삼축압축 하중 제어 시 시료강성에 따른 제어 adaptive control system

 

영신컨설턴트 (02) 529 8803 ystcha@naver.com 2021 2

 

 

삼축압축시험 대부분은 속도 변형제어로 수행합니다. 액상화 시험은 하중제어로 수행하고 시료의 강성에 맞게 속도를 제어합니다. 

 

The dynamic cyclic response of soil is important to many geotechnical engineering projects, including those in which structures and/or soil deposits may be subjected to earthquake, wave, wind and traffic loadings.

During such loadings the effects of stress reversal, rate-dependency and other dynamic phenomena create highly complex soil response (O’Reilly and Brown, 1991), which may not be captured during traditional static geotechnical testing.

 

Recognising this fact, laboratory element testing has evolved to enable dynamic tests to be performed on soil specimens using a wide range of test apparatuses, allowing determination of, amongst other parameters, the dynamic cyclic strength of a soil.

 

This strength is often found for saturated granular soils to assess their resistance to earthquake loadings, and is typically determined at large strain levels, in the order of 1 % double amplitude axial strain and above for triaxial test specimens (ASTM D5311-11; JGS 0541-2000).

 

closed-loop control 제어

 

These values are the proportional, integral, and differential gains, commonly abbreviated to PID, and the summation of these feedback terms is used to drive the loading actuator and correct the output response. Such a system is shown schematically in Figure, where e = error and u = summation of the feedback terms used to drive the actuator movement. Note this is the method historically used to run load-controlled tests in dynamic apparatuses produced by GDS Instruments, including the Dynamic Triaxial Testing System (DYNTTS). 

 

Block component schematic of PID control historically used in the GDS DYNTTS

종전의 제어

 

When using PID feedback control, the loading system is tuned to optimum performance by conducting tests on a tuning specimen with consistent properties (e.g., a rubber cylinder), observing the dynamic cyclic response, and then selecting suitable values for each fixed gain term.

 

This process results in excellent system performance when testing soil specimens that have similar initial stiffness to that of the tuning specimen, yet as already discussed the initial stiffness of a granular specimen tested as part of a liquefaction study may fall across a wide range.

 

In the case of liquefaction tests performed in a dynamic triaxial apparatus, the specimen stiffness reduces as the soil approaches a liquefied state, at which point the PID values initially set at the beginning of shearing become sub-optimal. This results in the applied axial loading amplitude reducing, with the liquefaction resistance potentially being overestimated (i.e., the test specimen may require more cycles to liquefy).

 

This problem has been the focus of development at GDS Instruments carried out to improve control systems used within dynamic test apparatuses such as the DYNTTS.

 

The primary solution has been to implement a form of an adaptive control system, which can assess specimen stiffness as a soil test progresses and ultimately adjust gain values as required.

 

These limitations have previously been recognised when controlling dynamic materials testing apparatuses (Hinton, 1997), with an adaptive control system instead being suggested as a suitable method for improving apparatus performance. Although an adaptive control system is not straightforward to define, general consensus states that a fixed gain system (such as the PID feedback) is not adaptive (Åström and Wittenmark, 1989).

 

This importantly means adaptive systems should be able to adjust their gain values based on specimen response, which in the case of liquefaction testing in a triaxial apparatus means adapting gains based on variations in soil stiffness.

 

Given the recognised improvement an adaptive control system may offer, development was carried out at GDS Instruments to implement a form of adaptive control for use in dynamic triaxial, hollow cylinder and direct simple shear apparatuses. A schematic of this adaptive control system is displayed in Figure , where FF = feedforward.

 

Block component schematic of adaptive control developed for the GDS DYNTTS.

시료 강성 순응 제어

 

To compare performance of the apparatus using PID feedback and adaptive control systems, the percentage error of the applied double amplitude axial load with respect to the target double amplitude axial load (i.e., 0.192 kN) was calculated from the test data.

 

ASTM 진동삼축 하중제어

 

Equation defines this percentage error, which is based on loading uniformity calculations given in the ASTM test standard for determining the cyclic triaxial strength of soil under load control (ASTM D5311-11).

 

 

Note

ΔPt = target double amplitude axial load (i.e., 0.192 kN), 진폭

ΔPc = applied single amplitude axial load in compression, and 압축

ΔPe = applied single amplitude axial load in extension 인장

 

 

모래시료 시험 예

Stress-strain response of LBFD specimens cyclically loaded under undrained conditions using (a) PID feedback, and (b) adaptive control. Note the target load amplitudes are shown by the horizontal dashed red lines.

 

 Axial strain of LBFD specimens cyclically loaded under undrained conditions using

(a) PID feedback, and (b) adaptive control.

 

 

 

참고문헌

 

ASTM Standard D5311, “Standard Tests Methods for Load Controlled Cyclic Triaxial Strength of Soil,” ASTM International, West Conshohocken, PA, 2013, DOI: 10.1520/D5311-11.

 

Åström, K. J., Wittenmark, B. 1989. Adaptive Control, Wokingham, Addison-Wesley.

 

Higuchi, T., Hyde, A. F. L., Yasuhara, K. 2000. Liquefaction criteria for a non-plastic silt. Proc. Int. Symposium onCoastal Geotechnical Eng. In Practice, Vol. 1.

 

Hinton, C. E. 1997. Adaptive PID Control of Dynamic Materials-Testing Machines Using Remembered Stiffness. Applications of Automation Technology to Fatigue and Fracture Testing and Analysis: Third Volume, ASTM STP1303, A. A. Braun and L. N. Gilbertson Eds., 111-119.

 

JGS Standard 0541-2000, “Method for Cyclic Undrained Triaxial Test on Soils.

 

O’Reilly, M. P., Brown, S. F. 1991. Cyclic Loading of Soils: from theory to design, Glasgow and London, Blackie.

 

Seed, H. B., Idriss, I. M. 1971. Simplified procedure for evaluating soil liquefaction potential. Journal of Geotechnical Engineering Division, ASCE, 97(9), 1249-1273.

 

 

비교 Graphs Comparing Adaptive Control Vs PID Performance

 

Below graphs show results from 2 deviator stress controlled tests of +/- 25kPa on identically prepared sand specimens.  One set of results uses PID only, the other set using GDS Adaptive Control.

 

 

Adaptive Control Performance Graph deviator stress +/- 25kPa 진동수 감소

 

 

Here the loading system correctly maintains the targeted deviator stress in blue as the test progresses up to cycle number 20. Here the PID gains are varied by the adaptive control firmware code, which works to reach the loading amplitude as the specimen softens. Note, in this test the double amplitude axial strain exceeds 20 % as the specimen fails, with the load target still being maintained, which is exactly how the test should have proceeded.

 

 

PID Only Performance Graph deviator stress amplitude of 25 kPa 진동수 증가

 

 

Note the reduction in deviator stress (i.e., the applied axial load) in blue occurring as the loading progresses past cycle number 20. Here the PID gains are fixed, so as the specimen softens the loading actuator does not move far enough to mobilise the targeted deviator stress amplitude of 25 kPa, and so full load during failure is not maintained. The axial strain applied to the specimen can be seen in orange, and does not exceed a double amplitude value of approximately 6 %.