Control Systems

I taught Control Systems (NEE-503) in the Department of Electrical and Electronics Engineering at Pranveer Singh Institute of Technology (PSIT), Kanpur, an institution affiliated with Dr. A.P.J. Abdul Kalam Technical University (AKTU), Uttar Pradesh, India. I also prepared the detailed course plan.

The course introduced undergraduate engineering students to the modelling, analysis, and design of feedback control systems. Its emphasis was both conceptual and numerical: students learned the physical meaning of feedback and stability, then applied analytical methods to representative electrical, mechanical, and electromechanical systems.

Course information

Learning outcomes

By the end of the course, students were expected to be able to:

• distinguish between open-loop and closed-loop systems and explain the role of negative feedback;
• derive transfer-function models for physical systems and simplify block diagrams and signal-flow graphs;
• analyse first- and second-order system responses using standard test signals and performance specifications;
• calculate steady-state error and interpret static error constants;
• assess stability using the Routh-Hurwitz criterion, root-locus construction, and frequency-response methods;
• interpret polar, inverse-polar, Nyquist, and Bode plots, including gain and phase margins;
• explain the function of servomotors, synchros, and stepper motors in control systems;
• design and compare lead, lag, and lead-lag compensation in the time and frequency domains; and
• convert between transfer-function and state-space representations and test controllability and observability.

Syllabus

Unit I — Foundations of control systems

• Open-loop and closed-loop control
• Servomechanisms and physical examples
• Transfer functions and modelling of physical systems
• Block-diagram algebra and reduction
• Signal-flow graphs and Mason’s gain formula
• Sensitivity, parameter variation, disturbance rejection, and negative feedback

Unit II — Time-response analysis

• Standard test signals
• First- and second-order system response
• Transient- and steady-state specifications
• Steady-state errors and error constants
• Proportional, integral, and derivative control concepts
• PI, PD, and PID compensation
• Higher-order approximations and performance indices

Unit III — Components, stability, and root locus

• AC servomotors, synchros, and stepper motors
• Stability concepts and necessary conditions
• Routh-Hurwitz criterion and special cases
• Root-locus rules and construction
• Effects of adding poles and zeros
• Angles of arrival and departure and breakaway points

Unit IV — Frequency-response analysis

• Relationship between time- and frequency-domain responses
• Polar and inverse-polar plots
• Nyquist plots and the Nyquist stability criterion
• Bode magnitude and phase plots
• Gain margin, phase margin, and relative stability
• Constant-M and constant-N circles

Unit V — Compensator design and state-space methods

• The control-system design problem
• Lead, lag, and lead-lag networks
• Compensation using root-locus and Bode-plot methods
• State variables, state equations, and output equations
• Conversion between transfer-function and state-space models
• Controllability and observability

Teaching approach

The lecture plan comprised 60 topic-focused sessions supported by tutorials. The sequence moved from physical intuition and mathematical modelling to analysis and design:

1. Model the system using transfer functions, block diagrams, and signal-flow graphs.
2. Characterise performance through transient response, steady-state error, damping, and pole locations.
3. Determine stability using algebraic, root-locus, and frequency-domain criteria.
4. Improve performance using controllers and compensating networks.
5. Generalise the model through state-space representation, controllability, and observability.

Worked numerical problems were integrated throughout the course, including block-diagram reduction, Mason’s gain formula, Routh-Hurwitz stability tests, root-locus construction, Bode and Nyquist analysis, margin calculations, compensator design, and state-space conversion.

Detailed lecture sequence

Representative applications

The course connected theory with practical engineering examples such as:

• servomechanisms and position-control systems;
• motor speed and motion control;
• industrial automation and process control;
• electrical and electromechanical system modelling; and
• feedback-based disturbance rejection and robustness.

Core reading

1. B. S. Manke, Linear Control Systems, 11th ed., Khanna Publishers, 2012.
2. Ashfaq Husain and Haroon Ashfaq, Control Systems, 1st ed., Dhanpat Rai & Co., 2011.
3. I. J. Nagrath and M. Gopal, Control Systems Engineering, New Age International.
4. Katsuhiko Ogata, Modern Control Engineering, Prentice Hall of India.
5. Benjamin C. Kuo and Farid Golnaraghi, Automatic Control Systems, Wiley India.

Teaching perspective

Teaching control theory shaped how I explain complex biological systems today. Both fields require learners to move between components, interactions, system-level behaviour, perturbations, and measurable outputs. This systems perspective now informs my teaching and research interests in genetics, genomics, biological networks, and AI-enabled biomedical discovery.