Geological sample cyclic testing control system and method

Abstract

A geological sample cyclic testing control system configured to control an actuator to apply a cyclic test to a sample according to a target testing profile, comprising: first and second transducers c

Description

Field of the Invention The present invention relates to geological sample cyclic testing control systems and methods. Background of the Invention Cyclic geotechnical tests, involving applying a plurality of test cycles to a sample of soil, may be used to understand the geological behaviour of the soil under repeated loading. Typically, a cylindrical specimen is trimmed, fitted inside a rubber membrane and constrained to restrict diameter change. Next, the specimen may be subjected to predetermined static testing conditions followed by dynamic testing conditions. The dynamic testing conditions may include, for example, applying cyclic axial or shear load or displacement to the specimen. The test cycles may have a frequency of up to 20Hz. Compared with most materials, geological materials, and specifically soils, are inherently complex and unpredictable when it comes to geotechnical cyclic testing. The stiffness of soil may depend significantly on current and historic loading. At the macro scale, the displacement required to achieve a target load may vary significantly within a single cycle of loading and also between load cycles. Similarly, the load required to achieve a target displacement may also vary significantly within a single loading cycle and between subsequent loading cycles. At the micro scale, soil may experience particle interlocking, breaking and sliding which may cause unforeseen peaks and troughs in instantaneous strength and stiffness. There is a need to understand how these variations in stiffness and strength develop under loading. To yield reliable scientific data, test standards have been developed and adopted in the geotechnical industry. The standards may demand that loads are applied according to a smooth sinusoidal variation with tight tolerances on amplitude variation. So, due to the inherent complexity of soil testing, it is not straightforward to apply a test to soil that meets the test standards. Early geotechnical tests used constant flow motors or pumps which, by their nature, were unsuitable for use in cyclic testing. Later, computer control and then local closed loop trajectory control within a test frame allowed more complex load conditions to be achieved. Such control systems are generally based on proportional-integral-derivative, PID, control where the control is based on error values with current (proportional), past (integral) and anticipated instantaneous (derivative) control errors being used to calculate a control effort needed to achieve and maintain a target. PID controllers work well to control highly repeatable, or reliable, systems where they may be finely tuned to match the system mechanics. For soil, PID control alone may not be sufficient to control execution of a cyclic test due to the variations in stiffness and strength a soil specimen may exhibit during testing. Accordingly, there is a need for an improved control system for cyclic testing of soil. Summary of the Invention At its most general, the present invention provides a control system configured to, repeatedly, receive a target and two observed values, calculate a control effort required to meet the target based on an instantaneous system stiffness, an adaptation of the target and a learning rate, and provide the control effort to an actuator in order to apply a predetermined cyclic test to a soil sample. The system includes a system stiffness model configured to update instantaneous system stiffness using an estimate of system compliance based on Kalman filtering of the two observed values. A profile analyser is configured to calculate the learning rate based on the target. The learning rate is used to limit a rate of change of the instantaneous system stiffness to promote system stability. A profile adaptor may adapt the target for control accuracy based on the target and one of the observed values. Based on the adapted target, compliance and one of the observed values, a PID control effort is generated. Based on the target and system compliance, a feed-forward, FF, control effort is generated. The PID and FF control efforts are used to control the actuator acting on the soil sample. According to a first aspect of the invention, there is provided a geological sample cyclic testing control system configured to control an actuator to apply a cyclic test to a geological sample according to a target testing profile, the system comprising: a first transducer configured to measure a first mechanical parameter of the geological sample and to output a first observed value; a second transducer configured to measure a second mechanical parameter of the geological sample and to output a second observed value; wherein the target testing profile comprises a plurality of target values of a target variable corresponding to the first mechanical parameter; a profile analyser configured to calculate a learning rate based on a first derivative of a normalised form of the target testing profile and a second derivative of the normalised form of the target testing profile; a system stiffness model configured to: receive the learning rate, the first observed value and the second observed value; iteratively predict and update, using a Kalman filter, an estimate of the first observed value at a current state based on the learning rate, the estimate of the first observed value at a previous state, an estimate of system compliance at a previous state, the first observed value and the second observed value to generate an estimate of system compliance at the current state; and update an instantaneous system stiffness value according to the estimate of system compliance at the current state; a profile adaptor configured to: receive the target testing profile and the second observed value; update a value of a scaling factor and a value of a bias based on the value of the scaling factor at the previous state and the value of the bias at the previous state, respectively, maximum and minimum values of the target testing profile and maximum and minimum values of the second observed value measured during a predetermined time period; and calculate an adapted testing profile according to the scaling factor and the bias; a proportional-integral-derivative, PID, controller configured to generate a PID control effort based on the adapted testing profile, the second observed value and the instantaneous system stiffness value; and a feed-forward, FF, controller configured to generate an FF control effort based on a first derivative of the target testing profile, a second derivative of the target testing profile and the instantaneous system stiffness value; wherein a plant control effort based on the PID control effort and the FF control effort is provided as a control signal to the actuator such that the cyclic test according to the target testing profile is applied to the geological sample. In some embodiments, the system comprises a system stiffness