A Model of Gear Transmission: Fractional Order System Dynamics

In this paper, we propose a modified version of the Proportional Integral Derivative (PID)-type iterative learning algorithm. It is very simple to implement on a digital control device for tracking control a continuous-time system. Matlab software is used to model and simulate control algorithms. The simulative application of it to control a gearing transmission system, such that its output response follows the desired trajectory, is then carried out computationally. Obtained studying results proves that this proposed iterative learning algorithm has provided a good output tracking behavior as expected and which is robust in the sense of reducing external disturbance effects.

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“…The mathematical model of GTS with backlash was already presented in detail in [3][5] [45] as follows:…”

Section: Stability Analysis Of Gtsmentioning

confidence: 99%

PID-Type Iterative Learning Control for Output Tracking Gearing Transmission Systems

Anh¹,

Nga

Hoc

2021

IJRCS

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“…It is assumed here in that rigidity of the teeth in mesh is equal to medium rigidity c 0 . By applying the above described procedure, we can demonstrate that this model is described by a system of differential equation, [2,6,7,8,9,10]…”

Section: Dynamic Models Of Gear Transmissionmentioning

confidence: 99%

Numerical methods for solving the dynamic behavior of real systems

Nikolić¹,

Djekic²,

Radakovic³

et al. 2014

Sci Publ State Univ Novi Pazar Ser A

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In this paper are shown dynamic models which represent the real systems. As an example, one gear couple has been presented. In this case, the simplified model two discrete masses with elastic and damped connections. Using the of mechanics and taking into account initial and basic principles conditions, the system of differential equations is established which describes physicality of motion. Such system of equations represents mathematical model at dynamical behavior of gear transmission. Established system of differential equations has been solved in analytical way with the aim of obtaining data for numerical analysis. The proper estimate of dynamical behavior of gear transmission and other systems can be on the basis of own frequency and of own form of oscillating. In the paper is presented the solution of the main form of oscillating and stress condition using finite elements method.

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“…20 It should be noted that most of the physical systems are inherently FO systems, hence one of the major applications of fractional calculus is the FO modeling of the physical systems in order to describe the systems more exactly. 21,22 Another significant utilization is to design the FO controller such as the tilt-integral-derivative controller, the CRONE controller, and fractional-order proportional–integral–derivative (FOPID) controller. 23 Owing to its supervior performance, the FOPIDs have been widely used in many fields.…”

Section: Introductionmentioning

confidence: 99%

Sliding mode observer-based fractional-order proportional–integral–derivative sliding mode control for electro-hydraulic servo systems

Cheng

Liu

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper proposes an observer-based sliding mode control method for electro-hydraulic servo systems with uncertain nonlinearities, external disturbances, and immeasurable states. The mathematical model is built based on the principle of electro-hydraulic servo systems. Owing to its highly robustness and finite time properties, the sliding mode observer is chosen and designed to estimate the velocity and the equivalent pressure online only using the position feedback. Then, in order to tackle the chattering problem of conventional sliding mode control and increase the control accuracy, a novel second-order sliding mode control scheme is proposed based on the fractional-order proportional–integral–derivative sliding surface and the state observer. The stability of the overall system is proved by Lyapunov theory. Finally, the detailed simulations are conducted, which include the comparative analysis of control performance with other methods and the study of observation performance.

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A Model of Gear Transmission: Fractional Order System Dynamics

Cited by 16 publications

References 14 publications

PID-Type Iterative Learning Control for Output Tracking Gearing Transmission Systems

PID-Type Iterative Learning Control for Output Tracking Gearing Transmission Systems

Numerical methods for solving the dynamic behavior of real systems

Sliding mode observer-based fractional-order proportional–integral–derivative sliding mode control for electro-hydraulic servo systems

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