State-Space PID: A Missing Link Between Classical and Modern Control

Abstract

PID control is widely applied in industry. However, it is classified as a classical control technique, in that transfer function method is used to represent the ideal and/or practical PID controller. Modern control concepts, such as state feedback, observer, are seldom found in PID research. This paper proposes a state-space PID structure to fill the gap. The classical ideal PID is first shown to be a state-feedback control structure with the plant output and its derivative and integral as the states, and then a model-independent observer is proposed to estimate the states, thus approximate the ideal PID as a observer-based state feedback control structure (state-space PID). Then it is shown that the proposed state-space PID structure is the dual of the linear active disturbance rejection control structure, and it is a general-purposed control structure in that any strictly-proper linear controller with integration can be implemented via the proposed structure. The design of the state-space PID can be done via the well-known pole placement algorithm in modern control. Simulation and experiment results show that state-space PID structure is a practical implementation of ideal PID, which naturally integrates the noise reduction that is separated from PID tuning, and it is a natural generalization of the classical PID to high-order cases.