Dynamic analysis and estimator design of a hydraulic drive system

Abstract

This paper deals with the dynamic analysis and state of the art estimator design through system inversion of a pedagogical hydraulic system, comprising variable displacement axial piston pump, high speed low torque hydraulic motor, proportional direction control valve, loading pump (bent axis) and a pressure relief valve at loading circuit. The hydraulic system has been modeled for simulation study and both the transient and the steady state responses have been validated experimentally. The necessary and sufficient conditions for the system to be observable have been obtained with respect to the minimum number of sensors placement. Thereafter, an estimator adaptive to varying load condition has been designed to have a good estimate of all the states using minimum sensors. All the estimated states have been compared with the responses from the test bed.

Appendices

Appendix 1

See Table 2.

Table 2 Summary of major components and instruments

Appendix 2

2.1 Notation

A _o :

Port opening area of the valve

A _dcv :

Port opening area of the direction control valve

A _lv :

Port opening area of the loading valve

C _d :

Co-efficient of discharge

D _lp :

Loading pump displacement rate

D _m :

Motor displacement rate

D _p :

Pump displacement rate

f :

Function

J :

Moment of inertia

K :

Bulk stiffness of fluid

L :

Angular momentum

M _p :

Maximum percentage overshoot

$\dot{P}_{1}$ :

Inertia torque

P _mi :

Pressure at inlet port of the hydro-motor

P _spply :

Supply pressure at pump plenum

P _pp :

Pressure at loading pump plenum

R _vlv :

Resistance offered by a valve

R _vlvdcv :

Valve port resistance

R _lv :

Resistance offered by the loading valve

R _fric :

Friction resistance on the hydro-motor shaft

R _lkgp :

Leakage resistance of the pump

R _mlkg :

Leakage resistance of the hydro-motor

R _lkglp :

Leakage resistance of the loading pump

t :

Time

t _p :

Time taken to reach first peak

t _r :

Rise time

t _∞ :

Time taken to reach steady state

$\dot{V}$ :

Flow

$\dot{V}_{1}$ :

Flow lost due to compression at pump plenum

$\dot{V}_{2}$ :

Flow lost due to compression at motor plenum

$\dot{V}_{3}$ :

Flow lost due to compression at pump plenum

$\dot{V}_{p}$ :

Flow supplied by the pump

$\dot{V}_{\text{m}}$ :

Flow supplied by the motor

$\dot{V}_{\text{lp}}$ :

Flow supplied by the loading pump

$\dot{V}_{\text{lkgp}}$ :

Leakage flow of the pump

$\dot{V}_{\text{lkgm}}$ :

Leakage flow of the motor

$\dot{V}_{\text{lkglp}}$ :

Leakage flow of the loading pump

$\dot{V}_{\text{dcv}}$ :

Flow passing through DCV

$\dot{V}_{\text{lv}}$ :

Flow passing through loading valve

ω _H :

Speed of the hydro-motor

ω _n :

Natural frequency

ω _E :

Speed of the prime mover (electric motor)

ρ :

Density of hydraulic oil

ξ :

Damping factor

ΔP :

Differential pressure

A, B, C, D :

Matrices of appropriate dimensions

O :

Observability matrix

U :

Input vector

E :

Feedback gain

X :

State vector

Y :

Output vector