model configured to: receive the learning rate, the first observed value and the second observed value; iteratively predict and update, using a Kalman filter, an estimate of the first observed value at a current state based on the estimate of the first observed value at a previous state and the first observed value; calculate system compliance based on the estimate of the first observed value at the current state and the second observed value; and update an instantaneous system stiffness value according to the system compliance and the learning rate. A geological sample may be a specimens of geological matter, such as rock or soil. Analysis of geological samples is used in many industries such as oil and gas, mining, construction and scientific research, to determine characteristics of a substrate. For example, geological sample analysis can be used to assess the suitability of a site for an infrastructure project. A geological sample may be a soil specimen. As discussed above, soil is prone to unpredictable behaviour during geotechnical testing. The initial static strength and / or stiffness of a soil specimen may vary depending on parameters of the soil specimen, such as the composition and dimensions of the specimen, as well as parameters of the testing setup, such as the constraining method and pressures used. Further, during the test, the specimen strength and / or stiffness may vary from the initial strength and / or stiffness depending on parameters of the particular test, e.g., loads and / or displacements applied. Accordingly, to setup a PID control system, a prediction of the initial static strength and / or stiffness of the soil specimen is required to tune the PID controller. Initial static strength and / or stiffness may be non-trivial to estimate. Typically, operators have selected one from a plurality of predetermined tunings for the PID controller based on their expertise. This method is vulnerable to operator error; a poor selection may lead to an unsuccessful test; one that does not meet the appropriate test standards. If the estimate of initial static stiffness is too low, the control provided by the PID controller may be sluggish and may not achieve the control targets (e.g., target displacements). If the estimate of initial static stiffness is too high, the control provided by the PID controller may be aggressive and overshoot or oscillate around targets. In addition, as the strength and / or stiffness of the specimen varies during a test, the estimate may become unsuitable while the test is running, effectively detuning the controller mid-test and degrading performance of the system and the quality of the resultant test data. So, even when the estimate of initial static stiffness is correct, the PID control will only perform well while the stiffness of the soil specimen remains in a limited range around that estimated stiffness. If the soil specimen softens during the test, the system may become sluggish and fail to achieve control targets. If the soil specimen hardens during the test, the system may become aggressive and start oscillating around the target. Accordingly, the present invention addresses the shortcomings of PID controllers by providing a system stiffness model configured to continually calculate system compliance and update an instantaneous system stiffness value for use by a PID controller and an FF controller. In this way, the present invention eliminates the need for manual prediction of initial stiffness of a soil specimen or manual selection of PID tuning parameters. Hence, opportunities for operator error are reduced and a level of expertise or experience required to successfully conduct tests using the control system of the present invention may also be reduced compared to conventional systems. By providing a system stiffness model continually updating the instantaneous system stiffness value, the accuracy of test control may be improved as the controllers are continually provided with updated estimates of instantaneous stiffness as the soil specimen stiffness varies during the test. In this way, also, control tracking under variable stiffness conditions may be improved. The control system of the present invention may therefore experience fewer test failures than conventional systems and a repeatability of tests may be improved. To moderate the control, the control system of the present invention includes a profile analyser calculating a learning rate which is used to regulate magnitude changes in instantaneous system stiffness value. In this way, a stability of the control system is improved. By providing the profile adaptor, the control system of the present invention may further adapt an input to the PID controller to mitigate systemic or inherent control errors, e.g., system losses or hardware deadbands or deadzones. By providing a feed-forward controller, system control may not rely solely on error to initiate change. In this way, varying stiffness of the soil specimen may not have to manifest as actual testing error in order to trigger a corresponding change in control effort. Instead, the system of the present invention may predict and provide an appropriate control effort based on the target testing profile and the instantaneous system stiffness value. In some embodiments, the system is configured to receive the target testing profile, the target testing profile comprising a waveform defined by a sine function or a haversine function. In this way, the system receives a cyclic test profile. In some embodiments, the system is configured to receive the target testing profile, the target testing profile comprising: normalised amplitude data for a single cycle of the cyclic test; a datum value about which the amplitude data is to be applied; a scaling factor by which the amplitude data is to be scaled; a maximum number of cycles to complete; and early termination conditions which, if met, cause the system to end the test before the maximum number of cycles has been completed. In this way, the system receives all the data required to run the test from the target testing profile. Accordingly, a level of skill or expertise required to successfully run the test may be reduced. In some embodiments, the first mechanical parameter and the second mechanical parameter are each one of a pair selected from the list: load and displacement; pressure and volume; pressure and displacement; torque and rotation. Other parameters may also be suitable. In this way, dependent and independent variables of a test performed using the system of the present invention may be any of any pair listed above. For example, the independent variable may correspond to load or displacement, while the dependent variable corresponds to the other one of load or displacement. In such an example, the target testing profile may also be in terms of load or displacement according to the first mechanical parameter. Accordingly, the control system is versatile. In some embodiments, the normalised version of the target testing profile is provided by normalising the target values of the target testing profile into a range from -1 to 1. In some embodiments, the learning rate is calculated based on a