THE STUDY OF METAL STRUCTURES AND THEIR MECHANICAL PROPERTIES

By MARY JOHNSON

CONTENTS INTRODUCTION TO MATLAB BASIC OPERATION OF MATLAB™ DATA ENTRY WORKSPACE ARITHMETIC OPERATIONS MANIPULATIONS OF COMPLEX NUMBERS ARRAY OPERATIONS ELEMENT-BY-ELEMENT ELEMENTARY MATHEMATICAL FUNCTIONS CELL ARRAY DATA TYPE GRAPHICS OUTPUT POLYNOMIALS WRITING MATLAB™PROGRAMS INTRODUCTION TO THE MATLAB™CONTROL SYSTEM TOOLBOX THE USE OF FUNCTIONS OF THE CONTROL SYSTEM TOOLBOX LTI MODEL STRUCTURES (SYS FORMS) TIME DOMAIN ANALYSIS FREQUENCY DOMAIN ANALYSIS ZEROS, POLES LTI VIEWER SIMULINK™ DESCRIPTION OF CONTINUOUS SYSTEMS IN THE TIME-, OPERATOR- AND FREQUENCY DOMAINS RELATIONSHIP BETWEEN THE TIME- AND THE FREQUENCY DOMAIN LAPLACE AND INVERSE LAPLACE TRANSFORMATIONS THE FREQUENCY FUNCTION CALCULATION AND VISUALIZATION OF THE FREQUENCY FUNCTION PLOTTING THE BODE AND THE NYQUIST DIAGRAMS OPERATIONS WITH BASIC ELEMENTS BASIC ELEMENTS OF A LINEAR SYSTEM PROPORTIONAL (P) ELEMENT INTEGRATING (I ) ELEMENT FIRST-ORDER LAG ELEMENT (PT1) SECOND-ORDER OSCILLATING (N) ELEMENT DIFFERENTIATING (D AND DT ) ELEMENTS THE EFFECT OF ZEROS DEAD-TIME ELEMENT EVALUATION OF THE CHARACTERISTICS OF THE ELEMENTS, THE EFFECTS OF POLES AND ZEROS STATE-SPACE REPRESENTATION OF CONTINUOUS SYSTEMS STATE TRANSFORMATION SOLUTION OF THE STATE EQUATION BY ANALYTICAL METHODS SOLUTION OF THE STATE EQUATION IN THE TIME DOMAIN SOLUTION OF THE STATE EQUATION IN THE LAPLACE OPERATOR DOMAIN CONTROLLABILITY, OBSERVABILITY DETERMINATION OF CONTROLLABILITY AND OBSERVABILITY ASSUMING CANONICAL FORM DETERMINATION OF CONTROLLABILITY AND OBSERVABILITY FROM ARBITRARY (NON-CANONICAL) REPRESENTATIONS NEGATIVE FEEDBACK QUALITY CHARACTERISTICS AND THE PROPERTIES OF NEGATIVE FEEDBACK REQUIREMENTS SET FOR CONTROL SYSTEMS DEMONSTRATING THE BASIC PROPERTIES OF NEGATIVE FEEDBACK RESULTING TRANSFER FUNCTIONS THE EFFECT OF THE POLES OF THE EXCITATION SIGNAL AND THE EFFECT OF THE POLES OF THE OPEN LOOP ON STEADY STATE BEHAVIOUR PROPERTIES OF THE STATIC RESPONSE RELATION BETWEEN THE FREQUENCY FUNCTIONS OF THE OPEN- AND CLOSED-LOOP RELATION BETWEEN THE OVERSHOOT OF THE STEP RESPONSE AND THE AMPLI?CATION OF THE FREQUENCY FUNCTION THE SENSITIVITY FUNCTION CONTROL STRUCTURES FEEDFORWARD CASCADE CONTROL STABILITY OF LINEAR CONTROL SYSTEMS BIBO STABILITY STABILITY ANALYSIS BASED ON THE LOCATION OF THE CLOSED-LOOP POLES STABILITY ANALYSIS USING THE ROUTH-HURWITZ CRITERION STABILITY ANALYSIS USING THE