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TECHNICAL PAPERS

Adaptive Output Force Tracking Control of Hydraulic Cylinders With Applications to Robot Manipulators

[+] Author and Article Information
Wen-Hong Zhu

Spacecraft Engineering, Space Technologies,  Canadian Space Agency, 6767 Route de l’Aeroport, Saint-Hubert, QC J3Y 8Y9, CanadaWen-Hong.Zhu@space.gc.ca

Jean-Claude Piedboeuf

Spacecraft Engineering, Space Technologies,  Canadian Space Agency, 6767 Route de l’Aeroport, Saint-Hubert, QC J3Y 8Y9, CanadaJean-Claude.Piedboeuf@space.gc.ca

A dual micro–macro valve system is used. The small valve, which has a flow rate of $1∕10$ as the big one, is connected in parallel with the big valve. The dual-valve system is properly adjusted such that the equivalent valve system is critically lapped.

Virtual decomposition control allows adaptive control to be performed with respect to individual subsystems such as the rigid links and the rigid/flexible joints, while keeping the $L2$ and $L∞$ stability of the entire system. Each subsystem is assigned a non-negative accompanying function. The technical merit is that the dynamic coupling at each “cutting point” between every two physically connected subsystems is uniquely represented by a scalar term namely “virtual power flow”—the inner product of the velocity error and the force error. With respect to a joint actuated by either one or two hydraulic cylinders, it typically has two “cutting points.” The summation of the two “virtual power flows” coming form the two connected links takes exactly the form of $(vr−v)(Fd−F)$, where $vr$ represents the required velocity. The term $(vr−v)(Fd−F)$ has to be canceled out in the joint controller design in order to achieve the $L2$ and $L∞$ stability of the entire system. This can be done by adding $(vr−v)∕kf$ to $f̂f$ at the right-hand side of 39. Once the $L∞$ stability of the entire system is achieved, the boundedness of the velocity $v$ as well as the boundedness of $Fd$ and $Ḟd$ are all guaranteed.

The experimental result shown in Fig. 6 demonstrates that the velocity related term $Kuv$ is very close to the control voltage $u*$.

J. Dyn. Sys., Meas., Control 127(2), 206-217 (Jun 08, 2004) (12 pages) doi:10.1115/1.1898237 History: Received October 21, 2003; Revised June 08, 2004

Abstract

An adaptive output force control scheme for hydraulic cylinders is proposed by using direct output force measurement through loadcells. Due to the large and somewhat uncertain piston friction force, cylinder chamber pressure control with Coulomb-viscous friction prediction may not be sufficient enough to achieve a precise output force control. In the proposed approach, the output force error resulting from direct measurement is used not only for feedback control, but also to update the parameters of an appropriate friction model which includes the Coulomb-viscous friction force in sliding motion and the output force dependent friction force in presliding motion. The $L2$ and $L∞$ stability is guaranteed for both the pressure force error and the output force error. Under bounded desired output force and its derivative, asymptotic stability of both the pressure force error and the output force error is also guaranteed. The experimental results demonstrate that a good pressure force control system does not necessarily guarantee a good output force control, and that adaptive friction compensation is superior to fixed-parameter friction compensation. The output force control transfer functions of a robot joint driven by two hydraulic cylinders in pull–pull configuration are limited by $±1.5dB$ up to $20Hz$, tested in free motion and in rigid constraint. The excellent output force (joint torque) control performance implies the dynamic equivalency between a hydraulic cylinder and an electrically-driven motor within the prespecified bandwidth. This allows to emulate an electrically-driven robot by a hydraulic robot.

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Figures

Figure 1

Pull–pull configuration cylinders

Figure 2

Single-rod cylinder

Figure 3

Pressure force tracking results between the desired pressure force Pd (dashed lines) and the measured pressure force P (solid lines) with different cases of parameter adaptation for k̂2p1 and k̂2n1. (a) and (b) correspond to ρ21=5000(Vs∕kN) and ρ21=50(Vs∕kN), respectively, with k2p1−=k2n1−=50(Vs) and k2p1+=k2n1+=100(Vs); (c) corresponds to k̂2p1=(k2p1−+k2p1+)∕2 and k̂2n1=(k2n1−+k2n1+)∕2, and (d) corresponds to k̂2p1=0 and k̂2n1=0.

