Stabilizing and positioning control of inverted flexible pendulum by means of H∞ servo control with partial-state feedback

Hidekazu Nishimura; Osamu Ohnuki; Kenzo Nonami; Takayoshi Totani

Stabilizing and positioning control of inverted flexible pendulum by means of H^∞ servo control with partial-state feedback

Hidekazu Nishimura, Osamu Ohnuki, Kenzo Nonami, Takayoshi Totani

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this study we formulate H^∞ servo compensator where displacement signals are used as the controlled variables and their time derivatives are used as partial-state feedback signals for stabilizing and positioning control of a cart and inverted flexible pendulum system. The feedback loop of the part of the state variables except the controlled variables is added to the feedback loop of the controlled variables in the design of the H^∞ compensator. Through this formulation the order of the designed compensator is reduced by the order of the weighting functions for the time derivative signals. By numerical calculations and experiments, we investigate the settling characteristics and the robust stability against a disturbance to the pendulum with two kinds of controllers, the output feedback controller by the displacement feedback and the output feedback controller adding the cart velocity feedback. It is shown that although the displacement-output feedback controller has a big overshoot in the step response and the positioning of the cart is difficult, by means of the partial-state feedback controller with a cart velocity feedback the overshoot can be reduced and stable positioning control of the cart is possible. Also it is verified that the servo compensator is superior to the regulator-based compensator in the settling characteristics.

Original language	English
Title of host publication	15th Biennial Conference on Mechanical Vibration and Noise
Editors	K.W. Wang, B. Yang, J.Q. Sun, K. Seto, K. Yoshida, al et al
Edition	3 Pt C
Publication status	Published - 1995 Dec 1
Externally published	Yes
Event	Proceedings of the 1995 ASME Design Engineering Technical Conference. Part C - Boston, MA, USA Duration: 1995 Sept 17 → 1995 Sept 20

Publication series

Name	American Society of Mechanical Engineers, Design Engineering Division (Publication) DE
Number	3 Pt C
Volume	84

Other

Other	Proceedings of the 1995 ASME Design Engineering Technical Conference. Part C
City	Boston, MA, USA
Period	95/9/17 → 95/9/20

ASJC Scopus subject areas

Engineering(all)

Cite this

Nishimura, H., Ohnuki, O., Nonami, K., & Totani, T. (1995). Stabilizing and positioning control of inverted flexible pendulum by means of H^∞ servo control with partial-state feedback. In K. W. Wang, B. Yang, J. Q. Sun, K. Seto, K. Yoshida, & A. et al (Eds.), 15th Biennial Conference on Mechanical Vibration and Noise (3 Pt C ed.). (American Society of Mechanical Engineers, Design Engineering Division (Publication) DE; Vol. 84, No. 3 Pt C).

Stabilizing and positioning control of inverted flexible pendulum by means of H^∞ servo control with partial-state feedback. / Nishimura, Hidekazu; Ohnuki, Osamu; Nonami, Kenzo et al.
15th Biennial Conference on Mechanical Vibration and Noise. ed. / K.W. Wang; B. Yang; J.Q. Sun; K. Seto; K. Yoshida; al et al. 3 Pt C. ed. 1995. (American Society of Mechanical Engineers, Design Engineering Division (Publication) DE; Vol. 84, No. 3 Pt C).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Nishimura, H, Ohnuki, O, Nonami, K & Totani, T 1995, Stabilizing and positioning control of inverted flexible pendulum by means of H^∞ servo control with partial-state feedback. in KW Wang, B Yang, JQ Sun, K Seto, K Yoshida & A et al (eds), 15th Biennial Conference on Mechanical Vibration and Noise. 3 Pt C edn, American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, no. 3 Pt C, vol. 84, Proceedings of the 1995 ASME Design Engineering Technical Conference. Part C, Boston, MA, USA, 95/9/17.

Nishimura H, Ohnuki O, Nonami K, Totani T. Stabilizing and positioning control of inverted flexible pendulum by means of H^∞ servo control with partial-state feedback. In Wang KW, Yang B, Sun JQ, Seto K, Yoshida K, et al A, editors, 15th Biennial Conference on Mechanical Vibration and Noise. 3 Pt C ed. 1995. (American Society of Mechanical Engineers, Design Engineering Division (Publication) DE; 3 Pt C).

Nishimura, Hidekazu ; Ohnuki, Osamu ; Nonami, Kenzo et al. / Stabilizing and positioning control of inverted flexible pendulum by means of H^∞ servo control with partial-state feedback. 15th Biennial Conference on Mechanical Vibration and Noise. editor / K.W. Wang ; B. Yang ; J.Q. Sun ; K. Seto ; K. Yoshida ; al et al. 3 Pt C. ed. 1995. (American Society of Mechanical Engineers, Design Engineering Division (Publication) DE; 3 Pt C).

