Limit cycles induced in type-1 linear systems with PID-type of relay feedback

Chen, Silu; Tan, Kok Kiong; Huang, Sunan

doi:10.1080/00207720902989304

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…. (13) This "transfer function," ( ), is real, positive, and frequency independent but dependent on the input amplitude . Its maximal value is ( ) = > 0, which is reached as → ∞, and its minimal value tends to zero if → .…”

Section: Controller Proposalmentioning

confidence: 99%

“…(ii) Dead-zone "transfer function" (13) is an idealization of the nonlinear phenomenon that is actually presented in the practical plant. Hence, not all the dynamics of the dead-zone nonlinearity is concentrated in (13).…”

Section: Complexitymentioning

confidence: 99%

“…As a matter of fact, compensation of friction in mechanical systems has been carried out to achieve a better control of position [4][5][6][7][8]. Limit cycles generated by the static and Coulomb friction have been treated in [1,[9][10][11][12][13][14] and the stability analysis of systems with friction has been introduced in [15][16][17]. On the other hand, underactuated mechanical systems, and in particular inverted pendulums, have attracted the attention of several researchers because they are an excellent benchmark to study position control, limit cycles, and system stability [18].…”

Section: Introductionmentioning

confidence: 99%

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Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

et al. 2019

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A frequency response-based linear controller is implemented to regulate the inverted pendulum on a cart at the inverted position. The objective is to improve the performance of the control system by eliminating the limit cycle generated by the dead-zone, induced by static friction, at the actuator of the mechanism. This control strategy has been recently introduced and applied by the authors to eliminate the limit cycle in the Furuta pendulum and the pendubot systems. Hence, the main aim of the present paper is to study the applicability of the control strategy to eliminate the limit cycle in the inverted pendulum on a cart. The successful results that are obtained in experiments corroborate that the approach introduced by the authors to eliminate the limit cycle in the Furuta pendulum and pendubot is also valid for the inverted pendulum on a cart.

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Section: Controller Proposalmentioning

confidence: 99%

Section: Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

et al. 2019

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“…Different forms of relay structures, such as hysteretic relay [6], relay with delay [7] and dual-relay [8] are proposed. Since 1990s, the application of relay feedback tends to identified the compounded linear and nonlinear model parameters in motion systems by tuning of relay parameters to excite oscillations, such as friction [9] and force ripples [10]. Although timedomain based method are occasionally used for system identification based on solving of a series of step-response equation, the application is applicable on identify the simple form of nonlinearity, such as Coulomb friction [11].…”

Section: Introductionmentioning

confidence: 99%

Identification and robust tracking control of a single-phase rotary motor with halbach permanent magnet array design

Chen

Teo

Kamaldin

et al. 2014

2014 IEEE International Conference on Mechatronics and Automation

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The single-phase electromagnetic motor with the circular permanent magnet Halbach array design, has advantage of large force constant compared with its 3-phase counterpart, if the rotation is within 60 degrees range from its neutral position. However, to authors' best knowledge, no existing literature mentions on tracking control application using such a single phase rotary motor, probably due to its angular dependent force sensitivity. This paper first models a typical two-pole single phase rotary motor with Halbach circular array, with consideration of back-EMF, friction torque and position dependent characteristic. Followed by this, a dualrelay configuration is applied to closed-loop identification of model-parameters by limit cycle experiments. Later, a composite controller, composes of a model-based controller, a time-delay controller and a sliding mode controller, is capable to achieve the high-speed tracking of reference trajectory with presentation of model uncertainty and disturbances. Simulation based on the actual design parameters shows the practical appeal of the proposed approach.

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A limited angle torque actuator with cylindrical Halbach and its large angle tracking control

Chen¹,

Kamaldin²,

Teo³

et al. 2019

Precision Motion Systems

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Limit cycles induced in type-1 linear systems with PID-type of relay feedback

Cited by 11 publications

References 17 publications

Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart

Identification and robust tracking control of a single-phase rotary motor with halbach permanent magnet array design

A limited angle torque actuator with cylindrical Halbach and its large angle tracking control

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