square of the first derivative of the normalised form of the target testing profile and a modulus of the second derivative of the normalised form of the target testing profile. In this way, an effect of first and second derivatives on the learning rate is modulated. For example, where the target testing profile is displacement, the first derivative is velocity and the second derivative acceleration, depending on the test type, one of the velocity and the acceleration may be tuned to have a greater impact on learning rate than the other. In some embodiments, the system stiffness model is configured to: predict, using the Kalman filter, the estimate of the first observed value at the current state based on the estimate of the first observed value at the previous state; and update, using the Kalman filter, the estimate of the first observed value at the current state based on a difference between the estimate of the first observed value at the current state and the first observed value at the current state. In this way, the output of the predict step may be used in the update step such that the filtering is recursive and minimal history of observations and estimates is required. In this way, the Kalman filter is resource efficient. Further, the Kalman filter is tolerant to a missed observation; a subsequent predict step may directly follow an earlier predict step. In this way, the Kalman filter is robust to system faults to some extent. In some embodiments, the system stiffness model uses a factored form of the Kalman filter and a Bierman algorithm to predict and update the estimate of the first observed value at the current state. In this way, the implementation of the Kalman filter in the present invention is efficient. In some embodiments, the system stiffness model is configured to calculate system compliance based on the estimate of the first observed value at the current state and a slew rate limited version of the second observed value. By using a slew rate limited version of the second observed value, a rate of change of the second observed value seen by the system stiffness model is moderated. In this way, drastic changes in the second observed value may have moderate effects on system compliance to promote a stability of the system. Further, in this way, implausible changes in the second observed value may be mitigated. In some embodiments, the scaling factor is updated based on the value of the scaling factor at the previous state and a ratio of a difference between the maximum and minimum values of the target testing profile and a difference between the maximum and minimum values of the second observed value measured during the predetermined time period. In this way, the ratio may be used to scale the adapted testing profile. In some embodiments, the scaling factor is updated based on a noise value measured in the second observed value during the predetermined time period. In this way, impacts of noise on the adapted testing profile may be mitigated. In some embodiments, the bias is updated based on the value of the bias at the previous state and a difference between the difference between maximum and minimum values of the target testing profile and the difference between maximum and minimum values of the second observed values measured during the predetermined time period. In this way, the difference may be used to bias the adapted testing profile. In some embodiments, the predetermined time period is one or more previous cycles of the cyclic test. In this way, data from the most recent cycle is used to calculate the adapted test profile. Accordingly, the adapted test profile may benefit from up to date data for improved accuracy. In some embodiments, the plant control effort is a sum of PID control effort and FF control effort. In this way, a combined control effort of the PID and FF controllers may drive the actuator. Accordingly, both predicted control effort and control effort based on error are provided to the actuator. In this way, the control may be both proactive and adaptive. According to a second aspect of the invention, there is provided a geological sample cyclic testing control method comprising: receiving, from a first transducer, a first observed value indicative of a first mechanical parameter of a geological sample; receiving, from a second transducer, a second observed value indicative of a second mechanical parameter of a geological sample; receiving a target testing profile comprising a plurality of target values of a target variable corresponding to the first mechanical parameter; calculating, by a profile analyser, a learning rate based on a first derivative of a normalised form of the target testing profile and a second derivative of the normalised form of the target testing profile; iteratively predicting and updating a system stiffness model, using a Kalman filter, an estimate of the first observed value at a current state based on the learning rate, the estimate of the first observed value at a previous state, an estimate of system compliance at a previous state, the first observed value and the second observed value to generate an estimate of system compliance at the current state; updating an instantaneous system stiffness value according to the estimate of system compliance at the current state; updating a value of a scaling factor and a value of a bias based on the value of the scaling factor at the previous state and the value of the bias at the previous state, respectively, maximum and minimum values of the target testing profile and maximum and minimum values of the second observed value measured during a predetermined time period; and calculating, using a profile adaptor, an adapted testing profile according to the scaling factor and the bias; generating, using a proportional-integral-derivative, PID, controller, a PID control effort based on the adapted testing profile, the second observed value and the instantaneous system stiffness value; generating, using a feed-forward, FF, controller, an FF control effort based on a first derivative of the target testing profile, a second derivative of the target testing profile and the instantaneous system stiffness value; and providing a plant control effort based on the PID control effort and the FF control effort as a control signal to an actuator to apply a cyclic test according to the target testing profile to the geological sample. In some embodiments, the method comprises iteratively predicting and updating, using a Kalman filter, an estimate of the first observed value at a current state based on the estimate of the first observed value at a previous state and the first observed value; calculating, using a system stiffness model, system compliance based on the estimate of the first observed value at the current state and the second observed value; updating an instantaneous system stiffness value according to the calculated system compliance and the learning rate. Brief Description of the Drawings Embodiments of the present invention will now be described by way of example only and with reference to the accompanying drawings, in which: Figure 1 shows a schematic control diagram of a geological sample cyclic