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Servomechanisms Theory

Instrumentation and Electronics Engineering and Design

Servomechanisms, Section 1, Theory
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Objectives of a Feedback Control System

The purpose of a feedback control system is to monitor an output (controlled variable) in a manner dictated by an input (reference variable) in the presence of spurious disturbances (such as random load changes).

The basic elements of a feedback control system would be to measures the output, compares the measurement with the desired value of the output as prescribed by the input, and uses the error (difference between actual output and desired output) to change the actual output and bring it into closer correspondence with the desired value of the output.

TOC

CHAPTER 1
PROPERTIES OF FEEDBACK CONTROL SYSTEMS
OBJECTIVES OF A FEEDBACK CONTROL SYSTEM
OPEN-LOOP VS CLOSED-LOOP SYSTEM CHARACTERISTICS
STABILITY AND DYNAMIC RESPONSE ..... .
TERMINOLOGY OF FEEDBACKCONTROL SYSTEMS

CHAPTER 2
DYNAMIC RESPONSE
LINEARIZATION
TRANSIENT RESPONSE
FREQUENCY RESPONSE
FORCED RESPONSE
STOCHASTIC INPUTS

CHAPTER 3
METHODS OF DETERMINING DYNAMIC RESPONSE OF LINEAR SYSTEMS
THE DIFFERENTIAL EQUATIONS
FACTORING AND CHARACTERISTIC PARAMETERS OF RESPONSE MODES
FACTORING
CHARACTERISTIC PARAMETERS OF RESPONSE MODES
First Order
Second Order
Third Order
Fourth Order
THE CONVOLUTION INTEGRAL
LAPLACE AND FOURIER TRANSFORMS
GENERAL THEOREMS

SOLUTION OF DIFFERENTIAL EQUATIONS
FREQUENCY RESPONSE
BLOCK DIAGRAMS AND SIGNAL-FLOW GRAPHS
BLOCK DIAGRAMS
SIGNAL-FLOW GRAPHS
APPROXIMATE NUMERICAL AND GRAPHICAL
METHODS OF DETERMINING TRANSIENT RESPONSE
ERROR COEFFICIENTS FOR DETERMINING RESPONSE TO AN ARBITRARY INPUT
RESPONSE TO STATIONARY STOCHASTIC INPUTS
USE OF ANALOG COMPUTERS FOR SIMULATION

CHAPTER 4
STABILITY OF FEEDBACK CONTROL SYSTEMS
INTRODUCTION
ROUTH CRITERION
NYQUIST CRITERION
ROOT -LOCUS METHOD

CHAPTER 5
GAIN DETERMINATION
PERFORMANCE CRITERIA AND DEFINITIONS
GAIN
VELOCITY CONSTANT .
ACCELERATION CONSTANT .
TORQUE CONSTANT
STATIC ACCURACY.
BANDWIDTH
PEAK MAGNITUDE

POLAR-PLANE REPRESENTATION
GENERAL3
DIRECT POLAR PLANE
INVERSE POLAR PLANE
EXACT AND ASYMPTOTIC-LOGARITHMIC REPRESENTATIONS
SEPARATE MAGNITUDE AND PHASE PLOTS
Magnitude Curves
Phase-Angle Curves
GAIN-PHASE PLANE
CLOSED-LOOP RESPONSE DETERMINATION
GENERAL
POLAR-PLANE TECHNIQUE
GAIN-PHASE PLANE TECHNIQUE (NICHOLS CHART)
NONUNITY -FEEDBACK SYSTEMS
SETTING THE GAIN FOR A SPECIFIED MP
POLAR-PLANE CONSTRUCTION
GAIN-PHASE PLANE CONSTRUCTION
APPROXIMATE PROCEDURES
PHASE MARGIN AND GAIN MARGIN
Phase Margin
Gain Margin
GENERAL COMMENTS ON THE PHASE-MARGIN
APPROXIMATE CLOSED-LOOP RESPONSE
ROOT-LOCUS METHOD

PROPERTIES OF ROOTS IN THE s PLANE
First-Order Root
Second-Order Root
GAIN DETERMINATION IN THE s PLANE

CHAPTER 6
COMPENSATION TECHNIQUES
INTRODUCTION
RESHAPING LOCUS ON GAIN-PHASE PLANE .
GENERAL
LAG COMPENSATION
LEAD COMPENSATION
PHASE-MARGIN AND ASYMPTOTIC METHODS
GENERAL
LAG COMPENSATION
LEAD COMPENSATION
FEEDBACK OR PARALLEL COMPENSATION
ALTERNATIVE DESIGN METHODS .
TYPICAL COMPENSATION NETWORKS .
D-C ELECTRIC .
A-C ELECTRIC .
MECHANICAL DAMPER .
HYDRAULIC AMPLIFIER
PNEUMA TIC CONTROLLER

CHAPTER 7
PERFORMANCE EVALUATION
RELATIONS BETWEEN FREQUENCY RESPONSE AND TRANSIENT RESPONSE
CLOSED-LOOP FREQUENCY RESPONSE FROM CLOSED-LOOP TRANSIENT RESPONSE
RELATIONS BETWEEN CLOSED-LOOP TRANSIENT RESPONSE AND CLOSED-LOOP POLEZERO CONFIGURATION
RELATIONS BETWEEN OPEN-LOOP FREQUENCY RESPONSE AND CLOSED-LOOP TRANSIENT RESPONSE
ERROR COEFFICIENTS
PERFORMANCE INDICES

CHAPTER 8
OPTIMIZATION METHODS FOR TRANSIENT AND STOCHASTIC INPUTS
CRITERIA OF PERFORMANCE
OPTIMUM SYNTHESIS OF FIXED-CONFIGURATION SYSTEMS
TRANSIENT INPUTS
STATIONARY STOCHASTIC INPUTS .
OPTIMUM SYNTHESIS OF FREE-CONFIGURATION
SYSTEMS WITH STATIONARY STOCHASTIC INPUTS
LIMITATIONS AND APPLICATION PROBLEMS

CHAPTER 9
SAMPLE-DATA SYSTEMS GENERAL THEORY
THE z TRANSFORM AND THEw TRANSFORM
THE z TRANSFORM
THE w TRANSFORM
OPERATIONAL METHODS
BASIC RELATIONS OF SAMPLED FUNCTIONS .... 9-6
ADDITIONAL PROPERTIES OF SAMPLED FUNCTIONS
DESIGN TECHNIQUES ..
PERFORMANCE EVALUATION

CHAPTER 10
NONLINEAR SYSTEMS
DESCRIBING FUNCTION PROCEDURES
PHASE-PLANE PROCEDURES
LIMITATIONS , COMPENSATION, AND OTHER METHODS


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