State estimation

The MPC needs the full state of the FastModel (the air, the layers of the walls, the panes, the radiator and buffer water) at the start of each horizon, but only the zone air temperatures are measured. Every estimator follows the cycle correct with the measurement of the step → use the state → predict with the inputs applied during the step (StateEstimator).

MovingHorizonEstimator(model, dt, start, settings=EstimatorSettings(window=12)) keeps the inputs applied and the measurements of the last window steps and, at each correct, finds the trajectory of the model closest to them with the moving horizon estimation of trano_optimization (Radau collocation, IPOPT): the measured air temperatures (measurement_noise), the model errors over each step (process_noise) and the deviation of the first state of the window from its prior (arrival_noise) are weighted by their standard deviations. When the window slides, the estimate of its second state becomes the prior of the next window; when an estimation fails, the prior is propagated over the step instead. Each estimation takes a fraction of a second.

On the boiler house of the tests started 2 K colder than the estimator assumes, the mean error over its 26 temperature states falls from 1.9 K to 0.05 K within a day, where the uncorrected model keeps 0.84 K; the closed-loop MPC with estimation costs the same as with the true state.

PerfectEstimator(plant) returns the true state of a simulated plant, to study the controller alone.