Nonlinear pole assignment control of state dependent parameter models with time delays

Abstract: This paper considers pole assignment control of nonlinear dynamic systems described by State Dependent Parameter (SDP) models. The approach follows from earlier research into linear Proportional-Integral-Plus (PIP) methods but, in SDP system control, the control coefficients are updated at each sampling instant on the basis of the latest SDP relationships. Alternatively, algebraic solutions can be derived off-line to yield a practically useful control algorithm that is relatively straightforward to implement on a digital computer, requiring only the storage of lagged system variables, coupled with straightforward arithmetic expressions in the control software. Although the analysis is limited to the case when the open-loop system has no zeros, time delays are handled automatically. The paper shows that the closed-loop system reduces to a linear transfer function with the specified (design) poles. Hence, assuming pole assignability at each sample, global stability of the nonlinear system is guaranteed at the design stage. The associated conditions for pole assignability are stated.