control//controller design
Controller design is the engineering of the law that maps a measured error or an estimated state to an actuator command, and choosing among its families is a decision about what model you have, what guarantees you need and what you can afford to compute every period. Every controller in this family shares the same report card: does it stabilize the loop, with what margins, at what actuator effort, at what online compute, and how mature is it in the field. A drone, a refinery column and a servo answer those questions differently, which is why the family exists.
Controller design is the engineering of the law that maps a measured error or an estimated state to an actuator command, and choosing among its families is a decision about what model you have, what guarantees you need and what you can afford to compute every period. Every controller in this family shares the same report card: does it stabilize the loop, with what margins, at what actuator effort, at what online compute, and how mature is it in the field. A drone, a refinery column and a servo answer those questions differently, which is why the family exists.
The members form a ladder. The PID controller, usually in a cascade, needs little model and some tuning tests; it runs at kilohertz on a microcontroller and flies the vast majority of drones. State feedback uses the whole state vector, with gains chosen by pole placement or, more sensibly, by the LQR, which writes the trade between error and effort as a price list and costs one matrix-vector product per period. When the state must be estimated, LQG puts a Kalman filter in front and loses the LQR's guaranteed margins. When limits are the problem, MPC plans a few seconds ahead inside them and pays one quadratic program per period. When the goal is a path rather than a point, trajectory tracking adds the nominal input as feedforward. When the plant drifts, gain scheduling and adaptive control retune the law, and learned or RL controllers (learning-based control) act only behind a safety filter.
Flyswatter or cannon.
A well-tuned PID cascade flies most drones in the world. The LQR pays when several inputs are really coupled and a decent model exists, and online it is as cheap as a PID. MPC pays when constraints are the problem (working against a limit, not hitting a wall) or when the future reference is known and worth anticipating. Otherwise the PID wins on engineering cost: any technician understands it and can retune it at three in the morning (flyswatter rule).
For a plant that changes, the book's ladder runs from least to most risk: PID with feedforward and anti-windup; gain scheduling on whatever can be measured; LQR or MPC for coupling and constraints; online estimation of a few bounded physical parameters; learned residuals on the model; RL where the model is intractable (contacts), the simulator is good and a safety filter exists. Each rung costs more data, engineering and validation, so climb only when the previous one has truly fallen short.
Modern control relocates error rather than removing it (error relocation). It lives in the linearization, valid only near the design point (a 38° tilt already extrapolates a hover model); in the estimate, whose error enters the command multiplied by KKK; in the horizon an MPC cannot see past; and in the solver, whose tolerance and run time are themselves delay.
Time-optimal control is the limit of arrive as soon as possible with bounded force: full thrust one way, then full thrust the other, which an MPC approaches when asked. It is called bang-bang, the same word used for the thermostat-like on-off control, which is a different thing (switching around a setpoint for want of a proportional actuator).
Maturity sorts the members (technology maturity): PID, cascade and gain scheduling are industry everywhere; LQR is industry in aerospace and mechatronics, mostly as an offline gain calculator; linear MPC has been industry in process plants for four decades; nonlinear MPC and RL on critical systems are niche or research.