Proportional-integral-plus (PIP) design for delta (d ) operator systems : part 1, SISO systems.

The paper presents a general approach to state variable feedback control of rapidly sampled linear systems described by discrete differential or delta (delta) operator transfer function models. This is based on the formulation of a special nonminimum state-space representation of the system which ensures that the state variable feedback control law can be implemented in terms of realizable compensation filters, thus avoiding the complication and limitations of state reconstruction filter (observer or Kalman filter) design. The necessary and sufficient conditions for the controllability and pole assignability of the proportional-integral-plus (PIP) controller obtained in this manner are developed and, in the case of SVF pole assignment, the relationships between the coefficients of the desired closed-loop characteristic polynomial and the control feedback gains are developed. Singleinput single-output deterministic systems are considered, but the approach can be extended to multivariable and stochastic systems, as described in two companion papers. The effectiveness of the design procedure is illustrated by both simulation and practical examples