Automatic Control with Experiments

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.

Auteur

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.

Prof. Dr. Ramón Silva-Ortigoza has been a Researcher at the Department of Mechatronics, CIDETEC-IPN, since 2006, being the author of several books in English and Spanish. His research interests include mechatronic control systems, mobile robotics, control in power electronics, and development of educational technology.

Contenu

1. Introduction

   1.1 An anti-aircraft gun control system

   1.2 History of automatic control

   1.3 Didactic prototypes

2. Physical system modeling

   2.1 Mechanical systems

   2.1.1 Translational mechanical systems

   2.1.2 Rotative mechanical systems

   2.2 Electrical systems 2.3 Transformers

   2.3.1 Electric transformer

   2.3.2 Gear reducer

   2.3.3 Rack and pinion

   2.4 Converters 2.4.1 Armature of a permanent magnet brushed DC motor

   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 3.2 An integrator

   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 3.5.3 Approximating transitory response of higher-order systems

   3.6 The case of sinusoidal excitations

   3.7 The superposition principle

   3.8 Controlling first and second order systems 3.8.1 Proportional control of velocity in a DC motor

   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 3.8.5 Proportional, PI and PID control of first order systems

   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 4.1 Block diagrams

   4.2 Rule of signs

   4.2.1 Second degree polynomials

   4.2.2 First degree polynomials 4.2.3 Polynomials with degree greater than or equal to 3

   4.3 Routh's stability criterion

   4.4 Steady state error

   4.4.1 Step desired output

   4.4.2 Ramp desired output 4.4.3 Parabola desired output

   4.5 Exercises

5. Time response-based design

   5.1 Drawing the root locus diagram 5.1.1 Rules to draw 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 5.2.3 Position control using a lead-compensator

   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 5.2.7 Proportional-integral-derivative (PID) control of an unstable plant

   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 6.1.2 A series RC circuit: output at resistance

   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 6.2.1 Relationship between time response and frequency response

   6.3 Common graphical representations

   6.3.1 Bode diagrams

   6.3.2 Polar plots 6.4 Nyquist stability criterion

   6.4.1 Contours around poles and zeros

   6.4.2 Nyquist path

   6.4.3 Poles and zeros 6.4.4 Nyquist criterion. A special case

   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 6.6.2 Open-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 6.7.3 PD position control of a DC motor

   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 6.8 Case of study. PID control of an unstable plant

   6.9 Exercises

7. The state variables approach

   7.1 Definition of state variables 7.2 Approximate linearization of nonlinear state equations

   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 7.4 Solution of a linear time invariant dynamical equation

   7.5 Stability of a dynamical equation

   7.6 Controllability and observability

   7.6.1 Controllability

   7.6.2 Observability 7.7 Transfer function of a dynamical equation

   7.8 A realization of a transfer function

   7.9 Equivalent dynamical equations

   7.10 State feedback control

   7.11 State observers 7.12 The separation principle

   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 Structural limitations in classical control

   8.1.1 Open-loop poles at origin

   8.1.2 Open-loop poles and zeros located out of origin

   8.2 Differential flatness

   8.3 Describing function analysis

   8.3.1 The dead zone nonlinearity [3], [4]

   8.3.2 An application example 8.3.3 The saturation nonlinearity [3], [4]

   8.3.4 An application example

   8.4 The sensitivity function and some limitations when controlling unstable plants

9. Feedback electronic circuits 9.1 Reducing effects of nonlinearities in electronic circuits

   9.1.1 Reducing distortion in amplifiers

   9.1.2 Dead zone reduction in amplifiers

   9.2 …