Forced dynamic control of non-minimum-phase plants via study of the classical inverted pendulum

The general problem of controlling a non-minimum-phase plant is tackled via study of the
classical inverted pendulum (IP). A full nonlinear model of the IP is used for simulation and a
linearised version is used for the controller design. The trolley position is controlled while keeping
the pendulum inverted by use of an input/output feedback linearisation method called Forced
Dynamic Control (FDC). This is generally more straightforward to apply than conventional
techniques such as linear state feedback with pole assignment but in its basic form yields right half
plane zero cancellation which creates an unstable closed loop mode. This is circumvented in this
paper by creating an artificial controlled output that is a weighted sum of the state variables such that
the right half plane zeros do not exist in the transfer function. Furthermore a non-oscillatory response
with a specified settling time is achieved with the aid of the Dodds settling time formula (Dodds,
2008). The computational delay introduced to eliminate the algebraic loop in the nonlinear model is
shown to have a negligible effect. Simulations are presented that demonstrate the correct operation of
the control system and determine differences between the ideal and actual step responses due to the
nonlinearities, parametric errors and external disturbances.

Citation:
Pedersen, J.L. and Dodds, S.J. (2010) ‘Forced dynamic control of nonminimum- phase plants via study of the classical inverted pendulum’ Proceedings of Advances in Computing and Technology, (AC&T) The School of Computing and Technology 5th Annual Conference, University of East London, pp.45-53..