Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

Shang, Dongyang; Li, Xiaopeng; Yin, Meng; Li, Fanjie

doi:10.3390/math9080896

Cited by 29 publications

(10 citation statements)

References 31 publications

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“…where ξ a1 and ω a1 denote the damping coefficient and the natural frequency coefficient of the poles. According to Equation (22), Equation ( 23) can be obtained.…”

Section: Controller Parameter Tuning Methods Based On Pole Placement ...mentioning

confidence: 99%

“…Under the literature [22], the expressions of the flexible load deformation could be obtained, as shown in Equation ().

({, \begin{array}{l} w ((), x, t) goodbreak= bold-italicϕ ((), x) bold-italicw ((), t) goodbreak= \sum_{i = 1}^{\infty} ϕ_{i} ((), x) w_{i} ((), t), \\ \frac{\overset{w}{true} ((), t)}{bold-italicw ((), t)} goodbreak= goodbreak- \frac{italicEI ϕ^{(4)} ((), x)}{italicρA bold-italicϕ ((), x)} goodbreak= goodbreak- bold-italicϑ, \\ bold-italicϑ bold-italicgoodbreak= ([], ω_{1}^{2} ω_{2}^{2} \dots ω_{\infty}^{2}), \\ ϕ_{i} ((), x) goodbreak= ch ((), β_{i} x) goodbreak- \cos ((), β_{i} x) goodbreak+ ς_{i} ((), sh ((), β_{i} x) goodbreak- \sin ((), β_{i} x)), \\ ς_{i} goodbreak= goodbreak- \frac{sh ((), β_{i} l) - \sin ((), β_{i} l)}{ch ((), β_{i} l) + \cos ((), β_{i} l)}, \\ ω_{i} goodbreak= β_{i}^{2} \sqrt{\frac{EI}{ρA},} \end{array})

where

bold-italicϕ ((), x)

and

bold-italicw ((), t)

denote the modal function and the modal coordinate; ρ , A , and EI denote the volume density, the flexible load cross‐section area, and the flexural rigidity; l denotes the flexible load length; ω i denotes the modal frequency; and β i denotes the characteristic roots of modal function equations.…”

Section: Mathematical Model Of a Dual Flexible Servo Systemmentioning

confidence: 99%

“…The servo system considering only flexible load is shown in Figure 1B. Under the literature [22], the expressions of the flexible load deformation could be obtained, as shown in Equation (3).…”

Section: Dynamic Model Of a Single Flexible Load Servo Systemmentioning

confidence: 99%

See 2 more Smart Citations

Speed control strategy of dual flexible servo system considering time‐varying parameters for flexible manipulator with an axially translating arm

Shang

Yin

et al. 2022

Asian Journal of Control

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Many factors lead to fluctuations of output speed in the motor side during the movement processes in a flexible manipulator with an axially translating arm. These factors include the time‐varying characteristics of manipulator parameters, external disturbance, and flexibility in the manipulator. The vibration of flexible manipulators is strengthened by fluctuations of output speed, which seriously affects the motion accuracy. Therefore, a variable parameters proportional–integral (PI) control strategy based on disturbance observer is adopted to reduce fluctuations of output speed in a dual flexible servo system. First, the dynamic model of the dual flexible servo system is established by the assumed mode method. Then, the variable parameters PI control strategy is applied to the servo system, and the controller parameters in different conditions are selected by pole placement strategies. Finally, numerical simulations and control experiments of the servo system are carried out. The results show that the control strategy using the variable parameters and disturbance observer could reduce fluctuations of output speed and improve the motion accuracy of flexible manipulators.

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“…where ξ a1 and ω a1 denote the damping coefficient and the natural frequency coefficient of the poles. According to Equation (22), Equation ( 23) can be obtained.…”

Section: Controller Parameter Tuning Methods Based On Pole Placement ...mentioning

confidence: 99%

“…Under the literature [22], the expressions of the flexible load deformation could be obtained, as shown in Equation ().

