Two applications of multivariable delta operator PIP control

The concept of the discrete differential or delta (δ) operator has been revived by Goodwin et al. (1988) to bridge the gap between the control theory expressed in terms of the continuous time derivative or Laplace (s) operator and the control system design implemented in the backward shift operator. To reflect this innovation, the PIP control design philosophy has been extended from backward shift to the δ operator nonminimum state space representation, based upon the definition of a state vector where the states are the input and output signals together with their discrete derivatives, as well as the required integral of error term. The control law is then implemented in terms of realisable delta operator filters. In this paper, we consider the design of a delta operator PIP controller and show how it can be applied to two multivariable control problems