Research Papers

High Performance Continuously Variable Transmission Control Through Robust Control-Relevant Model Validation

[+] Author and Article Information
Tom Oomen

e-mail: t.a.e.oomen@tue.nl

Stan van der Meulen

e-mail: s.h.v.d.meulen@ieee.org
Control Systems Technology Group,
Department of Mechanical Engineering,
Eindhoven University of Technology,
P.O. Box 513, 5600 MB,
Eindhoven, The Netherlands

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received May 25, 2012; final manuscript received May 6, 2013; published online August 30, 2013. Assoc. Editor: Gregory Shaver.

J. Dyn. Sys., Meas., Control 135(6), 061018 (Aug 30, 2013) (14 pages) Paper No: DS-12-1156; doi: 10.1115/1.4024784 History: Received May 25, 2012; Revised May 06, 2013

Optimal operation of continuously variable transmissions (CVTs) is essential to meet tightening emission and fuel consumption requirements. This is achieved by accurately tracking a prescribed transmission ratio reference and simultaneously optimizing the internal efficiency of the CVT. To reduce the power losses in a CVT, the absolute pressure levels are lowered, which increases the sensitivity to torque disturbances and increases the importance of disturbance feedforwards. This requires a high performance feedback controller for the hydraulic actuation system in a CVT. The aim of this paper is to develop a multivariable feedback controller for the hydraulic actuation system that is robust with respect to the varying system dynamics that are induced by the varying operating conditions, including transmission ratio changes. Hereto, new connections between system identification and robust control are exploited to achieve high performance. As a result, the varying system dynamics are directly evaluated in terms of closed-loop performance objectives. Subsequent robust control design reveals an increase of the control performance of almost a factor two in terms of the criterion value. This leads to improved simulated and measured closed-loop step responses, including a decrease in settling time from 0.4 s to 0.2 s. Finally, the designed robust controller is successfully validated in a standardized driving cycle experiment.

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Fig. 1

Photograph of the experimental setup with the CVT, where ①: primary servo valve, ②: secondary servo valve, ③: pressure measurement pp at primary hydraulic cylinder, ④: pressure measurement ps at secondary hydraulic cylinder

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Fig. 2

Schematic illustration of the hydraulic actuation system and the variator. The servo valves are fed from a shared accumulator, which is continuously pressurized to pacc = 50 bar. The pressure in the tank is equal to the atmospheric pressure patmospheric.

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Fig. 3

Control configuration

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Fig. 4

Controller interconnection structure for the hydraulic actuation system

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Fig. 5

Identified nonparametric frequency response function P˜o(ωi) for ωi∈Ωid (dotted) and nominal parametric model P∧ (solid)

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Fig. 6

Singular values of the nonparametric frequency response function estimate P˜o(ωi) for ωi∈Ωid prior to scaling with Wsc (solid blue) and after scaling with Wsc (dashed red), shaped system W2P˜o(ωi)W1 for ωi∈Ωid (dashed–dotted green)

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Fig. 7

Bode diagram of identified No, Do (blue dots), identified N∧,D∧ (dashed red)

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Fig. 8

M∧-Δu interconnection structure for the uncertain CVT model

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Fig. 9

Resulting model uncertainty norm-bound γ as a function of frequency from model validation procedure: data set using primary input of r2 (blue ×), data set using secondary input of r2 (green ⋄), parametric overbound resulting in Pid (solid blue)

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Fig. 10

Resulting model uncertainty norm-bound γ as a function of frequency: data sets on identification frequency grid Ωid (blue ×), data sets on validation frequency grid Ωval (green ⋄). In addition, a parametric overbound is shown that results in Pval (solid blue).

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Fig. 11

Controllers: initial controller Cexp (solid blue), optimal nominal controller CNP (dashed red), optimal robust controller CRP,val (dashed–dotted green)

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Fig. 12

Closed-loop step responses (r2→y): initial controller Cexp (solid blue), optimal nominal controller CNP (dashed red), optimal robust controller CRP,val (dashed-dotted green), optimal robust controller CRP,id (dotted magenta)

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Fig. 13

Closed-loop step responses (r2→y). Using optimal robust controller CRP,val: experimental result (solid blue), simulation result (dashed red). Using initial controller Cexp: experimental result (solid green), simulation result (dashed magenta).

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Fig. 14

Closed-loop experimental results for modified driving cycle (Left: Primary angular velocity ωp; Centre: Secondary torque Ts; Right: Speed ratio rs)

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Fig. 15

Closed-loop experimental results for modified driving cycle (Left: Primary pressure; Right: Secondary pressure) (solid blue: Measurement; dashed red: Reference)




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