Control of Uncertain Plants with Unknown Deadzone via Differential Neural Networks

Cruz, José Humberto Pérez; Rubio, José de Jesús; Linares-Flores, J.; Rangel, Eduardo

doi:10.1109/tla.2015.7273762

Cited by 14 publications

(6 citation statements)

References 14 publications

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“…The dynamic model for the constrained robotic arms with

n

degrees of freedom, considering the contact force and the constraints, it is given in the joint space as follows:

M false(p false) \overset{\cdot \cdot}{p} + C false(p, \overset{\cdot}{p} false) \overset{\cdot}{p} + G false(p false) = f false(p, \overset{\cdot}{p}, \overset{\cdot \cdot}{p} false) = τ,

where

p \in ℜ^{n \times 1}

is the position and

\overset{\cdot}{p} \in ℜ^{n \times 1}

is the velocity of the joint angles or link displacements in the robotic arm,

M false(p false) \in ℜ^{n \times n}

is the robot inertia matrix which is symmetric and positive definite,

C false(p, \overset{\cdot}{p} false) \in ℜ^{n \times n}

contains the centripetal and Coriolis terms, and

G false(p false)

are the gravity terms,

τ

denotes the deadzone,

f false(p, \overset{\cdot}{p}, \overset{\cdot \cdot}{p} false)

is a non‐linear function which describes the robot dynamics. The deadzone terms are represented as follows [1, 2]:

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ τ = D Z (w) = \{\begin{matrix} left left1em.1em \\ n_{r} (w - a_{r}) & w \geq a_{r} \\ 0 & a_{l} < w < a_{r} \\ n_{l} (w - a_{l}) & w \leq a_{l} \end{matrix}, \end{matrix}

…”

Section: Dynamic Model Of Robotic Arms With Deadzone and Gravitymentioning

confidence: 99%

“…2 shows the sliding mode controller denoted as SSM in the application to robotic arms with unknown behaviour in the deadzone and gravity denoted as plant and DZ. Remark 2 There are some works that consider the boundedness of some plant dynamics such as the neural network controller of [2], the super‐twisting controllers of [14, 15], the sliding mode controllers of [16, 17], the observer‐based sliding‐mode controllers of [18–20], and the least square controller of [34], taking in count these previous works, (10) and (11) which consider the boundedness of some plant dynamics are correctly used. In addition, the dynamics are not required to be known because only their upper bounds are utilised.…”

Section: Sliding Mode Control For the Regulation Of Robotic Arms Wimentioning

confidence: 99%

“…There is some interesting work about the control of systems with deadzone. In [1, 2], the control of non‐linear systems with input deadzone is investigated. In [3], the tracking control of systems with deadzone is considered.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sliding mode control of robotic arms with deadzone

Rubio

2017

IET Control Theory & Applications

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“…The dynamic model for the constrained robotic arms with

n

degrees of freedom, considering the contact force and the constraints, it is given in the joint space as follows:

M false(p false) \overset{\cdot \cdot}{p} + C false(p, \overset{\cdot}{p} false) \overset{\cdot}{p} + G false(p false) = f false(p, \overset{\cdot}{p}, \overset{\cdot \cdot}{p} false) = τ,

where

p \in ℜ^{n \times 1}

is the position and

\overset{\cdot}{p} \in ℜ^{n \times 1}

is the velocity of the joint angles or link displacements in the robotic arm,

M false(p false) \in ℜ^{n \times n}

is the robot inertia matrix which is symmetric and positive definite,

C false(p, \overset{\cdot}{p} false) \in ℜ^{n \times n}

contains the centripetal and Coriolis terms, and

G false(p false)

are the gravity terms,

τ

denotes the deadzone,

f false(p, \overset{\cdot}{p}, \overset{\cdot \cdot}{p} false)

is a non‐linear function which describes the robot dynamics. The deadzone terms are represented as follows [1, 2]:

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ τ = D Z (w) = \{\begin{matrix} left left1em.1em \\ n_{r} (w - a_{r}) & w \geq a_{r} \\ 0 & a_{l} < w < a_{r} \\ n_{l} (w - a_{l}) & w \leq a_{l} \end{matrix}, \end{matrix}

…”

Section: Dynamic Model Of Robotic Arms With Deadzone and Gravitymentioning

confidence: 99%

Section: Sliding Mode Control For the Regulation Of Robotic Arms Wimentioning

confidence: 99%

See 1 more Smart Citation

Sliding mode control of robotic arms with deadzone

Rubio

2017

IET Control Theory & Applications

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“…Along with tele-operation robotics systems, the control scheme for the actuators (such as a geared motor) with uncertain dead-zone nonlinearity induced by a gear backlash and imperfectly manufactured mechanical parts has been developed for a long times. The related works [21][22][23][24][25][26][27] utilized the inverse of dead-zone, adaptive estimation/control, and neural network to overcome dead-zone effect. [21] presents nonlinear modeling and identification of a DC motor rotating in two directions and verified the accuracy of proposed technique based on real time experiments.…”

Section: Introductionmentioning

confidence: 99%

“…[26] presented an adaptive control approach based on the two neural networks to control a DC motor system with dead-zone characteristics (DZC). [27] employed a differential neural network in order to identify the uncertain dynamics with unknown dead-zone which is modeled as a combination of a linear term and a disturbance-like term. Here, the Lyapunov analysis is used to show asymptotic converge of the identification error to a bounded zone.…”

Section: Introductionmentioning

confidence: 99%

Synchronous Control of 2-D.O.F Master-Slave Manipulators Using Actuators With Asymmetric Nonlinear Dead-Zone Characteristics

Jung

Jeon

2022

IEEE Access

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On the Output-Feedback Regulation for a Second-Order System with Unknown Parameters: An I&I and MRAC Based Approach

et al. 2021

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We propose an adaptive stabilization solution for a linear second-order system with unknown parameters, where only the position and the sign of the constant associated with the control input are known. The control strategy consists in proposing a filter system with its whole state available and having the same structure as the uncertain system. Then, based on the Immersion & Invariance approach, and the Model Reference method, we design an adaptive controller to stabilize the filter system. Finally, using the backstepping approach, we stabilize the original uncertain system. We carry out the convergence analysis using the traditional Lyapunov method, in conjunction with the Barbalat's Lemma. The obtained control strategy is simple and easy to implement. We assess the effectiveness of our adaptive control strategy through numerical simulations.

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Control of Uncertain Plants with Unknown Deadzone via Differential Neural Networks

Cited by 14 publications

References 14 publications

Sliding mode control of robotic arms with deadzone

Sliding mode control of robotic arms with deadzone

Synchronous Control of 2-D.O.F Master-Slave Manipulators Using Actuators With Asymmetric Nonlinear Dead-Zone Characteristics

On the Output-Feedback Regulation for a Second-Order System with Unknown Parameters: An I&I and MRAC Based Approach

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