One-Year Masters in Control Systems – Taught Courses Designation

The norm in most of the West is for the 24-month master of science degree, the United kingdom being the main exception. It is reasonable to assume that a longer course would provide avenues for more practice and to gain more in-depth knowledge of a field, experience and breadth. However, if we can sufficiently assess the basic minimum required by target employers (including universities recruiting PhD candidates), then we can better judge the sufficiency in terms of length, and content, of what is/should be taught. Every programme must have target industries for them to be relevant to the students and to society.

A well structured one-year programme should provide sufficiently for the masters degree in control systems engineering. For it to work, the one-year degree becomes necessarily more narrowly focused (industry, controller design methods, system class etc), and more intensive in order to provide sufficient experience for the graduates to stand in industry or proceed to further studies in academia.

We assume, for this note, that most of the employers would be non-academic, and these would likely be more into industrial, manufacturing, and process control systems than other application areas or industries (e.g. medical, military, vehicle systems)—in most parts of the globe. A shorter programme may lead it to focus on a particular industry, or deal mainly with the core essentials required for broad application if the programme is largely methodology focused. An industry focused programme, e.g., a degree titled ‘master of science in process control and industrial automation’ may relieve time pressures, if any. The more challenging type of programme in this light would be the methodology-oriented ones, as they would seek to produce more versatile controls graduates.

The Controls Curriculum Survey (CCS) report, November 5, 2009, by J. A. Cook and T. Samad, produced what amounts to a core syllabus for controls graduates. It was an informal survey, and respondents came from a representative variety of industries. The CCS report was obtained from: http://www.ieeecss.org/sites/ieeecss.org/files/documents/CSSSurvey07AugustData_v3.pdf (Linked confirmed 12 Mar. 2014). A first impression is that the general syllabus specified can be adequately covered in a 12-month programme.

A conclusion from the CCS report could be to de-emphasize, or offer only essential treatment (if any) of courses marked as ‘not required’ by more than 30 percent of respondents. These include: H-infinity and mu-analysis, and bond-graph models among others. Information like this may be helpful in determining the focus on selected topics for syllabi.

This paper would produce, influenced by the CCS, course designations, selectable topics for syllabi and include some recommended texts from which syllabi can be drawn for a methodology-oriented 12-month masters degree in control systems engineering. We first cover core course designation, and then we move on to some suggestions for syllabi (neither regarded as complete, absolute or exhaustive). A sample implementation (timetable) using the course scheduling framework described in https://iogbeide.com/other-notes/a-framework-for-course-scheduling/ will be presented in a later document.

Course Designation

Controllers are designed for models of systems. The control engineer may derive the models or get it from a domain expert. Either way, an understanding of mathematical and data-based modelling, and very importantly, model reduction techniques is necessary to facilitate the design. Lets therefore design two modelling courses: mathematical modelling and model reduction, and data-based modelling and control. The second modelling course is given a control aspect because it has good integration with discrete-time, self-tuning control, and machine learning based controller synthesis.

Control methods and design paradigms are applied to systems for the achievement of control objectives. The common classification of systems is: linear and nonlinear. We thus design two courses. First is ‘control of linear systems,’ and then, ‘control of nonlinear systems,’ providing holistic treatments of the two classes.

The extension of model predictive control (MPC) from applications in process plants to other areas like automotive and power systems makes it a very relevant topic for now and the near future. We believe a broad treatment transcending process control will be useful knowledge for the student. Dealing with fast, hybrid, network and nonlinear systems may thus be regarded as useful content for such a course.

Optimisation is at the core of MPC and would need be treated in some detail, along with topics in optimal control since the performance requirement of ‘optimality’ given considered constraint is often desired for real systems. We thus name a course, ‘optimisation in control,’ covering these topics and perhaps a little more.

Finally, the CCS emphasised the importance of students being able to implement controllers. An implementation oriented course is therefore necessary to build core skills in this area.

The six essential courses identified for the programme are:

  • Mathematical modelling and model reduction

  • Data-based modelling and control

  • Control of linear systems

  • Control of nonlinear systems

  • Optimisation in control

  • Control systems implementation

Process control and industrial automation may be added to the above list as mandatory given the general prevalence of process control related occupations. Other areas that may be of interest (and offered as options) include network and distributed systems control, robotics and autonomous systems, Fault-detection and fault-tolerant control, biologically inspired control (fuzzy, neural networks) etc. There may of course be overlaps in coverage/content.

Course Areas/Topics for Coverage

Some suggested areas/topics for coverage, comments, and/or recommended books for syllabi/curricula.

Mathematical modelling and model reduction:- Deriving linear and nonlinear, continuous and discrete-time models; hybrid systems and finite state machines; model validation and reduction, and analyses/control-oriented models. Emphasis on model reduction, control-oriented models.

Books for reference may include:

K. J. Astrom, R. M. Murray, “Feedback Systems,” Princeton University Press, 2008.

Data-based modelling and control in discrete time:- Discrete-time control, system identification, parameter estimation, machine learning techniques for modelling and control. Emphasis on intelligent use of application software for modelling (Matlab, Octave, Scilab, KNIME, Rapidminer) and discrete controller design.

Books for reference may include:

R. Johansson, “System Modelling and identification,” Prentice Hall, 1993.

Control of linear systems:- Modelling primer and system response/analysis; PID design, tuning, implementation, and integrator wind-up; nonlinear control of linear systems; multi-loop and multivariable control; state feedback and output feedback, and feed-forward and cascade control; controller structures and optimal (introductory), robust, and adaptive control.

Books for reference may include:

T. Glad and L. Ljung, “Control Theory – Multivariable and Nonlinear Methods,” Taylor and Francis, 2000.

G. C. Goodwin, S. F. Graebe, M. E. Salgado, “Control System Design,” Prentice Hall, 2001.

K. J. Astrom, R. M. Murray, “Feedback Systems,” Princeton University Press, 2008.

D. E. Seborg et al, “Process Dynamics and Control,” Wiley, 2011.

S. H. Zak, “Systems and Control,” Oxford University Press, 2002.

Control of nonlinear systems:- Lyapunov, input-output stability, and LaSalle’s invariance principle; backstepping, discontinuous dynamic systems and sliding mode control; Linearisation of nonlinear systems and feedback linearisation; dissipative systems and passitivity-based control; optimal, robust and adaptive nonlinear control; nonlinear observers, output regulation and disturbance rejection; switched, hybrid systems, and networked control systems.

Books for reference may include:

H. Marquez, “Nonliner Control Systems: Analysis and Design,” Wiley-Interscience, 2003.

Z. Ding, “Nonlinear and Adaptive Control Systems,” TheIET, 2013

S. S. Sastry, “Nonlinear Systems: Analysis, Stability, and Control,” Springer Verlag, 1999.

Optimisation in control:- Optimal control and model-predictive control of linear, nonlinear and hybrid systems.

Books for reference may include:

R. M. Murray, “Optimization-Based Control,” CALTECH, Draft v2.1a, 2010.

R. Weber, “Optimization and Control,” 2012.

F. Borrelli, A. Bemporad, M. Morari, “Predictive Control – for Linear and Hybrid Systems,” 2012.

L. C. Evans, “An Introduction to Mathematical Optimal Control Theory,” Available: math.berkeley.edu/~evans/control.course.pdf, Version 0.2.

See also Glad, Goodwin and Zak.

Control systems specification and implementation:- Requirements analysis and specification; real-time systems, embedded systems and programmable logic controllers; hardware-in-loop and rapid prototyping; sensing, actuation, and interfacing; industrial control networks, SCADA and DCS; issues in digital implementation and hybrid automata.

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