Control Systems

Making machines do what you want — reliably, quickly and stably. The mathematics of feedback. Open and closed loops, transfer functions and block diagrams, stability, root locus, Bode and Nyquist frequency response, PID tuning and modern state-space design — the tools behind drives, robots, grids and autopilots.

• 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.
• 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.
• Stability — A stable system returns to equilibrium after a disturbance. Learn BIBO stability, pole locations, the Routh–Hurwitz criterion, marginal stability and critical gain, and relative stability measures.
• Root Locus — The root locus plots how closed-loop poles move as a gain varies. Learn the sketching rules, asymptotes, breakaway points and jω crossings, and how to pick a gain for a desired damping ratio.
• Bode Plot — Bode plots show gain (dB) and phase versus log frequency. Learn asymptotic sketching, corner frequencies, bandwidth, gain and phase margins from the open-loop plot, and loop-shaping design.
• Nyquist — The Nyquist criterion determines closed-loop stability from the open-loop frequency response — even for open-loop unstable plants and systems with time delay. Learn the polar plot, encirclements of −1, and margins.
• PID — The PID controller is used in over 90 % of industrial loops. Learn what P, I and D each do, tuning with Ziegler–Nichols and practical rules, anti-windup, derivative filtering and a digital implementation.
• State Space — State-space models describe systems with first-order matrix equations. Learn states, the A, B, C, D matrices, conversion to transfer functions, eigenvalues and stability, controllability, observability, pole placement, observers and LQR.