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Research Papers

A Nonlinear Sliding Surface in Sliding Mode Control to Reduce Vibrations of a Three-Link Flexible Manipulator

[+] Author and Article Information
Francesco Ripamonti

Department of Mechanics,
Politecnico di Milano,
Via La Masa 1,
Milan 20156, Italy
e-mail: francesco.ripamonti@polimi.it

Lorenzo Orsini, Ferruccio Resta

Department of Mechanics,
Politecnico di Milano,
Via La Masa 1,
Milan 20156, Italy

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 24, 2016; final manuscript received April 10, 2017; published online June 12, 2017. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 139(5), 051005 (Jun 12, 2017) (10 pages) Paper No: VIB-16-1415; doi: 10.1115/1.4036502 History: Received August 24, 2016; Revised April 10, 2017

Many mechanical systems often show nonlinear behavior related to particular operating conditions or to the nonlinear characteristic of the elements (springs, dampers, etc.) making up the system. In these cases, common engineering practice is to linearize the equation of motion around a particular operating point and to design a linear controller. Although this approach is simple, its main disadvantage is that stability properties and validity of the controller are only local. For these reasons, over the last decades, nonlinear control techniques have been investigated more and more in order to improve control performance. In particular, in this paper, sliding mode control (SMC) technique, which is based on the model of the system (model-based), is considered because of its easy implementation, especially on simple mechanical systems, and the considerable robustness of the controller even under significant model uncertainties. This technique is analyzed numerically with respect to the pendulum system to better understand the influence of the control action on the system dynamics. A nonlinear sliding surface is also considered, recalling the terminal sliding mode (TSM) control already analyzed in the scientific literature. This sliding surface is characterized for the numerical system, and then it is applied experimentally in order to control a highly nonlinear system, consisting of a three-link flexible manipulator. For this system, a nonlinear modal model is developed, and a nonlinear observer is designed. Finally, results of experimental tests on the manipulator are reported, in order to compare the performances of the linear embedded control and the sliding mode controllers with the linear and nonlinear sliding surface.

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Figures

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Fig. 1

Stability analysis of the nonlinear sliding surface: example of stable and unstable motion in case a > 0 and b > 0

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Fig. 2

Simple pendulum swing-up numerical simulation with SMC and nonlinear sliding surface; settling time (left) and maximum torque (right) for different values of parameters a and b

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Fig. 3

Simple pendulum swing-up numerical simulation with SMC and nonlinear sliding surface; optimization for settling time (left) and for maximum torque (right)

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Fig. 4

Experimental test rig; three-link flexible manipulator (left) and sensor positions (right)

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Fig. 5

Three-link flexible manipulator experimental test rig; the complete control scheme

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Fig. 7

Three-link flexible manipulator experimental tests; ideal reference (left) and real trend without SMC (right)

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Fig. 8

Three-link flexible manipulator experimental tests; comparison between measured vibrations without SMC and with SMC for output 1 (first accelerometer integrated signal). SMC with linear sliding surface on the left and with parabolic sliding surface on the right.

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Fig. 9

Three-link flexible manipulator experimental tests; comparison between measured vibrations without SMC and with SMC for output 2 (second accelerometer integrated signal). SMC with linear sliding surface on the left and with parabolic sliding surface on the right.

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Fig. 10

Three-link flexible manipulator experimental tests; comparison between measured vibrations without SMC and with SMC for output 3 (third accelerometer integrated signal). SMC with linear sliding surface on the left and with parabolic sliding surface on the right.

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