Figure 4

Parameter adaptation of k̂2p1 (dashed lines) and k̂2n1 (solid lines). (a) corresponds to ρ21=5000(Vs∕kN) and (b) corresponds to ρ21=50(Vs∕kN), respectively.

Figure 5

Cylinder positions corresponding to Fig. 3

Figure 6

Valve control voltages corresponding to Fig. 3. The dashed line in (a) represents Kuv in 65.

Figure 7

Output force tracking results between the desired force Fd (dashed lines) and the measured force F (solid lines) with different cases of parameter adaptation for k̂cp and k̂cn under active k̂0. (a) and (b) correspond to c1=c2=100(1∕s) and c1=c2=1(1∕s), respectively, with c3=20(1∕s), under kcp−=kcn−=0 and kcp+=kcn+=2.0(kN); (c) corresponds to k̂cp=(kcp−+kcp+)∕2=1.0(kN) and k̂cn=(kcn−+kcn+)∕2=1.0(kN), and (d) corresponds to k̂cp=0 and k̂cn=0.

Figure 8

Parameter adaptation of k̂cp (dashed lines) and k̂cn (solid lines) associated with Fig. 7. (a) corresponds to c1=c2=100(1∕s) and (b) corresponds to c1=c2=1(1∕s), respectively.

Figure 9

Pressure force tracking results corresponding to Fig. 7. The dashed lines represent FPd and the solid lines represent FP.

Figure 10

Cylinder positions corresponding to Fig. 7

Figure 11

Valve control voltages corresponding to Fig. 7

Figure 12

Output force tracking results between the desired force Fd (dashed lines) and the measured force F (solid lines) with different cases of parameter adaptation for k̂cp and k̂cn under inactive k̂0=0. (a) and (b) correspond to c1=c2=100(1∕s) and c1=c2=1(1∕s), respectively, under kcp−=kcn−=0 and kcp+=kcn+=2.0(kN); (c) corresponds to k̂cp=(kcp−+kcp+)∕2=1.0(kN) and k̂cn=(kcn−+kcn+)∕2=1.0(kN), and (d) corresponds to k̂cp=0 and k̂cn=0.

Figure 13

Output force tracking results between the desired force Fd (dashed lines) and the measured force F (solid lines) subject to a 10Hz sinusoidal input with different cases of parameter adaptation of k̂fp and k̂fn defined by 5. (a) and (b) correspond to c6=c7=100[1∕(s(kN)2)] and c6=c7=1[1∕(s(kN)2)], respectively, under kfp−=kfn−=0 and kfp+=kfn+=4; (c) corresponds to k̂fp=(kfp−+kfp+)∕2=2 and k̂fn=(kfn−+kfn+)∕2=2, and (d) corresponds to k̂fp=0 and k̂fn=0.

Figure 14

Friction forces (dashed lines) versus output forces (solid lines) corresponding to Fig. 1

Figure 15

Cylinder position and valve control voltage corresponding to Fig. 1

Figure 16

Output force tracking results between the desired force Fd (dashed lines) and the measured force F (solid lines) subject to different step inputs and sinusoidal inputs with different amplitudes and frequencies. (a) and (b) are with step inputs of different amplitudes; (c) is with 1Hz sinusoidal inputs; and (d) is with 10Hz sinusoidal inputs.

Figure 17

Pressure force tracking results between the desired pressure force FPd (dashed lines) and the measured pressure force FP (solid lines) corresponding to Fig. 1

Figure 18

Transfer functions of the output force tracking control

Figure 19

Motion control of the first joint. (a) shows the joint position tracking result. The desired joint position is represented by the dashed line and the actual joint position is represented by the solid line. (b) shows the joint position tracking error. (c) shows the joint output force tracking result. The dashed line represents the desired force Fd and the solid line represents the actual output force F. (d) shows the valve control voltage.

Figure 20

Joint torque tracking results of the first five joints corresponding to the circle trajectory tracking control. In each figure, the dashed lines represent the desired joint torques Fdr(t) and the solid lines represent the actual joint torques Fr(t), where r(t) represents the actuation radius.

Errata

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