A two-loop robust controller for compensation of the variant friction force in an over-constrained parallel kinematic machine

Yen, Ping-Lang

doi:10.1016/j.ijmachtools.2008.05.008

Cited by 13 publications

(13 citation statements)

References 19 publications

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“…As shown in Fig. 2, a moving reference frame A uvw 6 − is assigned to the center point A 6 of platform I. Its u-axis is parallel to the distal axis of central U joint and the w-axis coincides with the axis of P joint of the UP limb.…”

Section: T5 Pkm Description and Inverse Position Analysismentioning

confidence: 99%

“…1(b) are defined at point B i to describe the configuration of UPS limbs, its u i -axis is collinear with the distal axis of the ith U joint while w i coincides with the axis of P joint of the ith UPS limb. By rotating frame A uvw 6 − about the w-axis with ψ ( 5 /4 ψ π = − ), the reference frame A uvw 6 − ′ ′ ′ is established at point A 6 . As shown in Fig.…”

Section: T5 Pkm Description and Inverse Position Analysismentioning

confidence: 99%

“…As an important complement of traditional 5-DoF numerical control machines with serial topology structures, the parallel kinematic machines (PKMs) with closed topology structures have several advantages in terms of high stiffness, good accuracy/dynamic performance, large load-weight ratio and easy integration with long guideways [5][6][7]. Those have been proved by successful applications of famous Tricept [8][9][10] and Sprint Z3 head [11][12] PKMs, not only in the aerospace machining but also in fields like automobile and aviation assembling, wielding, drilling.…”

Section: Introductionmentioning

confidence: 99%

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Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects

Lian

Sun

Song

et al. 2015

International Journal of Machine Tools and Manufacture

117

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a b s t r a c tIn order to carry out high-precision machining of aerospace structural components with large size, thin wall and complex surface, this paper proposes a novel parallel kinematic machine (PKM) and formulates its semi-analytical theoretical stiffness model considering gravitational effects that is verified by stiffness experiments. From the viewpoint of topology structure, the novel PKM consists of two substructures in terms of the redundant and overconstrained parallel mechanisms that are connected by two interlinked revolute joints. The theoretical stiffness model of the novel PKM is established based upon the virtual work principle and deformation superposition principle after mapping the stiffness models of substructures from joint space to operated space by Jacobian matrices and considering the deformation contributions of interlinked revolute joints to two substructures. Meanwhile, the component gravities are treated as external payloads exerting on the end reference point of the novel PKM resorting to static equivalence principle. This approach is proved by comparing the theoretical stiffness values with experimental stiffness values in the same configurations, which also indicates equivalent gravity can be employed to describe the actual distributed gravities in an acceptable accuracy manner. Finally, on the basis of the verified theoretical stiffness model, the stiffness distributions of the novel PKM are illustrated and the contributions of component gravities to the stiffness of the novel PKM are discussed.

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Section: T5 Pkm Description and Inverse Position Analysismentioning

confidence: 99%

Section: T5 Pkm Description and Inverse Position Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects

Lian

Sun

Song

et al. 2015

International Journal of Machine Tools and Manufacture

117

View full text Add to dashboard Cite

show abstract

“…They used unstructured dynamic uncertainty (multiplicative uncertainties and additive uncertainties) but not parametric uncertainty to represent the uncertainty of the system, and applied the conventional H  loop shaping synthesis method to design optimal robust controllers. Yen [9] proposed a two-loop robust controller for compensation of the variant friction force in an over-constrained parallel kinematic machine. A disturbance observer (DOB) was adopted as the inner-loop compensator to reduce the effects of the variant friction force.…”

Section: Introductionmentioning

confidence: 99%

“…The most important factors that degrade the nominal tracking performance are the uncertain load mass and viscous damping ratio. In conventional researches [6][7][8][9], the authors used an unstructured multiplicative dynamic uncertainty to cover all the uncertainties involving uncertain mass, uncertain damping ratio and unmodeled high frequency dynamics, and guaranteed robustness by shaping the complementary sensitivity function. Due to the conservative nature of unstructured uncertainties, a significant amount of performance will be sacrificed in the resulting closed loop system.…”

Section: Introductionmentioning

confidence: 99%

Double-loop robust tracking control for micro machine tools

Fan

Nagamune

Ding

2011

Sci. China Technol. Sci.

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This paper addresses double-loop robust tracking controller design of the miniaturized linear motor drive precision stage with mass and damping ratio uncertainties. As an inner-loop, a disturbance observer (DOB) is employed to suppress exogenous low frequency disturbances such as friction and cutting force. To further eliminate the residual disturbance and to guarantee the robust tracking to the reference input, a -synthesis outer-loop controller is designed. For eliminating the steady state error, a technique is proposed to design the -synthesis outer-loop controller with an integrator. A guideline to select the bandwidth of the Q-filter in the DOB is provided. Simulations using a model of a prototype micro-milling machine indicate that the proposed outer-loop synthesis scheme is superior to the H  suboptimal control in disturbance rejection performance and steady state tracking performance. Furthermore, it is shown experimentally that the proposed double-loop robust tracking controller improves the tracking performance of the stage by 29.6% over PID control with a DOB inner-loop. micro machine tools, robust tracking, -synthesis, disturbance observer Citation:Fan S X, Nagamune R, Fan D P. Double-loop robust tracking control for micro machine tools.

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Robust tracking control for micro machine tools with load uncertainties

Fan

Ding

Hong

et al. 2012

J. Cent. South Univ. Technol.

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The quality of the micro-mechanical machining outcome depends significantly on the tracking performance of the miniaturized linear motor drive precision stage. The tracking behavior of a direct drive design is prone to uncertainties such as model parameter variations and disturbances. Robust optimal tracking controller design for this kind of precision stages with mass and damping ratio uncertainties was researched. The mass and damping ratio uncertainties were modeled as the structured parametric uncertainty model. An identification method for obtaining the parametric uncertainties was developed by using unbiased least square technique. The instantaneous frequency bandwidth of the external disturbance signals was analyzed by using short time Fourier transform technique. A two loop tracking control strategy that combines the μ-synthesis and the disturbance observer (DOB) techniques was proposed. The μ-synthesis technique was used to design robust optimal controllers based on structured uncertainty models. By complementing the μ controller, the DOB was applied to further improving the disturbance rejection performance. To evaluate the positioning performance of the proposed control strategy, the comparative experiments were conducted on a prototype micro milling machine among four control schemes: the proposed two-loop tracking control, the single loop μ control, the PID control and the PID with DOB control. The disturbance rejection performances, the root mean square (RMS) tracking errors and the performance robustness of different control schemes were studied. The results reveal that the proposed control scheme has the best positioning performance. It reduces the maximal errors caused by disturbance forces such as friction force by 60% and the RMS errors by 63.4% compared with the PID control. Compared to PID with DOB control, it reduces the RMS errors by 29.6%.

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A two-loop robust controller for compensation of the variant friction force in an over-constrained parallel kinematic machine

Cited by 13 publications

References 19 publications

Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects

Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects

Double-loop robust tracking control for micro machine tools

Robust tracking control for micro machine tools with load uncertainties

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