Weekly Lectures

Week 1 — Introduction to Feedback Control

Key idea: A closed-loop system uses measurement and feedback to reduce error between the desired output and the actual output.

Topics

• Open-loop vs closed-loop control
• Reference, output, error, controller, actuator, plant, sensor
• Examples: room temperature, motor speed, mobile robot velocity

Worked example A motor is commanded to rotate at 1000 rpm. The measured speed is 850 rpm. The feedback error is:

error = reference - measurement = 1000 - 850 = 150 rpm

Mini activity Draw the control loop for a line-following robot and identify the sensor, controller, actuator, and plant.

Week 2 — Mathematical Modelling of Dynamic Systems

Key idea: A physical system can be represented by differential equations and converted into a transfer function for analysis.

Topics

• First-order systems
• Second-order systems
• DC motor model
• Thermal process model

Example model For a simple first-order process:

tau dy/dt + y = K u

where tau is the time constant and K is the static gain.

Week 3 — Transfer Functions and Block Diagrams

Key idea: Transfer functions describe the input-output relationship of linear time-invariant systems in the Laplace domain.

Topics

• Laplace-domain representation
• Transfer function G(s) = Y(s)/U(s)
• Block diagram reduction
• Series, parallel, and feedback connections

Practical link Use MATLAB or Python to simulate the step response of a first-order and second-order plant.

Week 4 — Transient Response

Key idea: Transient response tells us how fast and how accurately a control system responds after a change in input.

Performance measures

• Rise time
• Peak time
• Percent overshoot
• Settling time
• Steady-state error
• Natural frequency and damping ratio

Lab link Compare an underdamped response with an overdamped response and explain which is better for a positioning system.

Week 5 — Stability and Routh-Hurwitz Criterion

Key idea: A controller is only useful if the closed-loop system remains stable.

Topics

• Poles and stability
• Characteristic equation
• Routh table
• Stability margin concept

Mini task Determine whether the polynomial s^3 + 4s^2 + 5s + 2 is stable using a Routh table.

Week 6 — Root Locus Design

Key idea: Root locus shows how closed-loop poles move as controller gain changes.

Topics

• Root locus concept
• Dominant poles
• Gain selection
• Transient performance connection

Engineering question How does increasing proportional gain affect speed of response, overshoot, and stability risk?

Week 7 — Frequency Response and Bode Plots

Key idea: Frequency response helps evaluate bandwidth, gain margin, phase margin, and robustness.

Topics

• Sinusoidal input response
• Bode magnitude and phase plots
• Bandwidth
• Gain margin and phase margin

Practical link Estimate the usable control bandwidth of a motor system before noise amplification becomes a problem.

Week 8 — PID Control

Key idea: PID control combines proportional, integral, and derivative actions to improve tracking and disturbance rejection.

Topics

• Proportional action and steady-state error
• Integral action and offset removal
• Derivative action and damping
• PID tuning methods
• Anti-windup and derivative filtering

Controller form u(t) = Kp e(t) + Ki integral(e(t)) + Kd de(t)/dt

Week 9 — Digital Control and Sampling

Key idea: Real controllers are often implemented digitally, so sampling time and discrete approximation matter.

Topics

• Sampling time
• Discrete PID
• Zero-order hold concept
• Quantisation and sensor noise
• Real-time loop structure

Pseudo-code

error = reference - measurement;
integral = integral + error * Ts;
derivative = (error - previous_error) / Ts;
u = Kp*error + Ki*integral + Kd*derivative;
previous_error = error;

Week 10 — DC Motor Speed and Position Control

Key idea: Motor control is a central application of feedback control in robotics and automation.

Topics

• PWM control
• Encoder feedback
• Speed estimation
• Position loop vs speed loop
• Servo control structure

Practical link Implement a speed controller first, then use it inside a higher-level position controller.

Week 11 — Embedded Control Implementation

Key idea: A controller must be implemented with correct timing, safe limits, sensor reading, and actuator output.

Topics

• ADC input
• Timer interrupt
• PWM output
• Saturation limits
• Debugging embedded control loops

Engineering checklist Check sampling time, sensor scaling, output saturation, and emergency stop before closing the loop.

Week 12 — Robotics Motion Control Project

Key idea: Mobile robot control combines modelling, feedback, embedded software, sensors, and system testing.

Topics

• Differential-drive robot kinematics
• Wheel speed control
• Heading control
• Trajectory tracking concept
• ROS2-based system architecture

Final activity Design a controller for one robotic or industrial automation system and present the performance results.