Abstract
This paper proposes a robust servo controller deign for MIMO systems based on a linear shift invariant differential (LSID) operator and its inverse operator on Schwartz space using the internal model principle (IMP). To do this task, the followings are done. First, the basic concept idea of LSID operator and its invertible operator are described. Furthermore, the IMP is rearranged based on LSID operator and the IMP is modified by the properties of the LSID operator. Second, an extended system operated by the LSID operator to a given MIMO system with the given reference is obtained. Third, the controllability checking of extended systems is done. Fourth, a state feedback law is obtained by solving the pole assignment problem with all the poles of the extended system. Fifth, The proposed controller is applied for controlling the sideslip angle and yaw rate of a 4-wheel steering vehicle as a MIMO system with 2 inputs of steering angles of front and rear wheels and two outputs of the sideslip angle and yaw rate. Finally, simulation results are shown to verify the effectiveness of the proposed controller.
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References
Davison, E.J., Smith, H.W.: Pole assignment in linear time-invariant multivariable systems with constant disturbances. Automatics 7, 489–498 (1971)
Davison, E.J.: The output control of linear time-invariant multivariable systems with unmeasurable arbitrary disturbances. IEEE Trans. Autom. Control 17(5) (1972)
Kim, S.B., Oh, S.J., Jung, Y.G., Kim, H.S.: Application of bilinear transformation method to servo system design and position control for a cart system. Trans. KIEE 40(3) (1991)
Lv, H., Liu, S.: Closed-loop handling stability of 4WS vehicle with yaw rate control. J. Mech. Eng. 59(10), 595–603 (2013)
Furuta, K., Sano, A., Atherton, D.: State Variable Methods in Automatic Control. Wiley, Chichester (1988)
Furuta, K., Kim, S.B.: Pole assignment in a specified disk. IEEE Trans. Auto. Control 32(5), 423–427 (1987)
Kim, S.B., Furuta, K.: Regulator design with poles on a specified region. Int. J. Control 47(1), 143–160 (1988)
Kim, D.H: Servo Controller Design Using Polynomial Differential Operator Method and Its Applications, Doctor Thesis, Mechanical Design Engineering Department, Pukyong National University (2015)
Kim, D.-H., Nguyen, T.H., Pratama, P.S., Gulakari, A.V., Kim, H.-K., Kim, S.-B.: Servo system design for speed control of AC induction motors using polynomial differential operator. Int. J. Control Autom. Syst. 15(3), 1207–1216 (2017)
Acknowledgement
This research was conducted under the Pukyong National University Research Park (PKURP) for Industry-Academic Convergence R&D support program, which is funded by the Busan Metropolitan City, Korea.
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Kim, D.H., Kim, S.B. (2020). Robust Servo Controller Design Based on Linear Shift Invariant Differential Operator. In: Zelinka, I., Brandstetter, P., Trong Dao, T., Hoang Duy, V., Kim, S. (eds) AETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application. AETA 2018. Lecture Notes in Electrical Engineering, vol 554. Springer, Cham. https://doi.org/10.1007/978-3-030-14907-9_48
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DOI: https://doi.org/10.1007/978-3-030-14907-9_48
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