2009−08−14 Corresponding author: GONG Guo-fang, PhD; Tel: +86−571−87952500; E-mail:
[email protected]
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Fig.1 Hydraulic circuit of thrust system of shield machine [8]
Fig.2 Distribution of thrust cylinders in shield machine
The fluid flowing into each group is controlled by an appropriate input signal of the flow control valve while the working pressure is set by the pressure relief valve, so the cylinders in the same group can be arranged with one set of control valves. In this way, the components and the structure complexity are reduced. In addition, the motion control strategies are simplified largely. 2.2 Experimental system Fig.3 shows one group of the thrust system employed in the experiment [9]. Because this research is focused on the characteristics of flow and pressure control, the prototype system is simplified to some extent. There are six identical groups in all, as the circuit depicted in Fig.3. In fact, each group includes just one cylinder in this system. As shown in Fig.3, each group comprises a flow control proportional valve and a pressure relief proportional valve to achieve the flow and pressure compound control. The flow rate through flow control valve remains almost invariable as a pressure
compensation device maintains a constant level of pressure drop across the proportional valve, irrespective of system or load pressure changes. Besides, the distributed fluid flow also partly passes through the pressure valve to ensure that the system pressure stays at a constant level. By adjusting the electric current through the coils of the valves, the pressure and flow rate of the system can be regulated to meet the requirements of the thrust. When tunneling, solenoid b of three-way directional valve is energized, shifting the valve to its right position, and thus making cylinder piston rod move forward. Pressure sensor and displacement sensor real-timely measure the pressure and displacement of hydraulic cylinder, which are subjected to online data transmission to the central control system so as to compare with reference input signals to implement pressure and flow control respectively. When the shield stops for erecting the tunnel lining, the hydraulic cylinders should be able to perform the retraction action separately with the three-way valve working at left position. Meanwhile, the flow control valve is shorted by two-way directional valve to provide larger flow rate to make the rod move at higher speed. There also exist a counterbalance valve and a hydraulic lock for each thrust group, and the former assures a stable return movement while the latter locks the circuit to prevent leakage for safety protection when the cylinder thrust is released.
3 System modeling The synchronization problem of linear hydraulic actuators arises in many applications, and the synchronous operation of multiple hydraulic actuators has an important influence on system performance. Under
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Fig.3 Experimental thrust hydraulic system
varying heavy loads, this issue is the most pronounced in the shield thrust system when tunneling in straight line. Usually, there are three approaches to address the issue [9−10]. The first is to use a flow divider, and the performance is restricted by flow divider itself and the compressibility of the working fluid. The second is to make actuators connected mechanically, which increases the system complexity in turn. The third is electrohydraulic synchronization adopted in this work, which includes a closed loop system. Moreover, the last method can provide a much higher accuracy with simple operation [7]. Consider a thrust hydraulic system with n cylinders to counter the excavating load, as shown in Fig.4. Because the installation distance between cylinders is much longer than the trivial synchronization error and the issue of the synchronization motions in horizontal direction is dealt with, it is assumed that the thrust system has three degrees of freedom of moving along the horizontal direction, pitch motion and rotation [11]. Roll axis r is defined to be parallel to the line connecting cylinder 1 to cylinder 3 and pitch axis p is defined to be perpendicular to the line connecting cylinder 1 to cylinder 3.