({, \begin{array}{l} w ((), x, t) goodbreak= bold-italicϕ ((), x) bold-italicw ((), t) goodbreak= \sum_{i = 1}^{\infty} ϕ_{i} ((), x) w_{i} ((), t), \\ \frac{\overset{w}{true} ((), t)}{bold-italicw ((), t)} goodbreak= goodbreak- \frac{italicEI ϕ^{(4)} ((), x)}{italicρA bold-italicϕ ((), x)} goodbreak= goodbreak- bold-italicϑ, \\ bold-italicϑ bold-italicgoodbreak= ([], ω_{1}^{2} ω_{2}^{2} \dots ω_{\infty}^{2}), \\ ϕ_{i} ((), x) goodbreak= ch ((), β_{i} x) goodbreak- \cos ((), β_{i} x) goodbreak+ ς_{i} ((), sh ((), β_{i} x) goodbreak- \sin ((), β_{i} x)), \\ ς_{i} goodbreak= goodbreak- \frac{sh ((), β_{i} l) - \sin ((), β_{i} l)}{ch ((), β_{i} l) + \cos ((), β_{i} l)}, \\ ω_{i} goodbreak= β_{i}^{2} \sqrt{\frac{EI}{ρA},} \end{array})

where

bold-italicϕ ((), x)

and

bold-italicw ((), t)

Section: Mathematical Model Of a Dual Flexible Servo Systemmentioning

confidence: 99%

See 1 more Smart Citation

Speed control strategy of dual flexible servo system considering time‐varying parameters for flexible manipulator with an axially translating arm

Shang

Yin

et al. 2022

Asian Journal of Control

Self Cite

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show abstract

“…In practical application, the kinetic parameters of the object are often unknown, or only the nominal model is known, 16 which limits the application of the computed torque method. Since it has the property of approximating any nonlinear function, 17 the RBFNN can be used to approximate the unknown parameters of the kinetic model.…”

Section: Design Of Master Controllermentioning

confidence: 99%

A novel trajectory tracking control approach for uncertain 6-DOF manipulators based on fuzzy sliding mode of radial basis function neural network

Liu

Yang

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part I:

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Due to the influence of uncertain external disturbance and model error, the trajectory tracking of manipulators has some problems such as inaccuracy, low speed and severe chattering. To solve the problems mentioned, a sliding mode control method combined fuzzy controller and Radial Basis Function Neural Network (RBFNN) was proposed. The RBFNN was used to approximate the equivalent system model of manipulators, and the weights of their hidden layers were updated adaptively online. The robust item with the form of sliding mode had been set to compensate the uncertain external disturbances or the approximation errors of the RBFNN. A fuzzy controller was used to adjust the switching gain online adaptively and to solve the chattering of the sliding mode control. The stability and finite time convergence of the closed-loop system had been analyzed by using Lyapunov method. Finally, simulation experiments about trajectory tracking were implemented by MATLAB/SIMULINK, which shows that the proposed method can improve the position-tracking accuracy by more than 40%, the speed-tracking accuracy by more than 70%, and the cumulative-error accuracy by more than 40% compared with the comparison method. Moreover, there is no chattering. The proposed method has been proved to be efficient.

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“…To obtain the transfer function of the double flexible system is also the premise of the control stability of the servo system. According to the literature [25], it can be concluded that the influence of second-order modes on system output is only 1% of that of first-order modes. Therefore, only the first-order modal function of the system can be taken, and the transfer function of the system can be obtained according to Equation (22), as shown in Equation (23).…”

Section: Transfer Function Of Two Flexible Body Systemmentioning

confidence: 99%

Improved Vibration Suppression Strategy of Fuzzy PI Servo Control for Dual Flexible System with Flexible Joints

Liu

Wang

2023

Mathematics

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A high performance manipulator servo drive system is a double flexible system with flexible joints and flexible loads. Flexible joints are composed of elastic connecting elements, and flexible loads are flexible Euler beams with elastic deformation. The dual flexible system has highly nonlinear time-varying characteristics. This kind of characteristic will cause resonance of the double-flexible system and affect the dynamic characteristics of the system. In order to suppress the system resonance, the nonlinear dynamics model of the system with two flexible bodies is established. Then, the servo control method of double flexible body system is designed, and the range of PI controller parameters is determined by the same resistance pole assignment method. Then, a fuzzy control rule is designed to dynamically adjust PI controller parameters based on pole assignment. Finally, the improved fuzzy PI control strategy is simulated numerically. The simulation results show that the vibration of the double-flexible system can be effectively suppressed by establishing the precise dynamic model and designing PI controller parameters.

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Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

Cited by 29 publications

References 31 publications

Speed control strategy of dual flexible servo system considering time‐varying parameters for flexible manipulator with an axially translating arm

Speed control strategy of dual flexible servo system considering time‐varying parameters for flexible manipulator with an axially translating arm

A novel trajectory tracking control approach for uncertain 6-DOF manipulators based on fuzzy sliding mode of radial basis function neural network

Improved Vibration Suppression Strategy of Fuzzy PI Servo Control for Dual Flexible System with Flexible Joints

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