Bettayeb M, Boussalem C, Mansouri R, Al-Saggaf UM. Stabilization of an inverted pendulum-cart system by fractional PI-state feedback.
ISA Trans 2014;
53:508-516. [PMID:
24315056 DOI:
10.1016/j.isatra.2013.11.014]
[Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2013] [Revised: 08/20/2013] [Accepted: 11/12/2013] [Indexed: 06/02/2023]
Abstract
This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=K(p)x(t)+K(I)I(α)(x(t)). The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n-1 (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments.
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