In order to make the inverted pendulum stable, researches proposed kinds of control strategies: (i) Bang-Bong control strategy,(ii) PID control strategy,(iii) Sliding mode control strategy,(iv) Fuzzy Logic Control strategy, (v) Predictive control strategy, (vi) Fractional PID strategy. Bang-Bong control strategy required complex calculations. Another control strategy, such as PID control strategy is a conventional classic controller can be used to stabilize one output from the two outputs. Fractional order proportional-integral-derivative (FOPID) controller is the recent advances amendment controller of a conventional classical PID controller. The earliest studies concerning fractional calculus presented in the 19th century made by some researchers such as Liouville (1832), Holmgren (1864), and Riemann (1953) ,and others made some contributions in this field in the past.
Fractional order control calculus presented by Tustin for the position control of massive objects a half century ago. Provided some of the other researches were made by the searcher Manabe around (1960). However, the fractional-order control was not included in to Control Engineering Because of the major limitations of the possibilities and a lack of adequate amount of mathematical knowledge and computational power at this time (Aleksei Tepljakov, Eduard Petlenkov, Juri Belikov, and Jevgeni Finajev 2013).The researchers have concluded in the past decades that the (fractional order differential equations) could model diverse systems fuller than integer-order ones and provision an excellent instrument for describing dynamic processes.In fractional order controllers, in addition to parameters of the classical proportional-integral-derivative constants there are two extra parameters (Lambda and Miu) (M. Yahyazadeh,and M. Haeri 2008). Lambda and Miu parameters are the order of s in integral and derivative respectively so a specific algorithm is required to make tuning for the parameters of the FOPID Controller. This will improve the system performance in terms of flexibility and durability better than the classical PID controller.
The organization of this paper is as follows. Section 2 illustrates the mathematical modeling of the inverted pendulum system. Section 3 will introduce the control techniques that used in controlling the inverted pendulum system. In Section 4, we will give the control strategy containing the design procedures of LQR gains and FOPID gains with Kf gain that applied on the inverted pendulum system. Section 5, Simulation results of inverted pendulum system are shown in different control conditions. Section 6 gives the conclusions of the paper.