Left Half-Plane
A series of small games about control
THE LEFT HALF-PLANE
Where stable things live

Each game is a real system, one thing to tune, and a cost to bring down. Lower is better. A reference tells you what your number means. The world changes every midnight.

Season one

Four games, ordered as a curriculum

Each one adds an idea to the one before. Play them in order or don't. Every game has the same anatomy: what you tune, what the world hides from you, and what the cost is.

The name

The whole of stability in one picture

Every linear system responds as a sum of modes, each shaped like est. The numbers s are called the poles, and they live on a plane: the real part says whether a mode grows or dies, the imaginary part says how fast it wobbles.

Left of the axis, modes decay. On the axis, they ring forever. To the right, they grow until something breaks. So the left half-plane is where stable things live, and feedback is the art of moving poles into it, cheaply, and keeping them there when the world turns out to be different from the model.

Every game here is that art with one idea removed from its wrapping. The first game moves four poles at once with four numbers. The third lets you put them anywhere and then shows you where they really went.

How to read a score

A cost, a reference, and a world that changes at midnight

Lower is better

The score is the cost a control engineer would write on a whiteboard, in the units the system lives in: seconds, joules, an integral of error. The game never says correct. It says 8.65.

The reference

Every game runs the textbook answer in the same world you play in, and something naive next to it. Your number sits between them, or below both. That is all a score needs to mean something.

The daily seed

Gusts, lags, friction and noise are drawn from the date. You get the same world all day and a new one tomorrow, so there is nothing to memorise, only to understand.

Hidden dynamics

Every plant has something its manual leaves out. The textbook answer for the model is not the best answer for the world, which is the honest state of the field. Runs are kept in your browser only.

Riccati sets par. People beat par.

Season two and beyond

Nine more ideas, waiting for their game