Models of Mechanical Systems for Controllers Design

Arai, Fumihito; Fukuda, Toshio; Shoji, Yasumasa; Wada, Hiroshi

doi:10.1016/s1474-6670(17)50539-x

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…These equations describe a n-th order dynamical system. By comparison with the sliding mode equations (7)-(8) it can be observed that: equation (14) is the same as (7), equation (15) consists of m first-order differential equations that describe the change of the distances from the manifold 5. These distances decay at a rate determined by the elements of matrix D. For the systems represented in the controller canonical form the equations of motion is merely determined by matrices D and G. If matrix D is selected diagonal then (15) splits in m independent first order differential equations.…”

Section: -B 2 D(t + ))-B 2 U(nmentioning

confidence: 99%

“…Generally speaking, the reaching time in the system (14), (15) is infinite. The rate of decay is determined by matrix D and the reaching is guaranteed by virtue of equation (15). In the system with discontinuous control the reaching time is finite but real sliding mode exhibits the motion in the e-vicinity of the sliding mode manifold.…”

Section: -B 2 D(t + ))-B 2 U(nmentioning

confidence: 99%

“…In the system with discontinuous control the reaching time is finite but real sliding mode exhibits the motion in the e-vicinity of the sliding mode manifold. If the motion of the system inside the e-vicinity is accepted as the sliding mode motion, then system 14, (15) reaches this vicinity to a finite time determined by the matrix D. That is the basic difference from the systems with sliding modes. In the following sections the behavior of the systems with control (12) will be analyzed in more details and solutions without discontinuous term will be introduced.…”

Section: -B 2 D(t + ))-B 2 U(nmentioning

confidence: 99%

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Chattering-free sliding modes in robotic manipulators control

1996

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SummaryIn this paper sliding mode motion design is considered for nonlinear plants which are linear with respect to control input. The dynamics of the robotic manipulators is treated with and without those of the actuators. When the dynamics of the actuators is included a design of the sliding modes for the systems with discontinuous control is performed. If actuators' dynamics is negelected the control is assumed to be continuous quantity. By combining the variable structure systems and Lyapunov designs a new algorithm is developed which has all the good properties of the sliding mode systems while avoiding unnecessary discontinuity of the control thus eliminating chattering. Neither the explicit calculation of the equivalent control, nor high gain inside the boundary layer are used. The parameters of the control depend on the plant's gain matrix, and the gradients of the sliding mode manifold. This control method is then applied to develop a unified control strategy for the motion control systems including the path tracking control, the impedance control and the force control of a robotic manipulator. It is shown that all these tasks can be formulated in the same mathematical form in which selected so-called sliding mode functions must track their references. In this way the systems state is forced to remain on the selected manifold in the state space after reaching it. The solution is interpreted in both the Joint space and the Work space for n -degrees of freedom robotic manipulators.

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Section: -B 2 D(t + ))-B 2 U(nmentioning

confidence: 99%

Section: -B 2 D(t + ))-B 2 U(nmentioning

confidence: 99%

Section: -B 2 D(t + ))-B 2 U(nmentioning

confidence: 99%

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Chattering-free sliding modes in robotic manipulators control

1996

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“…of the system's states is forced to have value cp(t) Any control problem, for system (1)- (3), which can be mathematically represented in the form (4) can be solved applying control (12). Generally speaking the reaching time in the system (14), (15) is infinite and it is determined by the selection oflthe matrix D and the reaching is guarantied by the virtue of equation (15). That is the basic difference from the systems with sliding modes.…”

Section: The Continuous Control Designmentioning

confidence: 99%

“…and if D is selected such that all eigenvalues of [E-TD] are within the unity circle the stability conditions are fulfilled This system, like the system (14), (15) will, generally speaking, reach sliding mode mani-fold S in infinite time. If matrix D is selected diagonal with all elements equal dii=l/T then (18) becomes…”

Section: The Continuous Control Designmentioning

confidence: 99%

Chattering free sliding modes in robotic manipulators control

Şabanoviç

Wada²,

Şabanoviç³

Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93)

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-SlidingjMdd@trol(SMC) of t k systems linear with respect to control and its application to robotic manipulator control system design is presented. The controller is designed to provide sliding mode motion on the selected manifolds in the state space. These manifolds are selected as a linear combination of the state coordinates. This selection allows the formulation of the path tracking control, $Re force c o n t r a a n d impedance control problems to be very similar. Control is selected to satisfy selected Lyapunov function and stability criteria. 9-

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