Fundamental periodic control

The internal model principle (IMP) states that perfect asymptotic rejection/tracking of persistent inputs can only be attained by replicating the signal generator in a stable feedback loop [1]. The signal generator is also called "internal model"of the inputs. W. M. Wonham summarized IMP as "Every good regulator must incorporate a model of the outside world."Based on IMP [1,2], this chapter presents the fundamental periodic controllers for providing zero steady-state error compensation for periodic signals and elaborates their general design methodology. These IMP-based periodic controllers include repetitive control (RC) [3-21], multi-resonant control (MRSC) [22-34], and discrete Fourier transformation (DFT)-based RC [26,35-36]. The general design methodology comprises a standard internal model for periodic signals and the synthesis methods for universal plug-in structure periodic control (PC) systems. The relationship among these three fundamental periodic controllers will also be demonstrated.