The book outlines a new approach to the synthesis of nonlinear dynamic systems, a key problem in control engineering.

The suggested design formalism is based on the “binary” principle, which is essentially a dual treatment of signals in the dynamic system – as a phase variable in one circumstance and as a transformation operator in another. This principle opens up the possibility of handling control laws as ordinary phase variables and invokes feedback to generate such laws. The feedback mechanism, in this case, is exploited in a non-orthodox manner, leading to the occurrence of new types of feedback.

The efficiency of the new approach is demonstrated by constructing control systems that stabilize the motion of nonlinear dynamic plants with ill-defined dynamics. Stabilization is attained with continuous control and bounded gains.

Apart from solving the problems of ill-defined plant control, the binary principle is used advantageously for the development of nonlinear filters that separate close frequencies, for multiple differentiating noisy signals, and for the control of multi-connected systems.

The value of the binary principle is not confined to the control field; it may also be employed in studies of complicated dynamic systems in biology, biomechanics, social sciences, robotics, and biotechnology engineering, to name a few of the most promising applications.

About the Author
S.V. Emelyanov, Fellow of the Academy of Sciences of the USSR, has been engaged in solving many diverse problems of control. He is renowned for his pioneering efforts in the development of variable structure systems. The idea of incorporating unstable structures and sliding modes into the closed-loop control system for the purpose of system stabilization was also devised by the author of this book.

Translated from the Russian by Michael G. Edelev

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Introduction 7
1 BINARY SYSTEMS OF AUTOMATIC CONTROL. MOTIVATION, DEFINITIONS AND CONCEPTUALIZATION 10
1 Basic Principles and Definitions 10
1.1 Functional Diagrams of Control Systems in Classical Control Theory Setting 10
1.2 Block Diagrams of Adaptive Control Systems 12
1.3 The Concept of Operator-Variable and the Binary Principle 14
1.4 Generalized Elements of Binary Dynamic Systems 16
1.5 New Types of Feedback 17

2 The Principles of Control Under Uncertainty 18
2.1 Three Principles of Control for Solving Control Problems 18
2.2 Methods of Control for Ill-Defined Dynamic Systems 23

3 Generalized Block Diagrams of Binary Control Systems 28
3.1 Constructing Binary Control Systems 28
3.2 Structures of Binary Control Systems with Coordinate-Operator Feedback 29
3.3 Structures of Binary Control Systems with Coordinate-Operator and Operator Feedback 32
3.4 Structures of Binary Control Systems with Coordinate-Operator, Operator, and Operator-Coordinate Feedback 34

II FREE MOTION CONTROL 36
4 Definitions and Nomenclature 36
5 Time-Invariant Linear Coordinate Feedback 41
5.1 Finite Gain 41
5.2 High Feedback Gain 42
5.3 Constrained Control Signal 44
5.4 Imperfections 46
5.5 Linear Zone 49
5.6 Coordinate Feedback Under Inaccurate Information 51
5.7 Inaccuracies in Model Approximation 53

6 Coordinate-Operator Feedback 55
6.1 Proportional Coordinate-Operator Feedback 59
6.2 Proportional Coordinate-Operator Feedback with Magnitude Bounded Output 61
6.3 Nonlinear Time-Invariant Coordinate-Operator Feedback 67
6.4 Bang-Bang Coordinate-Operator Feedback 75
6.5 Bang-Bang Coordinate-Operator Feedback with Constraints and Dynamic Nonlinearities 79
6.6 Integral Coordinate-Operator Feedback 89
6.7 Integral Coordinate-Operator Feedback with a Constant Integration Rate 92
6.8 Inertial Coordinate-Operator Feedback 110
6.9 Integral Coordinate-Operator Feedback with Variable Integration Rate 118
6.10 Continuous Inertial Coordinate-Operator Feedback 124
6.11 Sur (2) Systems Under Integral Coordinate-Operator Feedback Law 128
6.12 Application of Algorithms with Inertial Coordinate-Operator Feedback to S System Control 136

7 Operator Feedback 154
7.1 (1) Systems with Integral Coordinate-Operator Feedback 160
7.2 Sp and Systems Under Imperfect Information 168
7.3 Spp (1) Systems with Inertial Coordinate-Operator Feedback 189
7.4 Quasicontinuous Control Algorithm 192
7.5 Spp (2) Systems with Integral Coordinate-Operator Feedback 206
7.6 S System Control with Algorithms 214

8 Operator-Coordinate Feedback 221
8.1 OCFB Generation Concepts 224
8.2 Suv (1) Systems with Proportional and Integral Coordinate-Operator Feedback 236
8.3 iS’ppv (1) Systems with Proportional Operator-Coordinate and Integral Coordinate-Operator Feedback 247
8.4 iSpV (1) Systems with Integral Laws of Coordinate-Operator and Operator-Coordinate Feedback 253
8.5 SppV (1) Systems with Integral Laws of Coordinate-Operator and Operator-Coordinate Feedback 258
8.6 Sppv (1) Systems with Inertial Laws of Coordinate-Operator and Operator-Coordinate Feedback 264

References
Index