Control System Fundamentals

Feedback, models and time response. Open and closed loops, the Laplace transform, transfer functions and block diagrams, modelling physical systems, first-order-plus-dead-time process models, and time-domain specifications with steady-state error.

• Open Loop — An open-loop system acts on a command without measuring the result. Learn how it works, its gain and calibration, why disturbances and parameter changes cause errors, and when open loop is the right choice.
• Closed Loop — Closed-loop (feedback) control measures the output and corrects the error. Learn the feedback equation, loop gain, sensitivity, disturbance rejection, steady-state error, and the stability trade-off feedback introduces.
• Laplace Transform — The Laplace transform turns differential equations into algebra. Learn the definition and region of convergence, common transform pairs, properties (derivative, integral, shift), transfer functions, poles and zeros, stability from pole locations, first- and second-order responses (ω_n, ζ, overshoot), and initial/final value theorems.
• Transfer Functions — Transfer functions describe a linear system's input–output behaviour in the Laplace domain. Learn how to derive them, poles and zeros, first- and second-order systems, time-domain specs and the final-value theorem.
• Block Diagrams — Block diagrams show how signals flow through a system. Learn series, parallel and feedback reduction rules, moving summing points and take-off points, and Mason's gain formula for complex signal-flow graphs.
• Modelling Physical Systems for Control — Controllers are designed from models. Learn how to write differential equations for electrical, mechanical, thermal, fluid and process systems, the analogies between them, linearisation around an operating point, transfer functions, first-order-plus-dead-time (FOPDT) process models, and system identification from a step test — with an Euler simulation of a draining tank.
• Time-Domain Response & Steady-State Error — How a control loop behaves in time. Learn standard test inputs, first- and second-order responses, poles and their meaning, damping ratio and natural frequency, rise time, peak time, overshoot and settling time, dominant poles, system type and error constants (Kp, Kv, Ka), and steady-state error — with Python formulas for every specification.