For positioning systems, advanced setpoint design methods can effectively reduce end-effector vibrations. An example where such methods are being applied is shown within image guided therapy (IGT) systems. A reduction of residual vibrations by an order of magnitude was achieved. This is beneficial for safety, drive-train design requirements and operator/patient perception.
How to move a heavy load accurately and quickly? Performance of such positioning systems is often limited by dynamics. Even though servo performance at the motor side is fine, the end-effector might show large oscillations, e.g. due to a disadvantageous mass distribution or a limited drive-train stiffness. A typical example of this phenomenon can be found in a C-arc system from Philips IGT Systems:
The animation shows a simple model of the drive-train compliance while moving. The end-effector represents the large C-arc, which is heavy compared to the motor. While moving the end-effector, the drive-train deforms due to its limited stiffness. Given that the position sensor is typically located at the motor side, the sensor measurement will deviate from the actual end-effector position resulting in residual vibrations after the movement.
Throughput and settling accuracy are prescribed by the system requirements. However, the motion profile itself is subject to design freedom which can be exploited by advanced setpoint design. Extensive experience at Philips Engineering Solutions with ever increasing servo performance requirements (both in customer projects and in in-house competence development projects) has shown the crucial impact and power of advanced setpoint design.
Advanced setpoint design
A generic control structure is shown below. Typically, both feedback and feedforward control are used to generate a force such that the system’s position accurately follows the setpoint. The control force excites the system dynamics resulting in unwanted vibrations.
A 3rd order polynomial setpoint (i.e., with limits on velocity, acceleration and jerk) is commonly used in motion systems. For the given application, overshoot is the main performance criterion. Two setpoint design methods have been explored to improve settling behavior of the end-effector: 1) Setpoint optimization reduces vibrations by shaping the parametrized setpoint. 2) An additional feedback setpoint filter reduces vibrations even more. Essentially, this filter is only applied to the feedback setpoint, not to the feedforward setpoint .
Experimental results are shown below:
Most applications provide motion profile design freedom. Settling performance can be improved by advanced setpoint design, especially settling performance at the end-effector. For the given application, residual vibrations were reduced by an order of magnitude.
 D. Bruijnen and N. van Dijk, “Combined input shaping and feedforward control for flexible motion systems,” 2012 American Control Conference (ACC), Montreal, QC, 2012, pp. 2473-2478.
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