Abstract
In conjunction with linear general integral control, this paper proposes a fire-new control design technique, named Equal ratio gain technique, and then develops two kinds of control design methods, that is, Decomposition and Synthetic methods, for a class of uncertain nonlinear system. By Routh’s stability criterion, we demonstrate that a canonical system matrix can be designed to be always Hurwitz as any row controller gains, or controller and its integrator gains increase with the same ratio. By solving Lyapunov equation, we demonstrate that as any row controller gains, or controller and its integrator gains of a canonical system matrix tend to infinity with the same ratio, if it is always Hurwitz, and then the same row solutions of Lyapunov equation all tend to zero. By Equal ratio gain technique and Lyapunov method, theorems to ensure semi-globally asymptotic stability are established in terms of some bounded information. Moreover, the striking robustness of linear general integral control and PID control is clearly illustrated by Equal ratio gain technique. Theoretical analysis, design example and simulation results showed that Equal ratio gain technique is a powerful tool to solve the control design problem of uncertain nonlinear system.
Highlights
The complexity of nonlinear system challenges us to come up with systematic design methods to meet control objectives and specifications
The main contributions are as follows: 1) a canonical system matrix can be designed to be always Hurwitz as any row controller gains, or controller and its integrator gains increase with the same ratio; 2) as any row controller gains, or controller and its integrator gains of a canonical system matrix tend to infinity with the same ratio, if it is always Hurwitz, and the same row solutions of Lyapunov equation all tend to zero; 3) theorems to ensure semi-globally asymptotic stability are established in terms of some bounded information
The striking robustness of linear general integral control and PID control is clearly illustrated by Equal ratio gain technique
Summary
The complexity of nonlinear system challenges us to come up with systematic design methods to meet control objectives and specifications. (2015) Equal Ratio Gain Technique and Its Application in Linear General Integral Control. For illustrating the practicability and validity of Equal ratio gain technique and the good robustness of linear general integral control, this paper addresses general integral control design again. Based on Equal ratio gain technique, this paper develops two kinds of systematic methods to design linear general integral control for a class of uncertain nonlinear system, that is, one is Decomposition method and another is Synthetic method. The striking robustness of linear general integral control and PID control is clearly illustrated by Equal ratio gain technique. All these mean that Equal ratio gain technique is a powerful tool to solve the control design problem of uncertain nonlinear system, and makes the engineers more design a stable controller.
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