State feedback with fractional integral control design based on the Bode’s ideal transfer function |
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| Authors: | U.M. Al-Saggaf I.M. Mehedi M. Bettayeb |
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| Affiliation: | 1. Electrical and Computer Engineering Department, Center of Excellence in Intelligent Engineering Systems, King Abdulaziz University, Jeddah, Saudi Arabia;2. Electrical &3. Computer Engineering Department, University of Sharjah, United Arab Emirates and Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, Saudi Arabia |
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| Abstract: | State feedback technique through a gain matrix has been a well-known method for pole assignment of a linear system. The technique could encounter a difficulty in eliminating the steady-state errors in some states. Introducing an integral element can effectively eliminate these errors. State feedback with fractional integral control is proposed, in this work, for pole placement of a linear time invariant system. The proposed method yields simple gain formulae. The paper presents the derivation of the design formulae. The method is applied to stabilise an inherently unstable inverted pendulum-cart system. Simulation and experimental results show the effectiveness of the proposed method for set-point tracking, disturbance rejection and stabilising the inverted pendulum. Comparison with the results obtained from applying Achermann’s formula is also presented. |
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| Keywords: | fractional order controller state space representation state feedback control state feedback with fractional integral control Bode’s ideal transfer function robust control |
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