Equal Ratio Gain Technique and Its Application in Linear General Integral Control ()
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.
Share and Cite:
Liu, B. (2015) Equal Ratio Gain Technique and Its Application in Linear General Integral Control.
International Journal of Modern Nonlinear Theory and Application,
4, 21-36. doi:
10.4236/ijmnta.2015.41003.
Conflicts of Interest
The authors declare no conflicts of interest.
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