So, the frequency of the hydraulic shaking motion that must be produced in the centrifuge environment will typically be on the order of 30 Hz to 300 Hz. Since real earthquake signatures as well as test waveforms are being reproduced, the hydraulic controls need to be able to respond very quickly to arbitrary inputs, using closed-loop control to make sure that the motion adequately follows the target inputs. “The motion controller responds by ‘playing back’ recorded stimulus,” said Dan Wilson, Associate Director of the Center for Geotechnical Modeling at UC Davis. “We typically use sine waves to check out the system and then move on to reproduce actual motions recorded in earthquakes such as the 1989 Loma Prieta or 1995 Kobe earthquakes, or just about any other recorded strong ground motion of interest.”

Recently, the UC Davis team upgraded the motion controller they use on their 1-m-radius centrifuge shaker. “Our old hydraulic controller was a homemade device that we couldn’t maintain,” said Wilson. “We wanted a controller that was highly reliable, capable of producing extreme, high-frequency waveforms under closed-loop control, and one that is easy to program for different applications. Plus, we wanted one that would interface easily to a PC running LabVIEW.” The researchers use the LabVIEW program by National Instruments to do filtering and scaling of the earthquake files, as well as collect data from instruments during the experiments.

The shaker on the 1-m radius centrifuge operates at 3000 psi with a peak force of around 4500 pounds, shaking a payload of around 150 pounds. It shakes with a peak stroke of ±6 mm and peak velocity of 0.3 m/s at frequencies up to 400 Hz (not all simultaneously). The high-frequency motions put a stress on hydraulic system components and controls. The frequencies are beyond the resonant frequencies of the oil column and the servo valve being used, and the mass that is being driven is very large compared to the reaction mass available. Plus, the payload (soil sample) can go from something very stiff to very soft during the testing (wet soil can liquefy during an earthquake). This means that the closed-loop controls will be receiving feedback that changes nonlinearly and rapidly during the simulation run.

Selecting the Motion Controller

Figure 3. The actuator, servo valve, and feedback LVDT are mounted below the soil and structure model. The steel beams support the model container in the g field and provide the reaction mass for shaking.

To upgrade the controls in the earthquake simulator, the UC Davis team selected an RMC70 Series motion controller from Delta Computer Systems of Battle Ground, WA. When running a simulation, the controller uses position feedback that it gets from a linear variable displacement transducer (LVDT) to close the position control loop. The motion controller is mounted in a box on the wall outside the centrifuge, and the LVDT and load cell feedback signals and the valve coil drive signal run over slip rings to the actuator on the centrifuge. The UC Davis team has been using Delta’s RMCTools software package to generate motion commands to check out the hardware. The tuning wizard was used as the starting point for all of the tuning. In the case of the shaker, the motion open loop is run at the highest frequencies.

The auto-tuning provided baseline PID coefficients used for feedback control at slower speeds. Typically, the UC Davis team starts out the system with a new model by doing linear motion at relatively slow speeds. Once the system is stabilized, the motion is switched to produce sine waves, and then the researchers switch to using more complex waveforms in proving out the hardware. Full simulation runs are then done using the filtered earthquake waveforms that are downloaded from the PC to the RMC using Modbus TCP/IP over Ethernet. One of the early challenges that needed to be overcome by the team was the ability to manage the high motion frequencies that were being produced. At the frequencies at which they were operating, some of the position feedback was out of phase with the motion.

The team needed to filter out higher-frequency feedback signals in order to keep the motion under control. The new control system has been used so far primarily for a study on using biobiological grouting methods for liquefaction remediation. In this work, researchers harness naturally occurring biological processes to create cemented sands in the hope they can reduce the risk of liquefaction. The project is a challenge to control because the researchers want to recreate the same motion in models that fully liquefy (i.e. become very soft) to models that are fully cemented (i.e. very stiff). Interesting things that the team has learned include how to tune a system that is very nonlinear in its response. The properties of the system change as it shakes, and soil changes to slurry. Getting the system to respond well under both sets of conditions is a challenge.

This article was written by Bill Savela of Delta Computer Systems. For more information, Click Here.


  1. Chou et al, “Centrifuge Modeling of Seismically-Induced Uplift for the BART Transbay Tube”, Journal of Geotechnical and Geoenvironmental Engineering (Print date TBD)
  2. B.L. Kutter, "Dynamic Centrifuge Modeling of Geotechnical Structures", Trans portation Research Record 1336, TRB, National Research Council, pp. 24-30, Washington, DC, 1992.
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