## Feedback Control Theory for EngineersTextbooks in the field of control engineering have, in the main, been written for electrical engineers and the standard of the mathematics used has been relatively high. The purpose of this work is to provide a course of study in elementary control theory which is self-contained and suitable for students of all branches of engineering and of applied physics. The book assumes that the student has a knowledge of mathematics of A-level or 0-2 level standard only. All other necessary pure and applied mathematics is covered for reference purposes in chapters 2-6. As a students' textbook it contains many fully worked numerical examples and sets of examples are provided at the end of all chapters except the first. The answers to these examples are given at the end of the book. The book covers the majority of the control theory likely to be encountered on H. N. C. , H. N. D. and degree courses in electrical, mechanical, chemical and production engineering and in applied physics. It will also provide a primer in specialist courses in instru mentation and control engineering at undergraduate and post graduate level. Furthermore, it covers much of the control theory encountered in the graduateship examinations of the professional institutions, for example I. E. E. Part III (Advanced Electrical Engineer ing and Instrumentation and Control), I. E. R. E. Part 5 (Control Engineering) and the new c. E. I. Part 2 (Mechanics of Machines and Systems and Control Engineering). |

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### Contents

1 | |

14 | |

Chapter 3 | 34 |

Chapter 4 | 44 |

Simple Electrodynamics 4 5 Abbreviations | 63 |

Chapter 6 | 84 |

Chapter 7 | 106 |

Chapter 8 | 157 |

Chapter 10 | 239 |

the Nyquist Diagram 10 4 The Nyquist Stability Criterion | 250 |

Chapter 11 | 278 |

Control Systems 11 4 The Design of Cascaded Compensating | 300 |

3 Inverse Nyquist Diagrams 12 4 Inverse | 306 |

Elements on Inverse Loci 12 6 Design of Parallel Compensated | 327 |

Chapter 13 | 329 |

Bode Diagram 13 4 Design of Compensating Devices using Bode | 361 |

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### Common terms and phrases

acceleration feedback actuator angular frequency angular position angular resonant frequency angular velocity Argand diagram armature asymptotic axis Bode diagram chapter circuit closed-loop frequency response compensated system complex number control engineering D-form d.c. motor damping dB/decade Determine device differential equation driving function electrical electronic amplifier error constant error detector example exponential lags field winding forward path frequency locus frequency response frictional torque given gyroscope H(ja handwheel Hence hydraulic inertia integral inverse Laplace transform log-modulus characteristic loop M-circle magnitude mechanical method Nichols chart Nyquist diagram Nyquist stability criterion open-loop transfer function output element parallel compensation phase angle phase margin phase-lag phase-lead network pneumatic potentiometer pressure proportional rad/s radian resistance rotation servomechanism shaft shown in Fig simple sine wave sinusoidal specification speed stable on closed transient response type 1 system uncompensated unity unstable valve vector velocity feedback velocity lag viscous frictional voltage zero