testing control system according to an embodiment of the first aspect of the invention; Figure 2 shows a schematic diagram of a soil specimen under test; Figure 3 shows a schematic diagram of a soil specimen under test; Figure 4 shows a schematic diagram of a soil specimen under test; and Figure 5 shows a flowchart of a geological sample cyclic testing control method according to an embodiment of the second aspect of the invention. Detailed Description With reference to Figure 1 there is illustrated a geological sample cyclic testing control system 100. The system 100 is configured to control an actuator 102 to apply a cyclic test to a geological sample 104 according to a target testing profile, x. The target testing profile may be received via a user interface 106. The system 100 comprises a first transducer 108. The first transducer 108 is configured to measure a first mechanical parameter of the geological sample 104 and to output a first observed value. The first observed value is labelled d in Fig. 1. The first observed value may be any one of load, displacement, pressure, volume, torque or rotation. In the example shown in Fig. 1, the first observed value, d, is displacement. Changes in displacement measured may be in the order of microns to millimetres. The system 100 further comprises a second transducer 110. The second transducer 110 is configured to measure a second mechanical parameter of the geological sample 104 and to output a second observed value. The second observed value is labelled y in Fig. 1. In the example shown in Fig. 1, the second observed value, y, is load. Maximum loads may be around 100kN. A resolution of load measurement may be between 0.05N and 5N. In other cases, the first and second observed values may be torque and rotation, which may be measured up to ±200Nm and ±360° respectively. In yet other cases, the first and second observed values may be pressure and volume, which may be measured up to 2MPa and 1,000,000mm3 respectively. The target testing profile, x, comprises a plurality of target values of a target variable corresponding to the first mechanical parameter. That is, where the first mechanical parameter is a displacement, the target variable of the target testing profile, x, is also a displacement. In other words, the first mechanical parameter, and by extension the first observed value, d, is the independent variable of the test. The system 100 further comprises a profile analyser 112. The profile analyser 112 is configured to calculate a learning rate, A, based on a first derivative of a normalised form of the target testing profile, xn, and a second derivative of the normalised form of the target testing profile, xn. The learning rate, A, may be a value between 0 and 1. In some cases, the learning rate, A, is calculated according to Equation 1, where A is learning rate, Ag is a learning weighting constant, aw is a first derivative weighting constant, xn is the first derivative of a normalised form of the target testing profile and xn is the second derivative of a normalised form of the target testing profile. A 1 Aq ClwXn T |Xn | (1) Predetermined minimum and maximum values for learning rate may be applied such that, if a learning rate calculated according to Equation 1 exceeds the predetermined maximum value, the learning rate is set to the predetermined maximum value and if a learning rate calculated according to Equation 1 is less than the predetermined minimum value, the learning rate is set to the predetermined minimum value. The system 100 further comprises a system stiffness model 114. The system stiffness model 114 is configured to receive the learning rate, A, the first observed value, d, and the second observed value, y. The system stiffness model 114 is further configured to iteratively predict and update, using a Kalman filter, an estimate of the first observed value at a current state, d, based on the estimate of the first observed value at a previous state, do(t), and the first observed value, d. Specifically, in some cases, the system stiffness model 114 is configured to generate an estimate of the first observed value at a current state, d, by minimising error, e, according to Equation 2, where e is the error, d is the first observed value and d is the first observed value at a current state. e = d — d (2) In some cases, a Kalman gain is generated according to methods known in the art. The system stiffness model 114 is further configured to calculate system compliance, C, based on the estimate of the first observed value at the current state, d, and the second observed value, y. In some cases, the system compliance, C, is calculated based on the estimate of the first observed value at the current state, d, and a slew rate limited version of the second observed value, yc. Accordingly, system compliance, C, may be calculated according to Equation 3 where d is the first observed value at a current state, yc is the slew rate limited version of the second observed value, C is the system compliance and do(t) is the estimate of the first observed value at a previous state. In some cases, do(t) is an instantaneous zero point of the first observed value. d=ycC + d0(t) (3) Compliance may have units of kN / mm. A typical minimum compliance value may be 0.00001 kN / mm and a typical maximum compliance value may be around 500kN / mm. For each of the first and second observed values, the system stiffness model 114 may be programmed to ignore changes in magnitude that do not exceed a predetermined threshold corresponding to an observable resolution for each reading. In this way, the system stiffness model 114 may avoid acting on measurement noise. Finally, the system stiffness model 114 is configured to update an instantaneous system stiffness value, S, according to the system compliance, C, and the learning rate, A. In this way, the learning rate, A, may be used to modulate the updating of instantaneous system stiffness value, S, with changes in system compliance, C. The learning rate, A, may be a value between 0 and 1. When learning rate, A, is 0, the instantaneous system stiffness value, S, may not be updated; S = S. When learning rate, A, is 1, the instantaneous system stiffness value, S, may be directly updated with the most recently calculated value of system compliance, C; S = C. In practice, a learning rate of 1 is very rarely used. A learning rate, A, between 0 and 1 acts to weight the impact of the system compliance, C, on the updated instantaneous system stiffness value, S. For example, a learning rate, A, near 0 updates the instantaneous system stiffness value, S, to slowly approach the system compliance, C, and a learning rate, A, near 1 updates the instantaneous system stiffness value, S, to rapidly approach the system compliance, C. The instantaneous system stiffness value, S, is output by the system stiffness model 114 for use by the controllers. The system 100 comprises a profile adaptor 116 configured to receive the target testing profile, x, and the second observed value, y. The profile adaptor 116 may also receive, as part of the target testing profile, x, a datum value, xo, about which amplitude data of the target testing profile, x, is