Stabilization using fractional-order PI and PID controllers
SE Hamamci - Nonlinear Dynamics, 2008 - Springer
Nonlinear Dynamics, 2008•Springer
This paper presents a solution to the problem of stabilizing a given fractional dynamic
system using fractional-order PIλ and PI λ D μ controllers. It is based on plotting the global
stability region in the (kp, ki)-plane for the PI λ controller and in the (kp, ki, kd)-space for the
PIλDμ controller. Analytical expressions are derived for the purpose of describing the
stability domain boundaries which are described by real root boundary, infinite root
boundary and complex root boundary. Thus, the complete set of stabilizing parameters of …
system using fractional-order PIλ and PI λ D μ controllers. It is based on plotting the global
stability region in the (kp, ki)-plane for the PI λ controller and in the (kp, ki, kd)-space for the
PIλDμ controller. Analytical expressions are derived for the purpose of describing the
stability domain boundaries which are described by real root boundary, infinite root
boundary and complex root boundary. Thus, the complete set of stabilizing parameters of …
Abstract
This paper presents a solution to the problem of stabilizing a given fractional dynamic system using fractional-order PIλ and PIλDμ controllers. It is based on plotting the global stability region in the (k p, k i)-plane for the PIλ controller and in the (k p , k i , k d)-space for the PIλDμ controller. Analytical expressions are derived for the purpose of describing the stability domain boundaries which are described by real root boundary, infinite root boundary and complex root boundary. Thus, the complete set of stabilizing parameters of the fractional-order controller is obtained. The algorithm has a simple and reliable result which is illustrated by several examples, and hence is practically useful in the analysis and design of fractional-order control systems.
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