ROUTH SCHEME STABILITY ANALYSIS BASED ON THE HURWITZ DETERMINANT STABILITY ANALYSIS BASED ON THE ROOT-LOCUS METHOD NYQUIST STABILITY CRITERION THE SIMPLI?ED NYQUIST STABILITY CRITERION THE GENERALIZED NYQUIST STABILITY CRITERION PHASE MARGIN, GAIN MARGIN, MODULUS MARGIN, DELAY MARGIN PHASE MARGIN, GAIN MARGIN DELAY MARGIN MODULUS MARGIN ROBUST STABILITY INTERNAL STABILITY DESIGN IN THE FREQUENCY DOMAIN CONTROL OF STABLE CONTINUOUS PROCESSES, YOULA PARAMETERIZATION PID REGULATOR DESIGN CHARACTERISTICS OF PID ELEMENTS CHARACTERISTICS OF THE PI ELEMENT CHARACTERISTICS OF THE PD ELEMENT CHARACTERISTICS OF THE PID ELEMENT DESIGN OF A PID REGULATOR DESIGN CONSIDERATIONS DESIGN OF A P REGULATOR DESIGN OF P, PI, PD AND PID REGULATORS REGULATOR DESIGN FOR A SECOND-ORDER OSCILLATING ELEMENT APPLYING EXPERIMENTAL TUNING RULES PID REGULATOR DESIGN FOR A DEAD-TIME SYSTEM REGULATOR DESIGN FOR A DEAD-TIME SYSTEM CONSIDERING THE PHASE SHIFT REGULATOR DESIGN FOR A DEAD-TIME SYSTEM USING PADE APPROXIMATION CONTROL OF AN UNSTABLE SYSTEM CONTROL OF AN UNSTABLE SYSTEM WITH A P REGULATOR CONTROL OF AN UNSTABLE SYSTEM WITH A PID REGULATOR HANDLING OF CONSTRAINTS STATE FEEDBACK CONTROL STATE FEEDBACK WITH POLE PLACEMENT INTRODUCING AN INTEGRATOR INTO THE FEEDBACK LOOP STATE ESTIMATION STATE FEEDBACK WITH STATE ESTIMATION GENERAL POLYNOMIAL METHOD FOR REGULATOR DESIGN ANALYSIS OF SAMPLED-DATA SYSTEMS DISCRETE-TIME SYSTEMS Z-TRANSFORMS DISCRETE-TIME IMPULSE RESPONSE AND PULSE TRANSFER FUNCTION INITIAL VALUE AND FINAL VALUE THEOREMS STABILITY OF SAMPLED-DATA SYSTEMS ANALYSIS OF CLOSED-LOOP SAMPLED-DATA SYSTEMS STATE SPACE EQUATION OF SAMPLED-DATA SYSTEMS DISCRETIZATION OF THE CONTINUOUS-TIME STATE EQUATION DERIVATION OF THE DISCRETE STATE EQUATION FROM THE PULSE TRANSFER FUNCTION DISCRETE REGULATOR DESIGN FOR STABLE PROCESSES DESIGN OF A YOULA PARAMETERIZED REGULATOR CONTROL OF A DEAD-TIME SYSTEM WITH A SMITH PREDICTOR DESIGN OF A DEAD-BEAT REGULATOR DESIGN OF DISCRETE PID REGULATORS COMPARING THE FREQUENCY CHARACTERISTICS OF CONTINUOUS AND DISCRETE SYSTEMS DESIGN OF A DISCRETE PID REGULATOR DISCRETE PID REGULATORS BEHAVIOUR OF THE BASIC REGULATORS REGULATOR DESIGN FOR A PRESCRIBED PHASE MARGIN STATE FEEDBACK IN SAMPLED SYSTEMS STATE FEEDBACK WITH EXTENSION WITH INTEGRATOR STATE FEEDBACK FROM THE ESTIMATED STATE VARIABLES GENERAL POLYNOMIAL METHOD TO DESIGN DISCRETE REGULATORS CASE STUDY MODELLING AND ANALYSING A HEAT PROCESS REFERENCES