Digital & Modern Control

Discrete time, state space, estimation and MPC. Controllers that run on computers: the Z-transform and digital filters, state-space models, state feedback and observers, LQR, Kalman filtering and model predictive control.

• Z-Transform — The Z-transform is the Laplace transform for discrete-time systems. Learn the definition and ROC, common pairs, the delay property z⁻¹, difference equations and transfer functions H(z), poles and zeros in the z-plane, stability (|p| < 1), frequency response on the unit circle, and mapping s to z (bilinear transform).
• Digital Filters & DSP — Digital filters process sampled signals in software or hardware. Learn FIR vs IIR, moving-average filters, windowed-sinc FIR design, linear phase and group delay, IIR biquads, filter order estimation, fixed-point implementation, DSP processors and MAC operations — with a Python FIR design.
• 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.
• State Feedback, Observers & LQR — Modern control in state space. Learn controllability and observability, pole placement by state feedback (and Ackermann's formula), reference tracking with N̄ or integral action, state observers (Luenberger) and the separation principle, and optimal LQR design with the Q/R trade-off — with a DC-motor servo designed and simulated in Python.
• Kalman Filtering & Model Predictive Control — Estimation and optimisation at the top of the control pyramid. Learn the Kalman filter (predict/update, gain, covariance, Q and R tuning), sensor fusion and the extended Kalman filter, and model predictive control (prediction horizon, cost function, constraints, receding horizon, offset-free MPC) — with a running Kalman filter and a constrained MPC in plain Python.