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 Electrohydraulic Pressure Control
Jack L Johnson, PE, BSEE
PUBLISHER: IDAS Engineering Inc, East Troy WI, USA, 1998


 

                                                            PREFACE

This is the first textbook that is devoted to the design and analysis of hydraulic circuits and systems
that use feedback control of hydraulic pressure. The early chapters are written at about a sophomore
to junior engineering/technologist theoretical level, however, the later chapters do make use of
calculus, transform methods and state variable diagramming methods to present the control problem
and strategy.

The book begins with a chapter on the effects of fluid compressibility and introduces the concept
of "hydraulic capacitance" as a convenient means of quantifying compressibility at the circuit level.
The advantage of the capacitance approach, which has been introduced by other authors more than
forty years ago, is that all the circuit analysis concepts (Kirchoff's laws, esp) can be borrowed from
the electrical engineering community and applied directly to the hydraulic circuit analysis problem.

That the effects of compressibility must be included can be readily seen in considering the factors
that affect the proper sizing of a control valve that is used to control the pressure in a load vessel that requires no thru-flow. Suppose that it is necessary to ramp the pressure up according to some
specified design pressure rise rate. Given that there is no thru-flow, the only need for the valve to open is to supply those "molecules" of hydraulic fluid that go to jam the molecules closer together in the compressed fluid. If the valve is not large enough, the rise rate will be choked off by the valve, and the design figure will not be met. This case is one that is taken on in the book. The case where the control valve must supply not only flow of compressibility, but also any thru-flow requirements
needed by the application.

The later chapters look into the dynamic response of the pressure control system in the Laplace
transform


NOTE: This book contains the background theory and all the pertinent derivations regarding the design and analysis of controlling pressure by means of electrohydraulic servo and proportional valving. It is the first textbook that is devoted to the subject. It is a necessary library addition for any engineer who intends to design pressure control loops and their handmaidens, force control loops, and is written for the third or fourth year undergraduate engineering student. Useful as a classroom text.


 

                                  TABLE OF CONTENTS

FLUID COMPRESSIBILITY, HYDRAULIC CAPACITANCE AND CAVITATION
A Fluid Compressibility Experiment
Capacitance Calculations
Thermal Effects Upon Bulk Modulus
Capacitances in Parallel
From Circuit Schematic to Analytical Schematic
A Series Implementable Capacitance
Capacitance in Series
Effective Capacitance of a Hydraulic Cylinder
Capacitance of a Gas Filled Accumulator
Adiabatic Accumulator Derivation
Effects of Envelope Expansion on Apparent Bulk Modulus
Line Length Limitations
Iso-Thermal Accumulator Derivation
Problem Set

CIRCUITS WITH CAPACITANCE AND LAMINAR LEAKAGE
Circuits with Capacitance and Leakage
When Pressure Waveshape is Known and Flow is Unknown
When Flow is Known and Pressure is Unknown
A summary of the RC Process
Application of the RC Circuit
Introduction to State Variable and Block Diagrams
Dynamic Response of the First Order System
Some Further Generalizations of the State Variable Diagram
The Transfer Function
Problem Set

CAPACITANCE DYNAMICS AND THE KNIFE-EDGED ORIFICE
Discharging
Time to Discharge to a Specified Pressure
Compressibility Flow During the Discharging Cycle
The Charging Cycle
Time Rate of Charge
Profiling Considerations
Design Strategies
Circuits with Through-Flow
Kuhfittig Equation
Addendum A -- Program Listing
Addendum B -- Tabulated Data for Kuhfittig
Addendum C -- Graphical Summary of Kuhfittig Data

PRESSURE LOOP CALIBRATION
Pressure Control -- A Case Study
Addendum A -- Basic Program Listing
Addendum B -- Calculated Data Chart

PRESSURE CONTROL LOOPS -- WHEN DISPLACEMENT FLOW IS NEGLIGIBLE
System Equations
State Variable Diagram
Closing the Pressure Loop
Block Diagram Reduction and Transfer Function
Steady-State Gain
Leak Free Valve
Hydraulic Frequency
Maximum Conditions for Stability
Design of the Pressure Loop with Integral Control
Open Loop Transfer Function
PI Control in the Pressure Control Loop
Root-Locus Analysis of the Pressure Control Loop
Commentary on the Example Problem

FORCE CONTROL LOOPS -- WHEN DISPLACEMENT FLOW IS SIGNIFICANT
Analytical Hydromechanical Schematic
Dynamic Equations
Sizing Components for the Force Control Loop
State Variable Diagram of the Force Control System-Open Loop
Summary of the Force Control Loop With Significant Displacement flow
Force Control Loop Under the Condition That Displacement Flow is Significant
Dynamic Equations of the Constant Speed, Hydromechanical System

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