Adaptive control system for grouting pressure stability based on fuzzy algorithm

2.1 Fluctuation principles of grouting pressure

Grouting pressure is usually driven and produced by the piston movement of the grouting pump and is transmitted by the continuous advance of the slurry itself [9]. When the system is designed, the following factors are mainly considered to affect the grouting pressure.

The damping characteristics of grouting hole formation. High-pressure, solid-liquid two-phase fluid is applied to the grouting hole. Therefore, the crack opening, direction, extended range, connectivity of grouted formation, the fillers in cracks, the roughness of fracture surface, and other geometric characteristics will create complex changes in the inner hole of the fluid motion. Such changes are caused by fluctuations in the grouting pressure [10]. The dimensionless damping coefficient ξ _T is used to comprehensively describe the damping characteristics of grouting hole formation. Under the circumstance of a certain pump capacity, when the damping coefficient ξ _T increases, the pressure drop rises, and the grouting pressure in hole drops. When ξ _T decreases, the pressure drop decreases, and the grouting pressure in the hole rises and becomes closer to the pumping pressure.

In Equation 1, P_L1 is the stock inlet pressure of grouting hole, MPa. P_L2 is the return outlet pressure of grouting hole, MPa. ξ _L is generalized damping coefficient. ρ is slurry density. Q _B is the quantity of flow through grouting hole (namely, return flow), L/min. S _L is the cross-sectional area of return pipe, m².

Pulsation characteristics of the grouting pump. When ξ _T or ξ _L changes, the working point of the grouting pump will also change. Because of the pressure pulsation produced by the P-Q characteristics of the pump, the fluid flow rate will suddenly increase or decrease to form water hammer phenomenon in the pipe, which causes substantial oscillation and fluctuation of liquid pressure in the pipe, reverses pressure and flow rate, and finally causes changes in grouting pressure [11].

The damping characteristic of the grouting hole formation is uncertain, the opening of control valve core can be electrically controlled, and the pulsation characteristic of the grouting pump reflects the influence of the three factors on the grouting pressure. In the filling process, the relevant information of factors was obtained by using a detecting device. The quantitative control value of grouting pressure fluctuation was determined based on balance control equation in the pipeline system. Then, the pressure was controlled by regulating the valve opening to maintain the stability of grouting pressure.

Parameter self-tuning fuzzy PID control algorithm is adopted in the algorithm design for system control program. By using the conventional PID control to eliminate the static coupling and the steady-state error, the fuzzy control is used to eliminate the dynamic coupling [12, 13]. Design idea for the program is as follows: when the pressure deviation is large, fuzzy control is used to speed up response; and when the pressure deviation is small after being in a steady state, switch to PID control to eliminate static error and improve control accuracy.

A control algorithm suitable for the pressure fluctuation characteristics is needed in grouting pressure stability control. The conventional PID controller assembles deviation ratio, integral control, and differential control to constitute controlled quantity by the linear combination, and controls the controlled object. The control law is as follows [14], deviation is composed of actual output and given values, as follows: e ( t ) = r ( t ) - y ( t )(2)

PID controlled quantity is obtained through linear combination of deviation ratio and integral and differential controls, and its expression is as follows: u ( t ) = K p [ e ( t ) + 1 T I ∫ 0 t e ( t ) dt + T D de ( t ) dt ](3)

The form of transfer function is as follows: G ( S ) = U ( S ) E ( S ) = K P ( 1 + 1 T I S + T D S )(4)

Where T _D is derivative time constant. T _I is integral time constant. K _P is proportionality coefficient.

Proportional control proposed means to achieve control by a timely proportional response to deviation signal e, as follows: u = K P e(5)

When the controlled object is on self-control balance, it may cause static error, and oscillation in hysteretic controlling system, thereby reducing dynamic characteristics of the system [15].

Integral control is done by proportional rate of change du/dt of deviation signal e against output signal u, as follows: du dt = 1 T I e(6)Or : u = 1 T ∫ 0 t edt(7)

Integral control cannot overcome static errors and may oscillate by hysteretic system phase and make the stability deteriorate [15], as shown in Fig. 1.

