control-systems

Learn how to generate smooth robot trajectories — trapezoidal velocity profiles, cubic and quintic polynomials — and how to combine feedforward and feedback to track them with minimal error on real arms and mobile robots.

Move beyond single-input PID to the state-space framework: the state vector, matrix dynamics, controllability, pole placement via state feedback, and LQR — the tool that scales to full robot arms and drones.

Master the proportional-integral-derivative controller: what each term fixes, the PID equation, integral windup, a discrete Python implementation, and a Ziegler-Nichols tuning guide for real loops.

Understand why feedback beats open-loop, how the classic closed-loop architecture works, and what the key performance metrics — rise time, overshoot, settling time, steady-state error — actually mean for a real system.