Fig.4 Diagram of acting forces in n-cylinder hydraulic thrust system
Fig.4 shows the forces acting on the hydraulic cylinders. The contact action between the cylinder and
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the load is equivalent to the spherical contact surface. From Newton’s second law and the conservation of angular momentum, the following equations can be obtained to represent the motion of the shield along horizontal direction and rotations about axes r and p: ⎧ ⎪−∑ Fi − ∑ Fri sin θ r − ∑ Fpi sin θ p = mx&&p i =1 i =1 ⎪ i =1 ⎪⎪ n σ ⎨∑ ( Fi + Fri sin θ r )(−1) ri lri = J rθ&&r ⎪ i =1 ⎪n ⎪∑ ( Fi + Fpi sin θ p )(−1)σ pi l pi = J pθ&&p ⎪⎩ i =1 n
n
(1)
where xp represents the position of the center of the load (xp=0 when the hydraulic cylinder extension is zero ), m is the total mass of the load, Fi represents the reaction force acting on cylinder i (i=1,2, …, n), lri (or lpi) is the moment arm for Fi (i=1,2, … , n) with respect to rotational axis r (or axis p), σri (or σpi) represents the moment factor, Jr (or Jp) represents the rotational moment of inertia of the load along axis r (or axis p), θr (or θp) represents the rotation angle along axis r (or axis p), and Fri (or Fpi) represents the friction force between load and cylinder along axis r (or axis p). Considering force Fi (i=1, 2, …, n) acting on the cylinder, the equations of motion for the cylinders can be represented by n
i =1
i =1
pi Ai − Fi − F fi − B pi x&i − ∑ Fri sin θ r − ∑ Fpi sin θ p = mi && xi ,
i=1, 2, …, n
(2)
where pi represents the pressure in the chamber of cylinder i, Ai represents the effective piston area, mi represents the piston mass of cylinder i, Ffi represents Coulomb friction, Bpi represents the viscous friction coefficient, and xi represents the position of cylinder group i relative to the tunnel lining ring. If the soils being thrust are equivalently taken as a mass-spring-damper system with stiffness ki and damping ratio bi [12−13], then the contacting effect can be modeled by the following equation: Fi = Fsi + ki xi + bi x&i , i=1, 2, …, n
p& i =
β V ( xi )
[− Ai x&i − K cei pi − K pqi x pi + K fqi uqi ]
i=1, 2, …, n where Kcei=Kci+Cti, x pi =
n
n
cylinder can be represented by the following equation:
(3)
where Fsi represents the earth pressure at rest in the neighborhood of acting point i. The oil flow into each group of cylinders is controlled by a proportional flow control valve. Considering the compressibility of the fluid in the cylinders and ignore the valve dynamics as well as leakage in the cylinders, the pressure dynamics in each
(4) K ui 2
s + 2ξ iω ni s + ω ni2
, β is the
bulk modulus of the working fluid, Vi represents the total fluid volume to the respective cylinder chamber, Kci and Kpqi are the flow-pressure coefficient and the flow coefficient of the pressure relief valve in group i, Kfqi is the flow coefficient of the flow control valve in group i, upi and uqi are the control input signals of the pressure and the flow valves, respectively, xpi is the poppet displacement of the pressure valve in group i, Cti is the leakage coefficient, Kui is the gain of the pressure valve, ξi and ωni are damping ratio and natural frequency of pressure valves in group i.
4 Control strategy Considering variations in loads, the volume of working chamber of cylinder and oil properties, a closed-loop control system with master/slave strategy was adopted in the thrust system. This means that one group of cylinders tracks the other group in displacement and keeps error within a specified range. Fig.5 shows the control model of two opposite cylinders. The synchronization control is attained by speed error feedback correction. Because the variation of load leads to discontinuous push velocity, the outer-loop control is to compensate discontinuous push velocity by means of regulating input voltage of the proportional pressure valve while the inner-loop control takes charge of the flow rate regulation with the flow control proportional valves [14−15]. There are cylinder 1 as a master, cylinder 2 as a slave, and controller 5 as a displacement compensator for synchronization control, differing from pure speed control circuit. Cylinder 1 is taken as the reference cylinder, whose movement has to be followed by cylinder 2. In this work, taking into account of the practicability as well as the engineering application requirements, controller 5 is designed as a proportional integral derivative (PID) controller with a dead band to prevent the oscillation as a result of highly frequent adjustments. As shown in Fig.6, the control parameters can be expressed as ⎧e(t ), e(t ) = y (t ) − r (t ) ＞ ε p(t ) = ⎨ ⎩ 0, e(t ) = y (t ) − r (t ) ≤ε
(5)
where r(t) is the input, y(t) is the output, e(t) is the error signal, and ε is a variable band parameter. Two displacement sensors measure the cylinder displacements
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Fig.5 Block diagram of dual-cylinder motion synchronization
Fig.6 Block diagram of PID control system with dead band
that are subtracted from one another. The displacement difference delivered to controller 5 will be checked to see whether it falls in the acceptable limit of error (dead band). If so, the output of controller 5 will be zero. Otherwise, controller 5 functions combining with embedded PID control algorithm and adding its output value to the reference input of flow valve of cylinder 2 so as to accompany cylinder 1 in displacement.
