On the Generalization of Integrator and Integral Control Action

Baishun Liu

doi:10.4236/ijmnta.2014.32007

Abstract

This paper provides a solution to generalize the integrator and the integral control action. It is achieved by defining two function sets to generalize the integrator and the integral control action, respectively, resorting to a stabilizing controller and adopting Lyapunov method to analyze the stability of the closed-loop system. By originating a powerful Lyapunov function, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established by some bounded information. Consequently, the justification of two propositions on the generalization of integrator and integral control action is verified. Moreover, the conditions used to define the function sets can be viewed as a class of sufficient conditions to design the integrator and the integral control action, respectively.

Highlights

Integral control [1] plays an important role in control system design because it ensures asymptotic tracking and disturbance rejection
The main contributions are as follows: 1) two function sets, which are used to generalize the integrator and the integral control action, respectively, are defined; 2) the integrator can be taken as any integrable function, which passes through the origin and whose partial derivative, induced by mean value theorem, is positive-define and bounded
The conditions on the function above can be viewed as a class of sufficient conditions to design an integrator; 3) the integral control action can be taken as any continuous differential increasing function with the positive-define bounded derivative

Summary

Introduction

Integral control [1] plays an important role in control system design because it ensures asymptotic tracking and disturbance rejection. In the presence of the parametric uncertainties and the unknown constant disturbances, the stabilizing controller is used to guarantee the stability of the closed-loop system, and the integrator and the integral control action are utilized to create a steady-state control action at the equilibrium point such that the tracking error is zero. This shows that the integrator and the integral control action are two indispensable components to design an integral controller.

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Methods

Conclusion