@inbook{502b70542604458b8a3a0800a9872003,

title = "Stabilizing and positioning control of inverted flexible pendulum by means of H∞ servo control with partial-state feedback",

abstract = "In this study we formulate H∞ servo compensator where displacement signals are used as the controlled variables and their time derivatives are used as partial-state feedback signals for stabilizing and positioning control of a cart and inverted flexible pendulum system. The feedback loop of the part of the state variables except the controlled variables is added to the feedback loop of the controlled variables in the design of the H∞ compensator. Through this formulation the order of the designed compensator is reduced by the order of the weighting functions for the time derivative signals. By numerical calculations and experiments, we investigate the settling characteristics and the robust stability against a disturbance to the pendulum with two kinds of controllers, the output feedback controller by the displacement feedback and the output feedback controller adding the cart velocity feedback. It is shown that although the displacement-output feedback controller has a big overshoot in the step response and the positioning of the cart is difficult, by means of the partial-state feedback controller with a cart velocity feedback the overshoot can be reduced and stable positioning control of the cart is possible. Also it is verified that the servo compensator is superior to the regulator-based compensator in the settling characteristics.",

author = "Hidekazu Nishimura and Osamu Ohnuki and Kenzo Nonami and Takayoshi Totani",

year = "1995",

month = dec,

day = "1",

language = "English",

series = "American Society of Mechanical Engineers, Design Engineering Division (Publication) DE",

number = "3 Pt C",

editor = "K.W. Wang and B. Yang and J.Q. Sun and K. Seto and K. Yoshida and {et al}, al",

booktitle = "15th Biennial Conference on Mechanical Vibration and Noise",

edition = "3 Pt C",

note = "Proceedings of the 1995 ASME Design Engineering Technical Conference. Part C ; Conference date: 17-09-1995 Through 20-09-1995",

}

TY - CHAP

T1 - Stabilizing and positioning control of inverted flexible pendulum by means of H∞ servo control with partial-state feedback

AU - Nishimura, Hidekazu

AU - Ohnuki, Osamu

AU - Nonami, Kenzo

AU - Totani, Takayoshi

PY - 1995/12/1

Y1 - 1995/12/1

N2 - In this study we formulate H∞ servo compensator where displacement signals are used as the controlled variables and their time derivatives are used as partial-state feedback signals for stabilizing and positioning control of a cart and inverted flexible pendulum system. The feedback loop of the part of the state variables except the controlled variables is added to the feedback loop of the controlled variables in the design of the H∞ compensator. Through this formulation the order of the designed compensator is reduced by the order of the weighting functions for the time derivative signals. By numerical calculations and experiments, we investigate the settling characteristics and the robust stability against a disturbance to the pendulum with two kinds of controllers, the output feedback controller by the displacement feedback and the output feedback controller adding the cart velocity feedback. It is shown that although the displacement-output feedback controller has a big overshoot in the step response and the positioning of the cart is difficult, by means of the partial-state feedback controller with a cart velocity feedback the overshoot can be reduced and stable positioning control of the cart is possible. Also it is verified that the servo compensator is superior to the regulator-based compensator in the settling characteristics.

AB - In this study we formulate H∞ servo compensator where displacement signals are used as the controlled variables and their time derivatives are used as partial-state feedback signals for stabilizing and positioning control of a cart and inverted flexible pendulum system. The feedback loop of the part of the state variables except the controlled variables is added to the feedback loop of the controlled variables in the design of the H∞ compensator. Through this formulation the order of the designed compensator is reduced by the order of the weighting functions for the time derivative signals. By numerical calculations and experiments, we investigate the settling characteristics and the robust stability against a disturbance to the pendulum with two kinds of controllers, the output feedback controller by the displacement feedback and the output feedback controller adding the cart velocity feedback. It is shown that although the displacement-output feedback controller has a big overshoot in the step response and the positioning of the cart is difficult, by means of the partial-state feedback controller with a cart velocity feedback the overshoot can be reduced and stable positioning control of the cart is possible. Also it is verified that the servo compensator is superior to the regulator-based compensator in the settling characteristics.

UR - http://www.scopus.com/inward/record.url?scp=0029430787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029430787&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0029430787

T3 - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE

BT - 15th Biennial Conference on Mechanical Vibration and Noise

A2 - Wang, K.W.

A2 - Yang, B.

A2 - Sun, J.Q.

A2 - Seto, K.

A2 - Yoshida, K.

A2 - et al, al

T2 - Proceedings of the 1995 ASME Design Engineering Technical Conference. Part C

Y2 - 17 September 1995 through 20 September 1995

ER -