Engineering and the Environment, University of Southampton

Knowledge and understanding
Having successfully completed the module, you will be able to demonstrate knowledge and understanding of:

• The implications of using feedback on accuracy and stability of a control system.
• Classical control actions and the consequences for accuracy, speed of response and stability.
• The construction and operation of a d.c. servomechanism for position and speed control.
• Block diagrams for representation of system dynamics and simple algebraic manipulations for block diagram reduction.
• Dynamic modelling of engineering system elements and the analogies between mechanical, electrical, fluid and thermal systems.
• Transfer function representation of system dynamics.
• State variable representation of system dynamics and the relationship with transfer functions.
• Poles and zeros and the relationship between system poles, transient response and stability.
• Closed loop system stability assessment using the Routh-Hurwitz technique.
• The root locus technique for predicting dynamic performance of closed loop systems.
• Frequency domain analysis of system dynamics using polar and Bode representations.
• Closed loop system stability and relative stability prediction using the frequency domain.

Cognitive (thinking) skills
Having successfully completed the module, you will be able to:

• Read, understand and interpret the literature relating to classical control system design.
• Recognise and select appropriate techniques for the modelling and analysis of classical, closed loop control systems.

Practical, subject specific skills
Having successfully completed the module, you will be able to:

• Select appropriate control actions for classical control systems.
• Design an experiment to investigate the dynamic performance of a d.c. servomechanism.

Key transferable skills
Having successfully completed the module, you will be better able to:

• Carry out experimental frequency analysis of dynamic systems.
• Plot system dynamics in the form of root loci, polar and Bode diagrams.

The aims of this module are to

• To introduce students to the principles of feedback control.
• To demonstrate and investigate its application to servomechanisms.

• To introduce the student to the formal basis for the analysis and design of dynamic systems which include feedback.
• To revise and extend the modelling of dynamic systems elements and to draw analogies between mechanical, electrical, fluid and thermal systems.
• To describe time and frequency domain methods of dynamic system analysis.
• To give the student direct experience of a d.c. servomechanism.

Introduction

• Brief history of the development of control
• Definitions and terminology
• Open & closed loop control<

• Construction & applications
• Block diagram

• On-off control
• P, I, D & PID control
• Velocity feedback
• Feed-forward

Block diagram algebra

Mathematical modelling of systems

• Through & across variables
• Models of system elements
• Analogous circuits

State variable representation of system dynamics

• Matrix representation of differential equations
• Representation of linear system dynamics
• System states & choice of state variables
• Representation of linear control systems
• State variable diagrams & simulation

Transient response of systems

• Poles & zeros and the s-plane
• Pole position & relationship with transient response
• Time response

Prediction of system performance

• Routh-Hurwitz stability analysis
• Root-Locus technique & construction of root-loci

Frequency response of systems

• Polar diagram representation
• Bode diagrams
• Stability and relative stability (gain & phase margins)

Teaching methods include

• Two lectures per week with occasional demonstrations and video material.
• A laboratory investigation of a d.c. servomechanism. Thiscomprises an introduction to the equipment and the investigation to be carried out, the main dynamic testing, a final session to discuss the results and relate to the servomechanism design.

• Hands-on laboratory work in small groups where servomechanism dynamics are investigated using a range of associated measurement instrumentation.
• Seven example sheets are used to reinforce each major topic of the course and solution sheets are provided as formative feedback, together with discussion in lecture periods if necessary.
• Past examination papers for the previous two years are provided, together with worked solutions, for consolidation of the complete course and as an indicator of the type of questions to be expected in the final assessment.

Secondary text

Feedback Control of Dynamic Systems
3rd edition, 1994, Franklin, G.F.br>Powell, J.D.
Emami-Naeini, A., Addison-Wesley

Control Systems Engineering
2nd edition, 1995, Nise, N.S., Addison-Wesley

Modern Control Engineering
3rd edition, 1997, Ogata, K., Prentice Hall Int.

Automatic Control Systems
6th edition, 1991, Kuo, B.C., Prentice Hall Int.

System Modelling and Control
3rd editiion, 1993, Schwarzenback, J.
Gill, K.F., Edward Arnold