# More details on Electrohydraulic Control of Pressure and Cylinder Force

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. It is useful as a classroom text

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, 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, especially) 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.

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