to be applied. The profile adaptor 116 is further configured to update a value of a scaling factor, Sc, and a value of a bias, Bi, based on the value of the scaling factor, Sc, at the previous state and the value of the bias, Bi, at the previous state, respectively, maximum and minimum values of the target testing profile, x, and maximum and minimum values of the second observed value, y, measured during a predetermined time period. In some cases, measurement noise on the second observed value, ynOise, is also used in determination of the scaling factor, Sc. Accordingly, the profile adaptor 116 may be configured to update a scaling factor, Sc, according to Equation 4 where Sc is the scaling factor, a is a scalar adaptation constant, xmax is the maximum value of the target testing profile during the predetermined time period, xmin is the minimum value of the target testing profile during the predetermined time period, ymax is the maximum value of the second observed value during the predetermined time period, ymin is the minimum value of the second observed value during the predetermined time period and ynOise is the measurement noise on the second observed value. Sc = Sc ^max ^min ymax ymin Vn oise (4) Further, the profile adaptor 116 may be configured to update a bias, Bi, according to Equation 5, where Bi is the bias, (3 is a bias adaptation constant, xmax is the maximum value of the target testing profile during the predetermined time period, xmin is the minimum value of the target testing profile during the predetermined time period, ymax is the maximum value of the second observed value during the predetermined time period and ymin is the minimum value of the second observed value during the predetermined time period. Bi = Bi + B((xmnr / X V IILLIA Xmin) {.ymax ymin)') (5) The predetermined time period may be the most recent completed time period of the cyclic test. The scaling factor, Sc, and bias, Bi, may be initially set to 1 before the test begins. Finally, the profile adaptor 116 is configured to calculate an adapted testing profile, Xout, according to the scaling factor, Sc, and the bias, Bi. Accordingly, the profile adaptor 116 may be configured to calculate an adapted testing profile xout according to Equation 6 where xout is the adapted testing profile, x is the target testing profile, xo is a datum value about which amplitude data of the target testing profile, x, is to be applied, Sc is the scaling factor and Bi is the bias. Xout = (x- x^Sc + x0 + Bi (6) The system 100 further comprises a proportional-integral-derivative, PID, controller 118. The PID controller 118 is configured to generate a PID control effort, upid, based on the adapted testing profile, xout, the second observed value, y and the instantaneous system stiffness value, S. Accordingly, the PID controller 118 may be in data communication with the profile adaptor 116, second transducer 110 and system stiffness model 114. The system 100 further comprises a feed-forward, FF, controller 120. The FF controller 120 is configured to generate an FF control effort, uff, based on a first derivative of the target testing profile, x, a second derivative of the target testing profile, x, and the instantaneous system stiffness value, S. Accordingly, the FF controller 120 may be in data communication with the user interface 106 and system stiffness model 114. Finally, a plant control effort, ua, based on the PID control effort, upid, and the FF control effort, uff, is provided as a control signal to the actuator 102 such that the cyclic test according to the target testing profile, x, provided via the user interface 106, is applied to the geological sample 104. With reference to Figure 2, there is illustrated a soil specimen 200 under test in a cyclic triaxial setup. The soil specimen 200 is disposed within a pressure chamber 202. The soil specimen 200 is isolated by a rubber membrane 204. The soil specimen 200 is supported from below by a base 206 and loaded from above by a presshead 208. The soil specimen 200 of Fig. 2 may be subject to one of vertical force and displacement (e.g., as shown by arrow 210) while the other is measured as a dependent variable. Alternatively, the soil specimen 200 of Fig. 2 may be subject to variations in one of chamber pressure and volume (e.g., as shown by arrow 212), while the other is measured as a dependent variable. With reference to Figure 3, there is illustrated a soil specimen 300 under test in a simple shear setup. The soil specimen 300 may be substantially cylindrical. A diameter of the soil specimen 300 may be constrained using a plurality of rings 302. The rings 302 may be formed of a metal material. The soil specimen 300 may be supported from below by a base 304. The base 304 may be moveable relative to a test chamber 306 via a first plurality of rollers 308. The soil specimen 300 may be loaded from above by a presshead 310. The presshead 310 may be supported relative to the test chamber 306 by a second plurality of rollers 312 disposed proximate a side 314 of the presshead 310. The soil specimen 300 of Fig. 3 may be subject to one of vertical force and displacement (e.g., as shown by arrow 316) while the other is measured as a dependent variable. Alternatively, the soil specimen 300 of Fig. 3 may be subject to one of horizontal, or shear, force and displacement (e.g., as shown by arrow 318) while the other is measured as a dependent variable. With reference to Figure 4, there is illustrated a soil specimen 400 under test in a hollow cylinder setup. The soil specimen 400 may be supported from below by a base 402 and loaded from above by a presshead 404. The soil specimen 400 of Fig. 4 may be subject to one of vertical force and displacement (e.g., as shown by arrow 406) while the other is measured as a dependent variable. Alternatively, the soil specimen 400 of Fig. 4 may be subject to one of torque and angular displacement (e.g., as shown by arrow 408) while the other is measured as a dependent variable. With reference to Figure 5, there is illustrated a geological sample cyclic testing control method 500. The method 500 starts at Start 502. At step 504, the method 500 comprises receiving, from a first transducer, a first observed value indicative of a first mechanical parameter of a geological sample; receiving, from a second transducer, a second observed value indicative of a second mechanical parameter of a geological sample; and receiving a target testing profile comprising a plurality of target values of a target variable corresponding to the first mechanical parameter. Next, at step 506, the method 500 comprises calculating, by a profile analyser, a learning rate based on a first derivative of a normalised form of the target testing profile and a second derivative of the normalised form of the target testing profile. At step 508, the method 500 comprises iteratively predicting and updating, using a Kalman filter, an estimate of the first observed value at a current state based on the estimate of the first observed value at a previous state and the first observed value. Then, the method 500 comprises, at step 510, calculating, using a system stiffness model, system compliance based on