Introduction to Discrete Linear Controls

¿PrefaceAcknowledgmentsChapter I Systems Theory and Discrete Linear Control Systems 1.1 Systems Theory 1.2 Discrete Systems 1.3 Control Theory 1.4 Control Systems 1.5 System Models ExercisesChapter II Discrete Control-System Models 2.1 Difference Equations 2.2 Control of Cylinder Diameter 2.3 Generalized Discrete Process Controller with Sampling 2.4 Production-Inventory Control System 2.5 Criminal Justice System Feedback Model 2.6 Conclusion ExercisesChapter III The Calculus of Finite Differences 3.1 Differences 3.2 Factorial Polynomials 3.3 Summations 3.4 The Calculus of Finite Differences and Linear Difference Equations ExercisesChapter IV Classical Solution of Linear Difference Equations with Constant Coefficients 4.1 The Nature of Solutions 4.2 The Homogeneous Solution 4.3 The Particular Solution 4.4 Boundary Conditions 4.5 Finding the Roots of the Characteristic Equation ExercisesChapter V The z Transform 5.1 The Basic Transform 5.2 Properties of the z Transform 5.3 Tables 5.4 Transformation of Linear Difference Equations 5.5 The z Transform as a Probability Generating Function ExercisesChapter VI Inverse Transformation 6.1 Contour Integration 6.2 Table of Transform Pairs 6.3 Power Series Expansion 6.4 Maclaurin Series Expansion 6.5 Partial Fraction Expansion 6.6 The Special Case of zn = 0 6.7 Transfer Functions 6.8 Solution of Difference Equations with Generalized Forcing Functions 6.9 Conclusion ExercisesChapter VII System Performance: Measures and Environmental Effects 7.1 Control-System Performance Criteria 7.2 The Cylinder-Diameter Controller 7.3 Impulse Perturbation 7.4 Step Perturbation 7.5 Sinusoidal Perturbation 7.6 Random Perturbations 7.7 Selection of K ExercisesChapter VIII Parameter Selection in First-Order Systems Considering Sampling and Instrumentation Errors 8.1 The Simple Proportional Process Controller with Measurement Error 8.2 Properties of Measurement Error ¿(i) 8.3 Sampling 8.4 Instrumentation 8.5 Distribution of Individual Product Units 8.6 Maximum Speed of Response with Bounded Steady-State Process-Output Variance 8.7 Maximum Speed of Response with Bounded Steady-State Variance of Individual Product Units 8.8 Maximum Speed of Response with Random Perturbation and Bounded Steady-State Process-Output Variance 8.9 Maximum Speed of Response with Random Perturbation and Bounded Steady-State Variance of Individual Product Units 8.10 Minimum Steady-State Mean-Square Deviation of Process Output 8.11 Minimum Steady-State Mean-Square Deviation of Individual Product Units 8.12 Maximum Steady-State Probability of Acceptable Process Output 8.13 Maximum Steady-State Probability of Acceptable Individual Product Units 8.14 Other Possibilities ExercisesChapter IX System Stability 9.1 General Definitions 9.2 Criterion for Stability of Discrete Linear Systems 9.3 Tests for Stability ExercisesChapter X Second-Order Systems 10.1 The Second-Order System 10.2 The Generalized Second-Order, Rapid-Response Process Controller 10.3 Responses of Generalized Second-Order Process Controller 10.4 Proportional-Plus-Difference Control 10.5 Proportional-Plus-Summation Control 10.6 Proportional Control with One-Period Delay ExercisesChapter XI nth-Order and Complex Systems 11.1 Signal Flow Graphs 11.2 Step-Function Response of nth-Order Generalized Process Controller 11.3 Effects of Delay on Process Controller Stability 11.4 Determination of Frequency Response from the System Transfer Function ExercisesReferencesIndex