Control Systems
Feedback is the idea that measuring the output and subtracting it from the input can beat any amount of careful calibration. These topics run the loop and show the error shrink, oscillate, or run away.
Start from the beginning →8 topics you can watch now, 14 still to come.
Foundations
What feedback buys, and what it costs.
- Open Loop vs Closed LoopStart here. Heat a room two ways, then change the weather halfway through and see which controller notices.
- Transfer FunctionsLaplace turns a differential equation into algebra, cascades into products, and stability into the sign of a pole.
- Modelling electrical and mechanical systems
- Signal flow graphs and Mason's rule
Time response
How the output gets to where it was told to go.
- Second-Order ResponseOne parameter reshapes the whole response — overdamped, critical, underdamped, undamped — on the same plot.
- Steady-State Error and System TypeWhy a proportional controller can never quite arrive, and why counting integrators answers the whole question.
- First-order response
- Time-domain specifications in detail
Stability
Whether the loop settles at all, decided before it is built.
- The Routh-Hurwitz CriterionAnswer whether any pole is unstable without finding a single one — and get the usable range of gain out of it.
- Root LocusWatch the closed-loop poles travel as gain rises: along the axis, breaking away, and finally crossing over.
- Effect of adding poles and zeros
- Lead and lag compensator design on the locus
Frequency response
Poke the system with every frequency and listen to the answer.
- Polar plots and the Nyquist criterion
- Nichols chart and closed-loop response
Compensator design
Changing the loop until it behaves the way the spec demands.
- Lead, lag and lead-lag compensators
- Ziegler-Nichols tuning in detail
State-space analysis
The same system written as first-order equations in a vector.
- State variables and state models
- State transition matrix
- Controllability and observability
- Pole placement by state feedback
About Control Systems
Control systems is about making a physical thing behave, and its central insight is that measuring the output and feeding it back changes the problem entirely. An open-loop system hopes; a closed-loop system corrects. Everything else here follows from that difference.
The catch is that feedback can destabilise as easily as it stabilises. Correct too weakly and the system never arrives; too strongly and it overshoots, oscillates, or runs away. Most of the subject is machinery for predicting which will happen before you build it — root locus, Bode plots, gain and phase margins.
These tools are visual by nature, and they are usually taught as static plots the student cannot interrogate. Watching poles migrate as gain increases, or a step response change shape as a margin closes, makes the connection between a plot and a behaviour concrete.
What to know first
- Signals and Systems, particularly transfer functions
- Laplace transforms, at least mechanically
Where it gets used
- Tuning a PID loop with an understanding of what each term does
- Recognising instability in a mechanical or thermal system as a control problem
- Reading a Bode plot to judge how much gain a system can tolerate