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

• Derivation of a closed-form model-plant mismatch expression for linear and time-invariant plants.
• The expression can be applied to single-input single-output as well as multiple-input multiple-output systems.
• The expression is applied to industrial data to show its applicability.

When a plant and its controller are sufficiently linear and time-invariant so that they can be represented by transfer functions, and this plant is under classical control (meaning the controller can also be represented by a transfer function), the model-plant mismatch (MPM) that often plagues industrial processes can be written as a closed-form expression. This includes a variety of controllers, among which the ubiquitous Proportional, Integral and Derivative (PID) controller. The MPM expression can then be used to identify 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 systems. The closed-loop data required for application of the expression has to be sufficiently exciting. If significant disturbances perturb the plant their values need to be available. In this article the expression is applied to industrial data to show its applicability.