When T _I is very large, integral action is very weak.

Differential control is assumed that the deviation of controlled variable is proportional to the derivative and output u of time, as follows: u = T D de dt = T D ( dr dt - dy dt )(8)

Although the static error of the system is not eliminated by differential control, the controller can help stabilize the system, and the response time is reduced; thus, the dynamic characteristics of the system can be improved [15].

3.1 Grouting simulating test bed

To test the feasibility of the system, a simulation test bed has been designed in accordance with grouting piping system, which is based on the Technical Specification for Cement Grouting Construction of Hydraulic Structures (DL/T5148-2001). The specific design framework is shown in Fig. 2.

Simulating test bed for grouting devices mainly includes SGB6-10 grouting pump, Switzerland KELLER pressure-resistant pressure sensor, K300 electromagnetic flow meter, LJ nuclear density meter, ZAZ series electric single seat control valve, LJ grouting automatic recorder, capacitive formation uplift sensor, host of LJ-IV grouting measurement and control system, perturbation valve V01, manual valve V02, quick-opening valve PV01, valve group composed of electric valve V02 and manual valve PV03, and adaptive control system for grouting pressure stability [16, 17].

The specific steps of the experiment are as follows.

Complete separate test for grout pump and regulating valve to obtain the performance curve and damping coefficient curve needed in the control program.

3.2 Grout pump test and result analysis

Before the grouting pressure stability test, the test of the grouting pump can provide a reasonable size source for the project. To cooperate with the study and to test the pump performance, the performance of the grouting pump was tested. In the performance testing, water medium was used as a grouting material [18]. The testing device is shown in Fig. 3, where both inlet and outlet of grout pump are connected with testing pipes. An electromagnetic flow meter is mounted in the inlet to detect flow, whereas a high-pressure regulating valve is mounted in the outlet to regulate flow.

In Table 1, the record of grout pump P-Q test data are listed. While in Fig. 4, P-Q curve of grout pump is afforded. In the pressure range of 1–5 MPa, the fluctuation deviation of the grouting pump is 1.2%, which meets the requirement of the pressure stability.

3.3 Valve test on grouting simulating test bed and result analysis

Through damping coefficient test on the valve of grouting pressure stabilizer, we obtain data to prepare software for grouting pressure stability control and calculation, as well as the pipeline hydraulic power balance control equations that are established based on such software. The test is conducted in a test bed for grouting pressure stability. In the test, and different pressures were used. Valve opening was controlled through the PLC [19, 20]. Before-and-after pressure values and liquid flow were read at different openings, and the damping value was calculated. The damping change in the grouting hole formation is the main factor causing the grouting pressure. The dimensionless damping characteristic and damping coefficient in the grouting hole formation are used to describe complex flow conditions. Under the circumstance of a certain pump capacity, when damping coefficient increases, the pressure drop rises, and the grouting pressure drops. When damping coefficient decreases, the pressure drop decreases, and the grouting pressure rises. Because it is determined by medium condition of grouting hole formation and is uncertain, it can be obtained through calculation based on the pressure and flow of stock inlet of grout hole and the detected value of pressure at the top of return outlet.

By using the grouting pump to provide pressure and to test the flow of the valve to carry out a separate test, the resistance coefficient curve was obtained in the control program. According to the requirements of the grouting pressure stability control calculation software, the pressure values used were 0.5, 1.5, and 2.5 MPa. The valve damping coefficient wastested.

In Table 2, changes in damping coefficient with different regulating valve openings at pressures of 0.5, 1.5, and 2.5 MPa are shown. In the experiment, the damping coefficient of regulating valve is almost unchanged at different pressures for a given opening. This result indicates that the damping coefficient of valve depends on the dimensionless quantity of the assembly structure and the opening degree. In Fig. 5, the damping coefficient of the value at different pressures is shown. When the opening is small, the damping coefficient of the valve is greatly reduced with increasing opening. When the opening is higher than 40%, the lowest damping coefficient is reduced to almost zero, whereas when the opening continues to increase, the damping coefficient remains almost unchanged.

