Abstract
This paper reports preliminary investigations for H\(_\infty \) control of cable-driven parallel robot. This methodology specially suits for multi-input multi-output systems including flexible modes, which is the case of cable robots with flexible cables. A nonlinear model is first developed accounting for flexible cables for the case where actuators are speed controlled. A first method based on a rigid model is proposed as an adaptation for speed-controlled actuators of the well-known Jacobian-based method. A low-pass filter is tuned in order to increase the reachable bandwidth. The H\(_\infty \) controller is derived from a linear dynamic model. One interest is that one single controller manages both the position of the end-effector and the cable tension. The simulation results show that improvements are possible in the bandwidth thanks to the H\(_\infty \) control.
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Notes
- 1.
Let \(T_{zv}(s)\) denote the transfer of the system with input \(v\) and output \(z\). The interconnection of \(G_e(s)\) and \(K(s)\) presented in Fig. 6 is \(T_{\tilde{z} \tilde{v}}(s) = \text{ lft}(G_e(s),K(s))\).
- 2.
The H\(_\infty \) norm \(\left\Vert G(s) \right\Vert_\infty \) of transfer \(G(s)\) is the maximum singular value of \(G(j \omega )\) over all the frequencies \(\omega \in \mathbb R ^+\). For single-input single-output systems, it reduced to the maximum gain.
- 3.
References
Abdelaziz, S., Esteveny, L., Renaud, P., Bayle, B., Barbé, L., de Mathelin, M., Gangi, A.: Design considerations for a novel mri compatible manipulator for prostate cryoablation. Int. J. Comput. Assist. Radiol. Surg. 6(6), 811–819 (2011)
Alikhani, A., Vali, M.: Modeling and robust control of a new large scale suspended cable-driven robot under input constraint. In: International Conference on Ubiquitous Robots and Ambiant Intelligence, Incheon, (2011)
Banavar, R., Dominic, P.: An LQG/\(\text{H}_\infty \) controller for a flexible manipulator. IEEE Trans. Control Syst. Technol. 3, 409–416 (1995)
Burke, J.V., Henrion, D., Lewis, A.S., Overton, M.L.: HIFOO—a Matlab package for fixed-order controller design and h-infinity optimization. In: IFAC Symposium on Robust Control Design, Toulouse, (2006). http://www.cs.nyu.edu/overton/software/hifoo/
Cuvillon, L., Laroche, E., Gangloff, J., de Mathelin, M.: A multivariable methodology for fast visual servoing of flexible manipulators moving in a restricted workspace. Adv. Robotics. doi:10.1080/01691864.2012.685230
Dallej, T., Gouttefarde, M., Andreff, N., Michelin, M., Martinet, P.: Towards vision-based control of cable-driven parallel robots. In: International Conference on Intelligent Robots and Systems. San Francisco, (2011)
Diao, X., Ma, O.: Vibration analysis of cable-driven parallel manipulators. Multibody Syst. Dyn. 21, 347–360 (2009)
Doyle, J., Glover, K., Khargonekar, P., Francis, B.: State-space solutions to standard \(H_2\) and \(H_{\infty }\) control problems. IEEE Trans. Autom. Control 34(8), 831–847 (1989)
Duc, G., Font, S.: Commande \(\text{ H}_\infty \) et \(\mu \)-analyse. Hermes Science Publications, Paris (1999)
Gahinet, P., Apkarian, P.: A linear matrix inequality approach to \(\text{ H}_\infty \) control. Int. J. Robust Nonlin. Control 4(4), 421–448 (1994)
Koç, H., Knittel, D., de Mathelin, M.: Modeling and robust control of winding systems for elastic webs. IEEE Trans. on Control Syst. Technol. 10, 197–208 (2002)
Korayem, M., Bamdad, M., Saadat, M.: Workspace analysis of cable-suspended robots with elastic cable. In: IEEE International Conference Robotics and Biomimetics, Sanya, pp. 1942–1947 (2007). doi:10.1109/ROBIO.2007.4522464
Kozak, K., Zhou, Q., Wang, J.: Static analysis of cable-driven manipulators with non-negligible cable mass. IEEE Trans. Robot. 22(3), 425–433 (2006). doi:10.1109/TRO.2006.870659
Ming, A., Higuchi, T.: Study on multiple degree-of-freedom positioning mechanism using wire-concept, design and control (part 1). Int. J. Jpn. Soc. Precis. 28(2), 131–138 (1994)
Pham, C.B., Yeo, S.H., Yang, G., Chen, I.M.: Workspace analysis of fully restrained cable-driven manipulators. Robot. Auton. Syst. 57(9), 901–912 (2009). doi:10.1016/j.robot.2009.06.004
Simoes, A., Apkarian, P., Noll, D.: Nonsmooth multi-objective synthesis with applications. Control Eng. Pract. 11(17), 1338–1348 (2009)
Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control. Wiley, Chichester (1996)
Trevisani, A.: Underconstrained planar cable-direct-driven robots: a trajectory planning method ensuring positive and bounded cable tensions. Mechatronics 20, 113–127 (2010)
Williams, R., Galina, P.: Translational planar cable-direct-driven robots. J. Intel. Robot. Sys. 37, 69–96 (2003)
Xianqiang, Y., Weihai, C., Su, Y., Wei, X.: Dynamic control of a 3-dof cable-driven robot based on backstepping technique. In: IEEE Conference on Industrial Electronics and Applications, Beijing, (2011)
Zames, G., Francis, B.: Feedback, minimax sensitivity, and optimal robustness. IEEE Trans. Autom. Control 28(5), 585–601 (1983)
Zi, B., Duan, B., Du, J., Bao, H.: Dynamic modeling and active control of a cable-suspended parallel robot. Mechatronics 18, 1–12 (2008)
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Laroche, E., Chellal, R., Cuvillon, L., Gangloff, J. (2013). A Preliminary Study for H\(_\infty \) Control of Parallel Cable-Driven Manipulators. In: Bruckmann, T., Pott, A. (eds) Cable-Driven Parallel Robots. Mechanisms and Machine Science, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31988-4_22
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