Control Systems - Level 2
Bang-Bang Control
Concept
Note: Bang-Bang Control, A.K.A. 2-step on-off controller. See on Wikipedia.
The simplest form of closed-loop control: look at the error (setpoint minus position), and if it’s positive, push hard forward; if negative, push hard back.
u(t) = +u_max if e(t) > 0
u(t) = −u_max if e(t) < 0
Press Start. The mass rushes to the setpoint - but overshoots, reverses, overshoots again, and settles into a limit cycle around the target. The control effort trace below shows the actuator slamming between +5 and -5.
Bang-bang is simple, cheap, and used in real systems (thermostats, for instance). But it’s noisy, wears out actuators, and never sits still. We can do much better by making the effort proportional to how far off we are.
Goal
Watch the response: the mass reaches the setpoint but then chatters around it forever. No amount of disturbance fooling will make it settle cleanly. This is why we need something smoother...the P controller, next.
Tune
d is an external disturbance force applied to the plant.