This textbook presents theory and practice in the context of automatic control education. It presents the relevant theory in the first eight chapters,

applying them later on to the control of several real plants. Each plant is studied following a uniform procedure: a) the plant's function

is described, b) a mathematical model is obtained, c) plant construction is explained in such a way that the reader can build his or her own plant to conduct experiments, d) experiments are conducted to determine the plant's parameters, e) a controller is designed using the theory discussed in the first eight chapters, f) practical controller implementation is performed in such a way that the reader can build the controller in practice, and g) the experimental results are presented. Moreover, the book provides a wealth of exercises and appendices reviewing the foundations of several concepts and techniques in automatic control. The control system construction proposed is based on inexpensive, easy-to-use hardware. An explicit procedure for obtaining formulas for the oscillation condition and the oscillation frequency of electronic oscillator circuits is demonstrated as well.

Prof. Dr. Victor Manuel Hernández-Guzmán is a Professor at Universidad Autonoma de Queretaro, Mexico, since 1995, where he teaches Classical and Modern (Linear and Nonlinear) Control in undergraduate and graduate academic programs. He is a researcher in the Automatic Control Systems field.

1. Introduction

1.1 An anti-aircraft gun control system

1.2 History of automatic control

1.3 Didactic prototypes

2.1 Mechanical systems

2.1.1 Translational mechanical systems

2.1.2 Rotative mechanical systems

2.2 Electrical systems

2.3.1 Electric transformer

2.3.2 Gear reducer

2.3.3 Rack and pinion

2.4 Converters

2.4.2 Electromagnet

2.5 A case of study. A DC-to-DC high-frequency series resonant power converter

2.6 Exercises

3. Ordinary linear differential equations

3.1 First order differential equation

3.1.1 Graphical study of the solution

3.1.2 Transfer function

3.3 Second order differential equation

3.3.1 Graphical study of solution

3.3.2 Transfer function

3.4 Arbitrary order differential equations

3.4.1 Real and different roots

3.4.2 Real and repeated roots

3.4.3 Complex conjugated and not repeated roots

3.4.4 Complex conjugated and repeated roots

3.4.5 Conclusions

3.5 Poles and zeros in higher-order systems

3.5.1 Pole-zero cancellation and reduced order models

3.5.2 Dominant poles and reduced order models

3.6 The case of sinusoidal excitations

3.7 The superposition principle

3.8 Controlling first and second order systems

3.8.2 Proportional position control plus velocity feedback for a DC motor

3.8.3 Proportional-derivative position control of a DC motor

3.8.4 Proportional-integral velocity control of a DC motor

3.9 Case of study. A DC-to-DC high-frequency series resonant power electronic converter

3.10 Exercises

4. Stability criteria and steady state error

4.2 Rule of signs

4.2.1 Second degree polynomials

4.2.2 First degree polynomials

4.3 Routh's stability criterion

4.4 Steady state error

4.4.1 Step desired output

4.4.2 Ramp desired output

4.5 Exercises

5. Time response-based design

5.1 Drawing the root locus diagram

5.2 Root locus-based analysis and design

5.2.1 Proportional control of position

5.2.2 Proportional-derivative (PD) control of position

5.2.4 Proportional-integral (PI) control of velocity

5.2.5 Proportional-integral-derivative (PID) control of position

5.2.6 Assigning the desired closed-loop poles

5.2.8 Control of a ball and beam system

5.2.9 Assigning the desired poles for a ball and beam system

5.3 Case of study. Additional notes on PID control of position for a permanent magnet brushed DC motor

5.4 Exercises

6. Frequency response-based design

6.1 Frequency response of some electric circuits

6.1.1 A series RC circuit: output at capacitance

6.1.3 A series RLC circuit: output at capacitance

6.1.4 A series RLC circuit: output at resistance

6.2 Relationship between frequency response and time response

6.3 Common graphical representations

6.3.1 Bode diagrams

6.3.2 Polar plots

6.4.1 Contours around poles and zeros

6.4.2 Nyquist path

6.4.3 Poles and zeros

6.4.5 Nyquist criterion. The general case

6.5 Stability margins

6.6 Relationship between frequency response and time response

6.6.1 Closed-loop frequency response and closed-loop time response

6.7 Analysis and design examples

6.7.1 Analysis of a nonminimum phase system

6.7.2 A ball and beam system

6.7.4 PD position control redesign for a DC motor

6.7.5 PID position control of a DC motor

6.7.6 PI velocity control of a DC motor

6.9 Exercises

7. The state variables approach

7.1 Definition of state variables

7.2.1 Procedure for first order state equations without input

7.2.2 General procedure for arbitrary order state equations with arbitrary number of inputs

7.3 Some results from linear algebra

7.5 Stability of a dynamical equation

7.6 Controllability and observability

7.6.1 Controllability

7.6.2 Observability

7.8 A realization of a transfer function

7.9 Equivalent dynamical equations

7.10 State feedback control

7.11 State observers

7.13 Case of study. The inertial wheel pendulum

7.13.1 Obtaining forms in (7.57)

7.13.2 State feedback control

7.14 Exercises

8. Advanced topics in control

8.1 Str…