Control Systems ELEN90055
Lecturer: Prof.
Dept. Electrical and Electronic Engineering
Partly based on material by Profs D. Nesic and M. Cantoni
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3 lectures/week x 12 weeks in , Medical Building • Mon & Wed 12-1pm, Thurs 10-11am (Melbourne time)
Lectures will also be live-streamed over zoom, with recordings made available afterwards (see Zoom tab in subject LMS website)
When possible, every alternate Thurs lecture slot will be used as a tutorial-style class, in which I’ll work through selected problems from a worksheet.
Lecturerconsultation:
Week 1 only: Fri 11am-12pm, room 214, level 2, EEE
Weeks 2-12: Monday 2.45 – 3.45pm , room 214, level 2, EEE
Other Resources on Subject Website
Worksheets – will be made available a few days before each tutorial-style lecture. Solutions will be released after each tutorial.
Supplementary Notes and Problem Sets by M. Cantoni – useful resources that you should read and attempt on your own
I’ll loosely follow Control System Design by Goodwin, Graebe and Salgado ( )
Other texts I’ll refer to:
• Modern Control Engineering by Ogata
( , 5th ed)
• Feedback Control of Dynamic Systems by Franklin, Powell & Emami‐Naeini (Pearson)
Workshop Classes
MATLAB/Simulink-based. Classes commence Fri Aug 5.
There are currently 9 workshop slots/week. Enrol in one fixed slot/week via the student system – some may be full and not accepting new enrolments.
7 of the workshops will be conducted in-person in EDS8, while 2 are online-only, via zoom.
Email me if all the workshop classes currently listed as available clash with other core subjects you’re doing.
Assessment
Mid-term written test (around week 7) – 10%
Final written exam (3 hours at end of semester; hurdle) –
Two workshop reports each worth 10%, including up to 2% in-class individual assessment each.
• The first report is due in Week 10, the second due date will be advised.
• Reports to be written in groups of max. 2, with others in the same class. Don’t miss your first few classes, which are when most groups are formed. Your demonstrator can help you form a group if you don’t know anyone else in the class.
Introduction to Control
Dynamical Systems Revisited
Any colelction of things that can change with time is a dynamical system
Defined by
• Variables that can change with time, i.e. signals. E.g. inputs (u) that can be freely adjusted, external disturbances (d) or references (r); outputs (y) that are measured and/or have special relevance for the application.
• A law or rule that describes how these signals interact and evolve over time for any input (and initial condition). E.g. differential equations, difference equations.
A few examples
https://msd.unimelb.edu.au/research/projects/completed/building-with-drones
https://upload.wikimedia.org/wikipedia/commons/f/fb/Signal_transduction_pathways.png
http://www.enhar.com.au/templates/images/wind_turbine.jpg
Modelling Dynamical Systems
Continuous-time signal
Continuous-time signal
Laplace transform
Fourier transform
Differential eq.
Laplace transform
Transfer function
Fourier transform
Frequency response
Control Systems
In a control system, an input signal u is chosen specially to try to make output signal y behave in a specified way – e.g. to quickly approach and remain close to close to some desired set-point.
If there are no disturbances and the input-output dynamics are “nice” (e.g. static or stably invertible), easy: just invert to find u that yields the desired y.
• But the real world has unmeasured disturbances, parameter deviations, or unstable/oscillatory dynamics.
Feedback Control. Measure y, then design a feedback controller that changes u to automatically compensate for these issues
Prevalence of control systems
Control systems are ubiquitous in our world
An enabling technology: essential for the reliable operation of most engineered and natural systems.
The success of control means it is often invisible to non-experts…till something goes wrong!
Transportation systems, cars, planes, drones, agriculture, irrigation, food processing,Household appliances, HVAC, TVs, phones, internet, telecommunication systems, manufacturing industry, chemical processes, digital technology, electrical power systems, medical technology…
Control and the Industrial Revolution
Industrial revolution was largely driven by the mass production, e.g.
in textiles industry.
A control system was
at the heart of machines that fuelled the industrial revolution.
Taken from http://boivieapedia.pbworks.com/f/1270415464/spinning_frame.gif
Watt’s fly-ball governor
1778, Watt based his design on similar governors in windmills.
1868, Maxwell analysed it and posed a control problem for Adams Prize.
1877, E.J. Routh won the Adams Prize. See animation on http://www.mekanizmalar.com/flyball_governor.html
Room temperature control
Desired temperature Actual temperature
Outside temperature
Controller
Components of Control System
Plant (room) – given dynamical system we want to control;
Sensor (thermometer) – measurement device
Actuator (heater) – device that enables us to affect the sensor
Note: if the sensor and actuator have their own dynamics, these are often combined with the plant to form a larger virtual plant
Controller – device that takes sensor measurements and sends control inputs to the actuator
Main Signals in a Control System
Output (actual temperature) – physical variable we are interested in controlling
Input (voltage signal to heater) – signal produced by controller to be fed to the actuator
Disturbance (outside temperature) – physical variable that affects the system dynamics; can’t be controlled
Noise – high frequency disturbances
Block diagram of feedback control
Signals (physical variables) represented by arrows Systems (devices) represented by boxes
NOTE THE FEEDBACK CONNECTION!
Tentative Schedule: weeks 1 – 4
Fundamental tools for open-loop dynamical systems:
Differential equation models; linearisation; step response; convolution; transfer functions; time-domain effects of poles and zeros; input-output stability; frequency response; Bode plots
see Chapters 3 and 4 of GGS
Tentative Schedule: weeks 5 – 9
Stability and performance of LTI feedback control systems
Closed-loop stability; closed-loop sensitivity functions; root-locus plots; Nyquist plots; relative stability; robustness to model uncertainty; fundamental limitations; the internal model principle; feedforward compensation
see Chapters 5, 8 and 10 of GGS
Tentative Schedule: weeks 10-12 Designing feedback controllers to meet
stability and performance specifications:
• Proportional (P), integral (I), lag and lead compensation; PID controllers and empirical tuning rules; classical loop-shaping; the polynomial approach to pole-placement;
see Chapters 6 and 7 of GGS
Time permitting: techniques for dealing with actuator constraints (Chapter 11 of GGS)
Conclusions
Control systems are an enabling technology that are ubiquitous but hidden in the engineered and natural world
An important feature of control systems is feedback
Block diagrams are a useful abstraction for understanding the operation of control systems
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