the estimate of the first observed value at the current state and the second observed value. At step 512, the method 500 comprises updating an instantaneous system stiffness value according to the calculated system compliance and the learning rate. At step 514, the method 500 comprises updating a value of a scaling factor and a value of a bias based on the value of the scaling factor at the previous state and the value of the bias at the previous state, respectively, maximum and minimum values of the target testing profile and maximum and minimum values of the second observed value measured during a predetermined time period. Next, at step 516, the method 500 comprises calculating, using a profile adaptor, an adapted testing profile according to the scaling factor and the bias. The 500 then comprises, at step 518, generating, using a proportional-integral-derivative, PID, controller, a PID control effort based on the adapted testing profile, the second observed value and the instantaneous system stiffness value; and generating, using a feed-forward, FF, controller, an FF control effort based on a first derivative of the target testing profile, a second derivative of the target testing profile and the instantaneous system stiffness value. Finally, at step 520, the method 500 comprises providing a plant control effort based on the PID control effort and the FF control effort as a control signal to an actuator to apply a cyclic test according to the target testing profile to the geological sample. The method ends at End 522. The invention may be further understood with reference to the following paragraphs. The claimed invention comprises a live soil model that effectively predicts stiffness in real time during loading and combines this with in test adaptions to the targeted datum and amplitude in order to improve tracking of cyclic control. This adaptive control system combines the following elements: • System stiffness model - continually monitors the system motion (combined load frame and specimen) to give a macro stiffness value. This eliminates the need to enter an initial stiffness estimate for the specimen under test and provides a baseline for stiffness that is updated continually during testing. The system stiffness model may: 1. monitor signal values for load and position; 2. apply recursive least squares method to suggest changes to stiffness and zero loading point estimates; 3. vary output stiffness and zero-point load estimates based on learning rate; and 4. output instantaneous stiffness and zero-point load estimate. • Profile analyser - predicts the rate of changes in system stiffness expected to be encountered within cycles and provides a learning rate to adjust the adaptation rate of the system stiffness model. The profile analyser may: 1. monitor the profile (or reference); 2. adjust the profile (or reference) value to account for datum (offset); 3. apply a model based exponential function to the adjusted profile (or reference) amplitude value; and 4. output the learning rate for the system stiffness model. • Profile (or reference) adaptor - adjusts the live targeted datum and amplitude values to overcome stiffness variations between cycles. The profiler adaptor may: 1. monitor the minimum and maximum achieved amplitude levels for the last complete period of the cyclic waveform (cycle n); 2. compare these to the initially targeted minimum and maximum reference values (at cycle 0), 3. calculate suggested ideal modified datum and amplitude references based on their proportional difference; 4. set the adaptation aggression using two linear scaling factors, one for amplitude and one for datum to scale the values of datum and amplitude for the upcoming cycle between the values used for cycle n-1 and the suggested ideal values; and 5. output updated datum and amplitude references for next cycle. The adaptive control system operates as follows. A detuned proportional-integral-derivative (PID) controller handles “static” loading, with automatic compensation from the system stiffness model to allow for variable complete system stiffness during cyclic load changes. A feed forward (FF) controller accounts for cyclic load changes and is scaled according to the system stiffness model which is in turn informed by the profile analyser as well as observed load and displacement values. The present invention is not limited to the specific steps, examples or structures illustrated. Further embodiments within the scope of the present invention may be envisaged that have not been described above, for example, the method 500 may comprise a greater number of steps than are illustrated in the figures. For example, the methods 500 may include further steps of receiving data, processing data calculating model parameters, generating control efforts, processing control efforts and / or providing control efforts to actuator(s). Further, the system may be configured to measure and provide control via other measurands. Further, the system 100 may comprise further components configured to contribute to, monitor or modulate the geological sample cyclic testing control. For example, further controllers of any suitable type may be used. The system 100 may be formed of any suitable number of components and materials. To provide reliable and repeatable cyclic testing of soil samples, an innovative control approach is required. The present invention provides an effective solution in a geological sample cyclic testing control system, providing a system stiffness model configured to continually calculate system compliance and update an instantaneous system stiffness value according to a learning rate for use by a PID controller and an FF controller. Accordingly, testing performed using the system of the present invention may conform to the strict test standards of the geotechnical industry by reducing opportunities for operator error and adapting the control during the test according to variations in the stiffness of the specimen. In this way, new possibilities for scientific testing of soil are enabled. Further, a level of expertise required to run a test is reduced and fewer test failures may occur compared with conventional testing. There has been herein described a geological sample cyclic testing control system configured to control an actuator to apply a cyclic test to a geological sample according to a target testing profile. The system comprising: first and second transducers configured to output first and second observed values; a profile analyser configured to calculate a learning rate based on the target testing profile; a system stiffness model configured to: calculate system compliance based on the first and second observed values and update an instantaneous system stiffness value; a profile adaptor configured to calculate an adapted testing profile according to a calculated scaling factor and bias; a proportional-integral-derivative, PID, controller and a feed-forward, FF, controller each configured to generate a respective control effort based on at least the instantaneous system stiffness value; the control efforts being provided as a control signal to the actuator. A method has also been described herein.

