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Fundamental periodic control

Fundamental periodic control

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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.

Chapter Contents:

  • Abstract
  • 2.1 Repetitive control (RC)
  • 2.1.1 Internal model of any periodic signal
  • 2.1.2 Classic RC scheme
  • 2.1.3 Digital RC system and design
  • 2.1.3.1 Steady-state error
  • 2.1.3.2 Asymptotic convergence rate
  • 2.1.3.3 Stability criteria
  • 2.1.3.4 Zero-phase compensation design
  • 2.1.3.5 Linear phase-lead compensation design
  • 2.1.4 Two alternative RC schemes
  • 2.2 Multiple resonant control (MRSC)
  • 2.2.1 Internal models of harmonics
  • 2.2.2 MRSC scheme
  • 2.2.3 Digital MRSC system and design
  • 2.2.3.1 Steady-state error
  • 2.2.3.2 Stability criteria
  • 2.2.3.3 Zero-phase compensation design
  • 2.2.4 RSC - Generalized integrator for sinusoidal signals
  • 2.3 Discrete Fourier transform (DFT)-based RC
  • 2.3.1 DFT-based internal model of interested harmonics
  • 2.3.2 DFT-based RC scheme
  • 2.3.3 DFT-based RC system and design
  • 2.3.4 Modified DFT-based RC scheme
  • 2.4 Basis function
  • 2.5 Summary
  • References

Inspec keywords: periodic control; signal generators; stability; signal processing; control system synthesis; closed loop systems; Fourier transforms; feedback; machine control; error compensation

Other keywords: discrete Fourier transformation; RC; IMP; repetitive control; zero steady-state error compensation; multiresonant control; signal generator; internal model principle; MRSC; stable feedback loop; general design methodology; DFT; fundamental periodic control; periodic signals; universal plug-in structure

Subjects: Stability in control theory; Integral transforms; Control of electric power systems; Integral transforms; Signal generators; Control system analysis and synthesis methods; Optimal control; Signal processing theory; Signal processing and detection

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