3.4 Self-regulation and control test for pressure fluctuation and result analysis

To simulate the grouting pressure, the opening of the valve is changed through the PV02 disturbance fluctuations. The pressure fluctuations are similar to the sine, cosine, square wave, or a random combination of these waves. When the opening of the disturbance valve PV02 is constantly changing, the pressure P will produce fluctuations. When the pressure fluctuation of P is greater than the allowable range value, the adaptive control system will be automatically adjusted. The command value and the final stable control value for the control valve opening degree are shown in Table 3, which is afforded by the adaptive control system transient analysis under different pressure conditions. The error of command value and final stability control value issued through calculation of adaptive control system is no more than 5%. The control time is greatly reduced, and the control accuracy is improved.

The valve regulating processes under the set values of two different pressures (0.50 and 2.0 MPa) are shown in Figs. 6 and 7. When the set pressure is 0.50 MPa, the allowed fluctuation amplitude is ± 0.025 MPa. When the setting pressure is 2.0 MPa, the allowed fluctuation amplitude is ± 0.10 MPa. From the Figure it can seen that at different pressures and for different disturbances, the pressures can be stabilized through the regulating valve. In the figure, areas A, B, and C are as follows:

Area A - fluctuations of grouting pressure under simulative disturbance (± 20% ∼ ± 45%).

Area B - Enable automatic grouting recorder (2–3 s).

Area C - under the effect of adaptive control system, wide range of grouting pressure fluctuations is controlled within the allowable deviation range (± 5%).

In Figs. 6 and 7, under the grouting pressures of 0.50 and 2.0 MPa, the fluctuation of grouting pressure can be transiently regulated and controlled within the range of ± 0.025–0.10 MPa, i.e., within 5% of the set pressure value by controlling the adaptive control system. If the pressure fluctuation is controlled by manually regulating the valve opening, in the event of fluctuation resulting from disturbance shown in the figures under the grouting pressures of 0.50 and 2.0 MPa, the fluctuation of grouting pressure is regulated and controlled at 20–45% of the set value. The fluctuation depends on actual circumstances of the operator, which is very unstable.

From the above mentioned analysis, the adaptive control system can be used to control the valve opening and regulate the operation indicators of grouting pressure fluctuation.

3.5 Engineering application and result analysis

To verify the results of laboratory tests, a field test was conducted at the grouting site in Jinghong Hydropower Station. Jinghong Hydropower Station is a class-six station among two reservoirs and class-eight stations along the middle and lower reaches of Lancang River. It is located upstream of Jinghong City, the capital of Xishuangbanna prefecture. Lithology from top to bottom in the test section is as follows: thickness of highly-weathered diorite, 0.80–9.80 m; thickness of weakly-weathered diorite with great change and diorite with weakly-weathered layer, 7.20–25.45 m; and slightly weathered diorite.

Upon reference to the requirements of the Design Institute and after considering many factors, three rows of grouting hole were set up in the grouting test area. In principle, the setting depth of the impervious curtain should be connected to the aquitard by 3 Lugeon. Between the first and the second row grout holes, as well as the second and the third rows, equilateral triangle arrangement is adopted. Length of grouting segment is controlled at around 3.0 m. The grouting methods are divided into slim hole, orifice-closed, no-bolt, and descending stage grouting methods, subject to actual situation at the site. The order of grouting engineering is designed based on the grouting hole, while construction of drilling grouting falls into three sequences. During grouting, isolation construction is used to ensure the lapping effect of the grouting curtain. For cement slurry, three proportions of stable slurry (2:1, 1:1, and 0.5:1) are used. Grouting pressure is shown in Table 4.

In the construction process, the inspection hole is used to test the construction effect. The result of core-collection check shows that although all the grouts of rock core in manholes have low strength, all cracks have been obviously filled. From the test results of 8 inspection holes of the whole project, it is obvious that the grouting effect can be achieved by the adaptive control system to control the grouting parameters. In the water testing for bedrock section in all curtain areas, the Lugeon is less than 1 Lu and the average seepage control effect increases by 15–60 times. Meanwhile, manpower and resources are saved, construction period is shortened, and engineering accidents are reduced. The water testing result for J5 manhole is listed in Table 5.