Optimal Controller for Dithered Systems with Backlash or Hysteresis

Hsiao, Feng‐Hsiag; Hwang, Jiing-Dong

doi:10.1023/a:1022607619198

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…Where,θ i denotes the input angle, θ o denotes the output angle; k 1 is reciprocal of co-rotating ratio, k 2 is reciprocal of reversal ratio; θ 1 is the width of gear clearance with responding to the co-rotating ratio, θ 2 is width of gear clearance for the reversal ratio. The practical experiments have indicated that some parameters have the same values in many cases [6]. Namely k 1 =k 2 , θ 1 =θ 2 .…”

Section: Nonlinear Gear Systemmentioning

confidence: 99%

Study of Improving Precision of Nonlinear Gear System with Clearance Using Numerical Approximation

Chen

2010

AMM

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The numerical approximation is proposed to explore the effective improvement of precision of position and velocity requirement in the mechanical transmission which hold the nonlinear gear system with clearance unit. The transfer function is adopted to compare the difference between the ideal model and model with the nonlinear gear system. The characteristics of the model with nonlinear gear system are detected by calculating the various parametric coefficients in the model. And then the numerical database is constructed to conveniently display the system performances, which also offers the plausible method to obtain optimum parametric coefficients using the numerical approximation. The tolerance equation between the approximate function and ideal function is set an objective function. The most optimum parameter can be obtained from the objective function by the optimization theory. The results show that these calculated optimum parametric coefficients can achieve the system stability, and improve the synthesis performance of control system. The proposed method in this study avoids to seeking for the approach to analyze the complex nonlinear system or build new control scheme, which is liable to use in the practical application. The simulative results demonstrate the effectiveness of the proposed method.

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Section: Nonlinear Gear Systemmentioning

confidence: 99%

Study of Improving Precision of Nonlinear Gear System with Clearance Using Numerical Approximation

Chen

2010

AMM

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“…The hysteretic part involves a nondimensional auxiliary variable z which is the solution of the nonlinear first order differential equation in (10). In this equation, A, β and γ are nondimensional parameters which control the shape and the size of the hysteresis loop, while n is an integer that governs the smoothness of the transition from elastic to plastic response.…”

Section: Application: Control Of a Hysteretic Oscillatormentioning

confidence: 99%

“…[9][10][11][12] In structural systems, feedback controllers in the presence of hysteretic components have been primarily encountered when dealing with smart actuators and base isolation schemes. A passivity-based controller has been recently proposed for a class of shape-memory alloys actuators.…”

mentioning

confidence: 99%

Adaptive backstepping control of a class of hysteretic systems

2003

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A backstepping-based adaptive control is designed for a class of one degree of freedom hysteretic system. The true hysteretic behavior does not need to be known for the controller design. A polynomial description is assumed with uncertain coefficients and an uncertain residual function. These uncertainties are bounded and lump the discrepancies between the adopted description and the real hysteretic behavior. The adaptive controller is able to handle these uncertainties and make the closed loop globally uniformly ultimately bounded when the system is subject to an unknown excitation from which a bound is known. The efficiency of the approach is tested by numerical simulations on a hysteretic system under a seismic excitation. This system is mathematically described by the differential Bouc-Wen model, which is widely used in structural dynamics.

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“…They have shown that the backlash compensation significantly improves the tracking properties compared to a linear controller. The introduction of a dither into systems with backlash has been extensively studied for years; see Hsiao and Hwang (1997) and references therein. For this approach, the kinematic model is used.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Proportional—Derivative and Nonlinear Control of Mechanical Systems with Dynamic Backlash

Mata-Jimenez¹,

Brogliato

2003

Journal of Vibration and Control

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In this paper, we focus on the analysis and control of a simple rigid-body mechanical system with clearance. Contrary to most of the existing works in the literature concerning control, we explicitly treat all the nonlinear non-smooth characteristics of this system considered as a rigid-body mechanical system with unilateral constraints and impacts (dynamic backlash). The model is therefore a hybrid dynamical system, mixing discrete events as well as continuous states. The regulation and tracking capabilities of the proportional—derivative (PD) scheme are investigated. In particular, a complete proof of the existence of a limit cycle for non-collocated PD control is provided, including viability constraints. It is concluded that tracking requires the development of specific control schemes. Consequently, we propose a hybrid control that may be used to track some desired trajectories in conjunction with a PD input. Throughout the paper, the particular features of unilaterally constrained mechanical systems are taken into account, such as the fundamental viability property of closed-loop solutions and controls. This work is a new approach to be considered for application in several areas including the control of kinematic chains with joint clearance and vibro-impact systems, as well as liquid slosh control. Numerical results are presented to illustrate the possible performance of the proposed control scheme and its robustness properties.

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Optimal Controller for Dithered Systems with Backlash or Hysteresis

Cited by 6 publications

References 11 publications

Study of Improving Precision of Nonlinear Gear System with Clearance Using Numerical Approximation

Study of Improving Precision of Nonlinear Gear System with Clearance Using Numerical Approximation

Adaptive backstepping control of a class of hysteretic systems

Analysis of Proportional—Derivative and Nonlinear Control of Mechanical Systems with Dynamic Backlash

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