A look at the pole/zero structure of a Stewart platform using special coordinate basis

The cubic hexapod, or Stewart platform, has become a popular approach to the problem of active control of vibration because it can be placed directly in the path of vibration transmission and provides 6-axis isolation. Typically the control approach has been to use classical techniques with a variety of sensors, but a multi-input, multi-output (MIMO) approach holds much promise. Before designing controllers, however, it is important to know a great deal about the model, particularly the zero structure. Information on the size and position (minimum vs. nonminimum phase) of system zeros is necessary in predicting the opportunity for robustness recovery in MIMO controller design. A technique known as special coordinate basis (SCB) was applied to a model of a hexapod that was constructed by the Hood Technology Corporation and the University of Washington. Examining sensors including load cells, geophones and linear variable differential transforms (LVDT), it was found that, though the use of other sensors offers some significant advantages for MIMO control over classical approaches, the well known robustness recovery tool known as loop transfer recovery (LTR), cannot be used because of the presence of small nonminimum phase zeros