Development and application of a model-plant mismatch expression for linear time-invariant systems

Abstract

When a plant and its controller are sufficiently linear and time-invariant so that they can be representedby transfer functions, and this plant is under classical control (meaning the controller can also be repre-sented by a transfer function), the model-plant mismatch (MPM) that often plagues industrial processescan be written as a closed-form expression. This includes a variety of controllers, among which the ubiq-uitous Proportional, Integral and Derivative (PID) controller. The MPM expression can then be used toidentify a representative transfer function of the “true plant” from the currently available plant model.The MPM expression works for single-input single-output as well as multiple-input multiple-output sys-tems. The closed-loop data required for application of the expression has to be sufficiently exciting. Ifsignificant disturbances perturb the plant their values need to be available. In this article the expressionis applied to industrial data to show its applicability.