Classical Control Systems Design

Objectives and Syllabus

Establishes the theoretical basis of control system design and analysis. Topics covered are - system characteristics; use of Laplace transforms, transfer functions, first order systems, leads, lags & time delays, second order systems & damping, response time, block diagram algebra, open & closed loop transfer functions, final value theorem, higher order system approximation, characteristic equation, stability: frequency response techniques: Bode diagram and stability criteria; gain & phase margin, polar plots, open & closed loop responses: root locus; Evans rules, pole zero cancellation, design of controllers, lead-lag compensators: non-linear systems; types of non-linearity, describing functions, phase plane techniques, limit cycles, gain scheduling: signal processing; amplitude characterisation, probability distributions, auto & cross-correlation techniques, frequency characterisation, Fourier transforms, spectral density.

Practical work consists of exercises involving these techniques using the MATLAB and SIMULINK packages.

Aims

To provide a thorough grounding in the analysis and design of control systems using linear methods, especially by means of root locus and frequency response.

Objectives

• To become familiar with the terminology and nomenclature of open and closed loop systems. 
• To develop an understanding of the transfer function relationships between input and output signals of single-input single-output systems. 
• To gain experience of using block diagram algebra to obtain open and closed loop transfer functions. 
• To develop a deep understanding of the significance of the characteristic equation in terms of poles and zeros in the s plane. 
• To be able to relate closed loop performance requirements to the design of negative feedback control systems. 
• To gain experience of using the root locus and frequency response methods for analysing and designing control systems.

Phasing

A prerequisite to this module is the Mathematics and Matlab (CME 8360) module.

Study Modes

This module is of one week's full-time intensive study consisting of a variety of formal lectures, informal tutorials for problem solving, and structured computer based laboratory work.  It is followed by an assignment to be carried out in the student’s own time.

Coursework

The time allocation for practical work provides for PC based activity using the Matlab and Simulink packages, including use of the Control System Toolbox.  Exercises are carried out on the analysis and design of simple control systems.  These are structured to reinforce the syllabus content on block diagram algebra, root locus and frequency response techniques.

Recommended Texts

• Dabney J B & Harman T L,  Mastering Simulink,  Prentice Hall,  2004. 
• Dutton K, Thompson S & Barraclough B,  The Art of Control Engineering,  Addison Wesley,  1997. 
• Hanselman D & Littlefield B,  Mastering Matlab,  Prentice Hall,  2005. 
• Love J,  Process Automation Handbook,  Springer,  2007
• Roffel B & Betlem B,  Process Dynamics and Control: Modelling for Control and Prediction,  Wiley,  2006. 
• Seborg D, Edgar T, Mellichamp, D and Doyle F,  Process Dynamics and Control,  3rd Edition, Wiley,  2011. 
• Wilkie, J, Johnson M and Katebi, R,  Control Engineering: An Introductory Course,  McMillan (Palgrave),  2002.

Topics Included

System characteristics:  Revision of Laplace transforms and transfer functions.  Block diagram algebra.  Open and closed loop transfer functions.  Steady state response and offset.  Use of final value theorem.  Characteristic equation.  The s-plane.  Concept of poles and zeroes.  Significance of roots.  Form of response and nature of stability.  Manipulation of transfer function equations and application to control problems.  Routh test.  Second order systems: damping factor and natural frequency.  Critical damping.  Underdamped systems: response time, overshoot, decay ratio, etc.  Higher order systems: approximation by lag plus delay.

Linear systems design:  Introduction to frequency response techniques.  Concepts of attenuation and phase shift.  Bode diagrams.  Bode stability criterion.  Gain and phase margins.  Polar plots.  Use of Nichols chart.  Use of Nyquist stability criterion.  Relationship between open-loop and closed-loop responses.  Real-time and frequency dimensions of s-plane.  Significance of poles and zeros.  Evan's rules.  Construction and interpretation of root locus.  Equivalence of dominant roots.  Effect of time delay on system response and stability.  Design of lead-lag compensators and PID controllers.  Pole zero placement and cancellation.