5 Simulation
Fig.7 Velocity curves of dual cylinders control system
The simulation was carried out in AMESim and Matlab/Simulink environments simultaneously, called co-simulation. The first one was for hydraulic modeling while the second was for control model creating. To simulate the actual working condition, the loads applied on two cylinders were unequal, with a difference of 2 MPa. In addition, different values of the parameters were assigned to the proportional valves to make them perform distinctly in dynamics. Figs.7−8 illustrate the simulation results of synchronous motion control. Although the two cylinders have a dramatic difference at working pressure, the moving velocity is in agreement with each other after the shaking response at the starting point. As a result, the displacement of the following cylinder follows the
Fig.8 Synchronous error of dual cylinders control system
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reference cylinder precisely with a maximum error of about 3 mm, as shown in Fig.8, which definitely satisfies the requirements in engineering applications. In Fig.7, the reference and following cylinders response differently under the step signal excitation, because of the difference between the component parameters of the actuators as well as the tracking and adjusting action of the controller.
6 Experiments In this project, experiments were conducted with an earth pressure balance (EPB) shield simulative test rig consisting of a shield machine, an earth box filled with pressurized earth of different characteristics, and a PLC control system [14]. For synchronous motion control, unequal load is applied on the hydraulic cylinders installed in symmetric position. Fig.9 shows the experimental results of the synchronous motion control in the case of simulating shield tunneling through soft clay layer in the test soil box [14]. It can be seen from Fig.9(a) that the velocity curve of the following cylinder is much smoother than that of the reference one, but both are kept at the level of 36 mm/min. This control scheme has proven to be
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effective in obtaining good motion synchronization performance as shown in Figs.9(b) and (c), achieving a high displacement agreement through experiment with the displacement error being limited within ±3 mm, under large pressure difference of two thrust cylinders caused by uneven, and varying loads applied on the excavated soil as shown in Fig.9(d). The experimental results are quite in agreement with those of simulation. Furthermore, the velocity consistency against pressure difference verifies good thrust pressure and speed behavior of this control system. Fig.10 demonstrates that the shield posture trends through a certain experiment section. From the figures, we can derive that the pitch angle is less than 0.8˚ and changes within a range from −0.79˚ to −0.74˚ while the rotation angle curve travels between 3.0˚ and 2.5˚. Combining the above results, it can be seen that the designed control system is able to realize the thrust cylinders motion synchronization and has a good accommodation to disturbances. So the pressure and speed compound control system and the design of control system mentioned above are suitable to shield tunneling applications and can accomplish the work of driving the shield tunneling construction. In the experiment, the loads applied on two thrust
Fig.9 Measured synchronous motion behavior of two symmetric cylinders: (a) Velocity; (b) Displacement; (c) Displacement error; (d) Pressure
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Fig.10 Posture angles of shield machine: (a) Pitch angle; (b) Rotation angle
cylinders have a difference of about 2 MPa, which is large enough to simulate the actual conditions at tunneling site. The errors of ±3mm in displacement and less than 1˚ in angle in a tunneling cycle can also be taken as the deviation correction references in a single lining ring.
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7 Conclusions and future work (1) An electro-hydraulic thrust system of the shield adopting group control method is presented and reduced into a simplified experimental system to carry out the excavating experiments. Thrust motion dynamics modeling as well as synchronous control between the thrust cylinders is studied. (2) The closed-loop master/slave control scheme guarantees a low synchronous error by applying controllers for compensating the displacement error between the reference and following cylinders. The test results show that the synchronous error can be kept within ±3 mm under large pressure difference, and the shield posture angle variations are limited within 1˚. (3) Soil characteristics are quite complicated and cannot always be seen as invariable. Further research on this project will be conducted by taking into account of uncertain geological conditions and nonlinearities of soil dynamics and electro-hydraulic system encountered in the in-situ tunneling.
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