Review and recent development of internal model design

Abstract

Robust output regulation is a controller design theory for achieving reference tracking and disturbance rejection as well as system stability. The main feature of the theory is that the reference and/or disturbance signals have explicit structural description, especially by an exosystem. By decoding this structural information, the desired steady state/input of the system can be completely characterised, albeit not measurable or implementable due to system uncertainty. The steady state/input description simply copies the exosystem dynamics for simple systems, however, it relies on more complicated steady-state generators in most non-linear scenarios. Once the steady state/input is characterised, it can be estimated by an internal model. Proper construction of internal model can well compensate for the desired steady state/input resulting in a stabilisation problem about an equilibrium point. The control objective is achieved if such a stabilisation problem is solved. This paper does not ambitiously aim at a complete overview picture of the three decade development of output regulation theory. It attempts to show a small trail in the garden of vast collections of output regulation results that may lead the audience from simple to advanced internal model design techniques. In particular, it reviews the simple PID structure, the p-copy internal model for linear systems, various internal models for non-linear systems, and the recent development of generalised internal model to accommodate adaptive scheme.

Keywords:

• Internal model
• output regulation
• non-linear systems
• steady-state generator
• PID

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Australian Research Council [grant number DP150103745].