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Frequency-based Design Method for Model-Free Controllers

Marcos Moreno-Gonzalez, Antonio Artuñedo, Jorge Villagra

Abstract

Model-Free Control (MFC) has been applied to a wide variety of systems in which it has shown its performance. MFC offers "model-free operation", but the controller design requires some information from the nominal plant. This paper introduces a new design method for model-free controllers that uses minimal data about the system and retrieves a set of stable controller configurations. This method is specifically developed for first-order model-free controllers, but can be extended to second-order controllers, and it relies in a frequency analysis of the controller and the plant. The main feature of the design method is decoupling the design of the main control parameter alpha from the rest, providing specific values for it. The efficacy of the proposed method will be showcased with some relevant application examples.

Frequency-based Design Method for Model-Free Controllers

Abstract

Model-Free Control (MFC) has been applied to a wide variety of systems in which it has shown its performance. MFC offers "model-free operation", but the controller design requires some information from the nominal plant. This paper introduces a new design method for model-free controllers that uses minimal data about the system and retrieves a set of stable controller configurations. This method is specifically developed for first-order model-free controllers, but can be extended to second-order controllers, and it relies in a frequency analysis of the controller and the plant. The main feature of the design method is decoupling the design of the main control parameter alpha from the rest, providing specific values for it. The efficacy of the proposed method will be showcased with some relevant application examples.

Paper Structure

This paper contains 18 sections, 25 equations, 10 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. MODEL-FREE CONTROL WITH ULTRA-LOCAL MODEL
  3. DESIGN OF $\alpha$
  4. First Order Ultra-local Model
  5. Second Order Ultra-local Model
  6. DESIGN OF THE $PD(z)$ CONTROLLER
  7. Module Condition
  8. Phase Condition
  9. SIMPLIFIED DESIGN METHOD
  10. Simplified module condition
  11. Simplified phase condition
  12. INVERTED PENDULUM CONTROL DESIGN
  13. VEHICLE LONGITUDINAL CONTROL DESIGN
  14. Identified vehicle longitudinal dynamics
  15. Inner loop iPD design
  16. ...and 3 more sections

Figures (10)

  • Figure 1: Block diagram of the iPD controller
  • Figure 2: The iPD controller as an ILFC
  • Figure 3: Inverted pendulum with cart
  • Figure 4: Stability set of the inverted pendulum controller
  • Figure 5: Step response of the inverted pendulum
  • ...and 5 more figures

Theorems & Definitions (1)

  • Remark 1