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Exponential Tracking Control of Hydraulic Proportional Directional Valve and Cylinder via Integrator

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Hydraulics Research Laboratory. Exponential Tracking Control of ... Hydraulic System Model. Differentiable Approximation for Fluid Dynamics. Control Objective ... – PowerPoint PPT presentation

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Title: Exponential Tracking Control of Hydraulic Proportional Directional Valve and Cylinder via Integrator


1
Exponential Tracking Control of Hydraulic
Proportional Directional Valve and Cylinder via
Integrator BacksteppingJ. Chen, W. E. Dixon,
J. R. Wagner, D. M. Dawson Departments of
Mechanical and Electrical/Computer
EngineeringClemson University, Clemson, SC 29634
Oak Ridge National Laboratory, Oak Ridge, TN
37831
2
Presentation Outline
  • Literature Review
  • Hydraulic System Model
  • Differentiable Approximation for Fluid Dynamics
  • Control Objective
  • Error System Development
  • Nonlinear Controller Design
  • Stability Analysis
  • Numerical Results
  • Summary

3
Literature Review
  • Gamble et al. (1994) presented a comparison of
    sliding mode control with state feedback and PID
    control for proportional solenoid valves.
  • Vossoughi et al. (1995) created, and
    experimentally verified, a globally linearizing
    feedback control law for electro-hydraulic
    valves.
  • Bobrow et al. (1996) developed an adaptive
    hydraulic servo-valve controller which uses
    full-state feedback for simultaneous parameter
    identification and tracking control.
  • Alleyne (1996) developed a Lyapunov-based control
    algorithm for the control of an electro-hydraulic
    actuator. A gradient parameter adaptation scheme
    was included for compensating parametric model
    uncertainties.
  • Zheng et al. (1998) proposed a nonlinear adaptive
    learning algorithm for a proportional valve to
    accommodate valve dead zones, valve flow
    saturation, and cylinder seal friction.
  • Bu et al. (1999) designed a discontinuous
    projection based adaptive robust controller for
    single-rod hydraulic actuators with time-varying
    unknown inertia.

4
Hydraulic System Model Cylinder Dynamics
  • Cylinder dynamics can be written as
  • The hydraulic flow force F is defined as

Externally applied load (neglected for
simplicity)
(spring / damping term)
5
Hydraulic System Model Pressures and Flows
  • The pressures dynamics of the piston and rod side
    can be written as
  • Fluid flow of the piston and rod side can be
    written as

Remark The hydraulic cylinder is assumed to be
constructed such that some volume always
remains in the piston and rod sides of the
cylinder
6
Hydraulic System Model Spool Dynamics
P
z
P


S
T




m

s
P

P

R
P
Q
Q
R
P
  • The spool dynamics can be related to as
    follows
  • The spool dynamics can now be rewritten as

(solenoid control force)
neglected for simplicity
(spring / damping term)
7
Bosch NG6 Servo - Solenoid Control Valve
8
Hydraulic System Model Solenoid Model
9
Differentiable Approximation for Fluid Dynamics
  • Differentiable approximation for the fluid
    dynamics

real model
where
Remark Supply and tank pressures are assumed to
satisfy the following inequalities
10
Control Objective
  • The control objective is to force the piston
    position of a hydraulic cylinder to track a time
    varying reference trajectory.
  • It is assumed that all system parameters are
    known (Exact Model Knowledge) and all signals are
    measurable (Full State Feedback)
  • Define the piston tracking error as
  • Define the filtered tracking error as
  • where is a positive control
    gain
  • It can be shown that if , then

11
  • After taking the time derivative of , the
    primary open-loop error system can be written as
  • Based on the previous equation and the subsequent
    stability analysis, the desired hydraulic flow
    force is designed as follows
  • After substituting the control design into the
    open-loop error system, the closed-loop error
    system for can be obtained as

Obtained by adding and subtracting the desired
hydraulic flow force
(Auxillary force tracking error signal)
12
Error System Development
  • After taking the time derivative of ,
    using the pressure dynamics, the second open-loop
    error system is obtained as
  • where,
  • The auxillary control input is now
    designed as
  • Based on this design, the closed loop error
    system for becomes

Desired spool position function
13
Error System Development (cont.)
  • After taking the time derivative of ,
    the open-loop error system for can be
    obtained
  • Then the open-loop error system for can
    be rewritten as
  • where,
  • here, the notation denotes the partial
    derivative of with respect to
  • The desired spool velocity is now designed as

(Spool velocity tracking error)
14
Error System Development (cont.)
  • After substituting into the open-loop
    error system for ,we obtain
  • After taking the time derivative of ,
    the open-loop dynamics for can be
    determined as follows
  • Based on the subsequent stability analysis, the
    control input is designed as follows
  • which allows us to write the closed loop dynamics
    for as follows

15
Stability Analysis
  • A non-negative function is defined as follows
  • Then V(t) can be lower and upper bounded as
    follows
  • where,
  • After taking the time derivative of V(t) and
    substituting the closed loop error system, we
    obtain

16
Control Strategy
  • After utilizing the above inequalities, we can
    show

Pressure
Position
Force
Flow
Control Voltage
Desired Position
Error
Desired Force
Desired Flow
Cylinder Control
Desired Pressure
Electrical Control
Solenoid Control
Controller
17
Numerical Results
  • A PD and nonlinear controller shall track a
    sinusoidal position for the cylinder piston
    subject to nonlinear load conditions within 3 of
    the specified position
  • The desired trajectory is
  • Comparison of Commanded solenoid voltages for PD
    and nonlinear controllers
  • Comparison of Fluid pressures for PD and
    nonlinear controllers
  • Comparison of Positions and tracking errors for
    PD and Nonlinear controllers

18
Numerical Results
PD Controller
Nonlinear Controller
19
Numerical Results
PD Controller
Nonlinear Controller
20
Numerical Results
21
Experimental Test Stand
Control Valve
Piston side Pressure Transducer
Rod side Pressure Transducer
LVDT
Cylinder
22
Summary
  • Present the mathematical models for hydraulic
    system
  • Develop a differentiable approximation for the
    fluid flow dynamics
  • Proposal a model based nonlinear controller for
    hydraulic system.
  • Validate the controller with numerical and
    experimental results
  • Investigate both PD and nonlinear controller
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