TUPOLEV AIRCRAFT SINCE 1922

By ABIGAIL MARTINEZ

CONTENTS DEVELOPING THE FOUNDATION ENGINEERING UNITS INTERNATIONAL SYSTEM OF UNITS (SI) US/IMPERIAL UNITS SYSTEM COMPARING THE SI AND US/IMPERIAL UNITS SYSTEMS BLOCK DIAGRAMS EXAMPLES OF SUMMATION (OR COMPARISON) DEVICES DIFFERENTIAL EQUATIONS USING THE ‘D’ NOTATION SPRING–MASS SYSTEM EXAMPLE THE STANDARD FORM OF SECOND-ORDER SYSTEM TRANSFER FUNCTION PRIMER ON COMPLEX NUMBERS THE COMPLEX SINUSOID CHAPTER SUMMARY CLOSING THE LOOP THE GENERIC CLOSED LOOP SYSTEM THE SIMPLEST FORM OF CLOSED LOOP SYSTEM THE CONCEPT OF STABILITY RESPONSE TESTING OF CONTROL SYSTEMS THE INTEGRATION PROCESS HYDRAULIC SERVO-ACTUATOR EXAMPLE CALCULATING FREQUENCY RESPONSE FREQUENCY RESPONSE OF A FIRST-ORDER LAG FREQUENCY RESPONSE OF A SECOND-ORDER SYSTEM AIRCRAFT FLIGHT CONTROL SYSTEM EXAMPLE CONTROL SYSTEM ASSUMPTIONS OPEN LOOP ANALYSIS CLOSED LOOP PERFORMANCE ALTERNATIVE GRAPHICAL METHODS FOR RESPONSE ANALYSIS THE NYQUIST DIAGRAM DERIVING CLOSED LOOP RESPONSE FROM NYQUIST DIAGRAMS THE NICHOLS CHART GRAPHICAL METHODS – SUMMARY COMMENTS AND SUGGESTIONS CONTROL SYSTEM COMPENSATION TECHNIQUES CONTROL SYSTEM REQUIREMENTS COMPENSATION METHODS PROPORTIONAL PLUS INTEGRAL CONTROL PROPORTIONAL PLUS INTEGRAL PLUS DERIVATIVE CONTROL LEAD–LAG COMPENSATION LAG–LEAD COMPENSATION FEEDBACK COMPENSATION APPLICATIONS OF CONTROL COMPENSATION PROPORTIONAL PLUS INTEGRAL EXAMPLE LEAD–LAG COMPENSATION EXAMPLE CLASS 2 SYSTEM DESIGN EXAMPLE INTRODUCTION TO LAPLACE TRANSFORMS AN OVERVIEW OF THE APPLICATION OF LAPLACE TRANSFORMS THE EVOLUTION OF THE LAPLACE TRANSFORM PROOF OF THE GENERAL CASE APPLYING LAPLACE TRANSFORMS TO LINEAR SYSTEMS ANALYSIS PARTIAL FRACTIONS LAPLACE TRANSFORMS – SUMMARY OF KEY POINTS ROOT LOCUS ROOT LOCUS CONSTRUCTION RULES CONNECTING ROOT LOCUS TO CONVENTIONAL LINEAR ANALYSIS ROOT LOCUS EXAMPLE DEALING WITH NONLINEARITIES DE?NITION OF NONLINEARITY TYPES CONTINUOUS NONLINEARITIES ENGINE FUEL CONTROL SYSTEM EXAMPLE DISCONTINUOUS NONLINEARITIES STABILITY ANALYSIS WITH DISCONTINUOUS NONLINEARITIES THE TRANSPORT DELAY SIMULATION ELECTRONIC CONTROLS ANALOG ELECTRONIC CONTROLS THE OPERATIONAL AMPLI?ER BUILDING ANALOG CONTROL ALGORITHMS THE DIGITAL COMPUTER AS A DYNAMIC CONTROL ELEMENT SIGNAL CONVERSION DIGITAL CONTROLLER ARCHITECTURES THE STABILITY IMPACT OF DIGITAL CONTROLS DIGITAL CONTROL DESIGN EXAMPLE CREATING DIGITAL CONTROL ALGORITHMS THE INTEGRATOR THE FIRST-ORDER LAG THE PSEUDO DERIVATIVE CONCLUDING COMMENTARY AN OVERVIEW OF THE MATERIAL GRAPHICAL TOOLS COMPENSATION TECHNIQUES INTEGRAL WIND-UP AVOID USING PURE DERIVATIVE ACTION MECHANICAL STIFFNESS ESTIMATES ARE ALWAYS HIGH LAPLACE TRANSFORMS AND ROOT LOCUS TECHNIQUES NONLINEARITIES DIGITAL ELECTRONIC CONTROL THE WAY FORWARD DEVELOPING THE FOUNDATION CLASSICAL FEEDBACK CONTROL THEORY IS AN INHERENTLY MATHEMATICAL SUBJECT AND AS SUCH CAN SCARE OFF THE WOULD-BE PRACTITIONER IF PRESENTED IN RIGOROUS MATHEMATICAL FORM WHILE THERE IS NO WAY TO FULLY ABSORB AND APPLY THE BASIC CONCEPTS OF FEEDBACK CONTROL WITHOUT ANY MATHEMATICS IT IS DE?NITELY POSSIBLE TO EASE INTO THE SUBJECT MATTER GRADUALLY THUS ALLOWING THE READER TO PURSUE WITH SOME CURIOSITY, AND HOPEFULLY SOME EXCITEMENT, THE SUBTLETIES OF CLOSED LOOP SYSTEM BEHAVIOR THIS CHAPTER ATTEMPTS TO PROVIDE THE READER WITH A BASIC UNDERSTANDING OF THE TERMINOLOGY ASSOCIATED WITH CONTROL THEORY AND THROUGH THE USE OF SIMPLE EXAMPLES TO FAMILIARIZE THE READER WITH SOME OF THE KEY MATHE- MATICAL TOOLS NEEDED TO APPLY FEEDBACK CONTROL PRINCIPLES TO ENGINEERING PROBLEMS TO BEGIN WITH WE NEED TO DISCUSS THE ISSUE OF ENGINEERING UNITS SINCE THERE ARE FUNDAMENTAL DIFFERENCES BETWEEN THE STANDARDS IN USE AT TEACHING INSTITUTIONS AND WITHIN INDUSTRY BOTH IN EUROPE AND THE UNITED STATES THIS IS FOLLOWED BY A DISCUSSION REGARDING THE USE OF BLOCK DIAGRAMS AS A WAY TO DESCRIBE THE FUNCTIONALITY OF CLOSED LOOP CONTROL SYSTEMS DIFFERENTIAL EQUATIONS DESCRIBE THE DYNAMIC BEHAVIOR OF PHYSICAL SYSTEMS AND ARE AT THE CORE OF FEEDBACK CONTROL THEORY HERE, HOWEVER, THEY ARE TRANSFORMED FROM THE MATHEMATICS DOMAIN INTO AN EASY TO ASSIMILATE BLOCK DIAGRAM FORM USING SIMPLE EXAMPLES