A comparison of software-based approaches to identifying FOPDT and SOPDT model parameters from process step response data

• A range of modern software approaches to system identification are compared.
• The approaches identify parameters for both FOPDT and SOPDT transfer functions.
• The methods can be used for systems with both zero and non-zero initial conditions.
• Aspects relating to the design of PI controllers are considered.
• The design methods exploit stability boundary loci in the KC–KI plane.

System identification is the experimental approach to deriving process models, which can take many forms depending upon their intended use. In the work described in this paper, the ultimate aim is to use them in the design of controllers for regulating engineering processes. Modelling always involves approximations since all real systems are to some extent non-linear, time-varying, and distributed. Thus, it is highly improbable that any set of models will contain the ‘true’ system structure. A more realistic aim is therefore to identify a model that provides an acceptable approximation, in the context of the application in which it is used. In controller design, a first step is often to determine the model using step and frequency response data. This paper compares different modern software approaches that exploit step response data, where the aim is to determine either a first- or second-order-plus-dead-time (FOPDT or SOPDT) transfer function. They include an integral equation method, an algorithm available in the MATLAB Optimization Toolbox, and recently developed in-house software that uses a particle swarm optimisation (PSO) approach.