Discontinuous Automatic Control

Discontinuously working elements (on-off controls) are widely used in automatic control systems. From an engineering point of view they are attractive because they are nearly always Simpler, more rugged, and cheaper to build than continuous controls. But prediction of their effects in the controlled system is sometimes so complicated that engineers have avoided discontinuous control where it would have been preferable to continuous control. Originally published in 1953. The **Princeton Legacy Library** uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. CONTENTS Introduction PART I. DISCONTINUOUS CONTROL OF A MOVING BODY WITH A SINGLE DEGREE OF FREEDOM 1. The Differential Equation of Motion 2. Description of the Controlling Mechanism 2.1. Discontinuouslyappliedforcesormoments 2.2. Discontinuous velocity of application of forces or moments 2.3. Imperfections of the controlling mechanism 3. The Solutions of the Differential Equation of Motion and its Continuity Qualities 3.1. Position control 3.2. Velocitycontrol 4. Complete Theory of the Motion with Position Control 4.1. The representation of the motion in the phase plane 4.2. Different types of motion 4.3. The control function F * and its behavior in the neighborhood of switch points 4.4. The loci of the end, starting, and rest points 4.5. Periodic motions 4.6. Complete survey of the possible motions 4.7. Selection of the system and the coefficient k for a given mechanical problem 5. Complete Theory of the Motion with Velocity Control 5.1. The representation of the motion in the phase space 5.2. Different types of motion 5.3. The control function F1* as a function of x, x', and b 5.4. Complete survey of the possible motions 5.5. Selection of the system and the coefficients k and k for a given mechanical problem PART II. INFLUENCE OF CONTROL MECHANISM IMPERFECTIONS ON THE MOTION OF A BODY WITH A SINGLE DEGREE OF FREEDOM 6. Effects upon Motion with Position Control 6.1. Constant lag dependent upon the value of the control function (threshold) 6.2. Direct time lag 6.3. Neutral zone 6.4. Relative importance of the three types of imperfections 7. Effects upon Motion with Velocity Control 7.1. Constant lag dependent upon the value of the control function (threshold) 7.2. Direct time lag 7.3. Neutral zone 7.4. Importance of these imperfections in systems with velocity control PART III. DISCONTINUOUS CONTROL OF A MOVING BODY WITH MORE THAN ONE DEGREE OF FREEDOM 8. The Longitudinal Motion of a Missile (Discontinuous Position Control) 8.1. Equations of motion, the control equation, and their formal solutions 8.2. Continuity qualities of the solutions 8.3. Representation of the motion in the phase space 8.4. Examples 8.5. The occurrence of end points and the influence of time lag on the controlled motion 8.6. Periodic motions 8.7. Discussion of the general behavior of a missile under discontinuous position control Appendix I. Tables VII and VIII Appendix II. Construction of logarithmic spirals by an approximate method Index Discontinuously working elements (on-off controls) are widely used in automatic control systems. From an engineering point of view they are attractive because they are nearly always Simpler, more rugged, and cheaper to build than continuous controls. But prediction of their effects in the controlled system is sometimes so complicated that engineers have avoided discontinuous control where it would have been preferable to continuous control. Originally published in 1953. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905