Claims

1. A geological sample cyclic testing control system configured to control an actuator to apply a cyclic test to a geological sample according to a target testing profile, the system comprising:a first transducer configured to measure a first mechanical parameter of the geological sample and to output a first observed value;a second transducer configured to measure a second mechanical parameter of the geological sample and to output a second observed value;wherein the target testing profile comprises a plurality of target values of a target variable corresponding to the first mechanical parameter;a profile analyser configured to calculate a learning rate based on a first derivative of a normalised form of the target testing profile and a second derivative of the normalised form of the target testing profile;a system stiffness model configured to:receive the learning rate, the first observed value and the second observed value;iteratively predict and update, using a Kalman filter, an estimate of the first observed value at a current state based on the learning rate, the estimate of the first observed value at a previous state, an estimate of system compliance at a previous state, the first observed value and the second observed value to generate an estimate of system compliance at the current state; andupdate an instantaneous system stiffness value according to the estimate of system compliance at the current state;a profile adaptor configured to:receive the target testing profile and the second observed value;update a value of a scaling factor and a value of a bias based on the value of the scaling factor at the previous state and the value of the bias at the previous state, respectively, maximum and minimum values of the target testing profile and maximum and minimum values of the second observed value measured during a predetermined time period; andcalculate an adapted testing profile according to the scaling factor and the bias;a proportional-integral-derivative, PID, controller configured to generate a PID control effort based on the adapted testing profile, the second observed value and the instantaneous system stiffness value; anda feed-forward, FF, controller configured to generate an FF control effort based on a first derivative of the target testing profile, a second derivative of the target testing profile and the instantaneous system stiffness value;wherein a plant control effort based on the PID control effort and the FF control effort is provided as a control signal to the actuator such that the cyclic test according to the target testing profile is applied to the geological sample.

