Abstract
In this study, an algebraic stability test procedure is presented for fractional order time delay systems. This method is based on the principle of eliminating time delay. The stability test of fractional order systems cannot be examined directly using classical methods such as Routh-Hurwitz, because such systems do not have analytical solutions. When a system contains the square roots of s, it is seen that there is a double value function of s. In this study, a stability test procedure is applied to systems including sqrt(s) and/or different fractional degrees such as s^alpha where 0 < ? < 1, and ? include in R. For this purpose, the integer order equivalents of fractional order terms are first used and then the stability test is applied to the system by eliminating time delay. Thanks to the proposed method, it is not necessary to use approximations instead of time delay term such as Pade. Thus, the stability test procedure does not require the solution of higher order equations.
Highlights
The systems shown by differential equations with real orders instead of integer orders are called fractional order systems [1]
An algebraic stability test procedure based on the principle of eliminating time delay is presented for fractional order systems with a single time delay
A fractional order equation has been turned into an integer-order one, and the stability test has been applied to the system
Summary
The systems shown by differential equations with real orders instead of integer orders are called fractional order systems [1]. The CFE method is preferred to obtain integer order approximations of FOS. The stability test is applied to the system by eliminating time delay As it is known, in general, analytical stability test procedures of time delay systems require to use some approximation methods such as Pade. We need to use higher order Pade approximations instead of time delay term to obtain more reliable results This process makes the analysis of time delay systems more complicated. The stability test procedure does not require the solution of higher order equations This makes the proposed method practical and preferable. An algebraic stability test procedure is presented for fractional order time delay systems.
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