Hyper Sliding Mode Control: A Novel Approach Achieving Robustness With Model Order Uncertainty

A novel approach to the control of plants with model order uncertainty as well as
parametric errors and external disturbances is presented, which yields a specified closed loop dynamic
response. Its foundations lie in sliding mode control, but the set of output derivatives fed back extend
to a maximum order of rmax −1, where rmax is the maximum likely rank of the plant. In
conventional sliding mode control, the number of output derivatives fed back is a set of state variables
equal in number to r −1, where r is the rank of the plant and derivatives of higher order than r −1,
which are not state variables, are not fed back, meaning that the plant order must be known in
advance. In hyper sliding mode control, originated by the author, although the output derivatives of
higher order than r are not plant state variables, they become state variables of the closed-loop system
and take part in the sliding mode. Thus, in cases where the maximum order of the output derivative
exceeds r −1, the order of the closed-loop system is greater than that of the plant, which is a small
price to pay for retaining the extreme robustness properties of sliding mode control.
The method is illustrated by means of simulations of a motion control system employing a permanent
magnet synchronous motor. An initial evaluation of the method is made by considering three plants
with different orders and ranks, the first being the unloaded drive, the second being the drive
controlling the motor rotor angle with a mass-spring load attached and the third being the drive
controlling the load mass angle of the same attached mass-spring load. The simulations indicate that
the control system does indeed yield robustness including plant order uncertainty.

Citation:
Dodds, S.J. (2006) ‘Hyper Sliding Mode Control: A Novel Approach Achieving Robustness With Model Order Uncertainty’ Proceedings of the AC&T, pp.142-148.