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Reinterpreting PID Controller From the Perspective of State Feedback and Lumped Disturbance Compensation

Xinyu Shi

Abstract

This paper analyzes the motion of solutions to non-homogeneous linear differential equations. It further clarifies that a proportional-integral-derivative (PID) controller essentially comprises two parts: a homogeneous controller and a disturbance observer, which are responsible for stabilizing the homogeneous system and compensating for the lumped disturbances (non-homogeneous components) of the system respectively. Based on this framework, the impact of measurement noise on control performance is examined, and a parameter tuning scheme for the traditional PID controller is provided. Finally, as examples, controllers are designed for two representative control problems: a trajectory tracking controller for an underactuated vertical takeoff and landing (VTOL) aircraft in the time domain, and a lateral controller for a vehicle in the distance domain.

Reinterpreting PID Controller From the Perspective of State Feedback and Lumped Disturbance Compensation

Abstract

This paper analyzes the motion of solutions to non-homogeneous linear differential equations. It further clarifies that a proportional-integral-derivative (PID) controller essentially comprises two parts: a homogeneous controller and a disturbance observer, which are responsible for stabilizing the homogeneous system and compensating for the lumped disturbances (non-homogeneous components) of the system respectively. Based on this framework, the impact of measurement noise on control performance is examined, and a parameter tuning scheme for the traditional PID controller is provided. Finally, as examples, controllers are designed for two representative control problems: a trajectory tracking controller for an underactuated vertical takeoff and landing (VTOL) aircraft in the time domain, and a lateral controller for a vehicle in the distance domain.

Paper Structure

This paper contains 9 sections, 48 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Motion of the Solution to a Non-Homogeneous Linear Differential Equation
  3. State Feedback and Lumped Disturbance Compensation
  4. Control Design and Tuning Scheme
  5. PI and PID Controllers
  6. Control Design Examples
  7. Trajectory Tracking Control for Underactuated VTOL Aircraft
  8. Lateral Control of the Vehicle
  9. Discussion and Conclusion

Figures (2)

  • Figure 1: Schematic diagram of vehicle lateral path tracking in Frenet--Serret frame
  • Figure 2: Schematic diagram of vehicle lateral path tracking in vehicle frame

Theorems & Definitions (2)

  • Remark 1
  • Remark 2