2. The system of claim 1, wherein the system is configured to receive the target testing profile, the target testing profile comprising a waveform defined by a sine function or a haversine function.

3. The system of claim 1, wherein the system is configured to receive the target testing profile, the target testing profile comprising:normalised amplitude data for a single cycle of the cyclic test;a datum value about which the amplitude data is to be applied;a scaling factor by which the amplitude data is to be scaled;a maximum number of cycles to complete; andearly termination conditions which, if met, cause the system to end the test before the maximum number of cycles has been completed.

4. The system of any preceding claim, wherein the first mechanical parameter and the second mechanical parameter are each one of a pair selected from the list: load and displacement; pressure and volume; pressure and displacement; torque and rotation.

5. The system of any preceding claim, wherein the normalised version of thetarget testing profile is provided by normalising the target values of the target testingprofile into a range from -1 to 1.

6. The system of any preceding claim, wherein the learning rate is calculatedbased on a square of the first derivative of the normalised form of the target testingprofile and a modulus of the second derivative of the normalised form of the target testing profile.

7. The system of any preceding claim, wherein the system stiffness model is configured to:predict, using the Kalman filter, the estimate of the first observed value at the current state based on the estimate of the first observed value at the previous state; andupdate, using the Kalman filter, the estimate of the first observed value at the current state based on a difference between the estimate of the first observed value at the current state and the first observed value at the current state.

8. The system of any preceding claim, wherein the system stiffness model uses a factored form of the Kalman filter and a Bierman algorithm to predict and update the estimate of the first observed value at the current state.

9. The system of any preceding claim, wherein the system stiffness model is configured to calculate system compliance based on the estimate of the first observed value at the current state and a slew rate limited version of the second observed value.

10. The system of any preceding claim, wherein the scaling factor is updated based on the value of the scaling factor at the previous state and a ratio of a difference between the maximum and minimum values of the target testing profile and a difference between the maximum and minimum values of the second observed value measured during the predetermined time period.

11. The system of any preceding claim, wherein the scaling factor is updated based on a noise value measured in the second observed value during the predetermined time period.

12. The system of any preceding claim, wherein the bias is updated based on the value of the bias at the previous state and a difference between the difference between maximum and minimum values of the target testing profile and the difference betweenmaximum and minimum values of the second observed values measured during the predetermined time period.

13. The system of any preceding claim, wherein the predetermined time period is one or more previous cycles of the cyclic test.

14. The system of any preceding claim, wherein the plant control effort is a sum of PID control effort and FF control effort.

15. A geological sample cyclic testing control method comprising:receiving, from a first transducer, a first observed value indicative of a first mechanical parameter of a geological sample;receiving, from a second transducer, a second observed value indicative of a second mechanical parameter of a geological sample;receiving a target testing profile comprising a plurality of target values of a target variable corresponding to the first mechanical parameter;calculating, by a profile analyser, a learning rate based on a first derivative of a normalised form of the target testing profile and a second derivative of the normalised form of the target testing profile;iteratively predicting and updating a system stiffness model, using a Kalman filter, an estimate of the first observed value at a current state based on the learning rate, the estimate of the first observed value at a previous state, an estimate of system compliance at a previous state, the first observed value and the second observed value to generate an estimate of system compliance at the current state;updating an instantaneous system stiffness value according to the estimate of system compliance at the current state;updating a value of a scaling factor and a value of a bias based on the value of the scaling factor at the previous state and the value of the bias at the previous state, respectively, maximum and minimum values of the target testing profile and maximum and minimum values of the second observed value measured during a predetermined time period;calculating, using a profile adaptor, an adapted testing profile according to the scaling factor and the bias;generating, using a proportional-integral-derivative, PID, controller, a PID control effort based on the adapted testing profile, the second observed value and the instantaneous system stiffness value;generating, using a feed-forward, FF, controller, an FF control effort based on a first derivative of the target testing profile, a second derivative of the target testing profile and the instantaneous system stiffness value; andproviding a plant control effort based on the PID control effort and the FF control effort as a control signal to an actuator to apply a cyclic test according to the target testing profile to the geological sample.

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