pumpingStation/wiki/modes/mpc.md

---
title: MPC (Model-Predictive Control)
mode: mpc
tier: 3
status: placeholder
updated: 2026-04-22
---

# MPC mode — *Tier 3 template*

> **Status — not yet implemented.** Not even in the schema today. This page reserves the shape for when the time comes.

## Why this is Tier 3

The levelbased/flowbased/powerBased modes are all **memoryless or near-memoryless transfer functions**. You give them the current state; they give you a demand. You can draw them as 2D plots.

MPC is different. At each tick the controller solves an optimisation over a prediction horizon:

```
minimise   Σ  cost(state(t+k), command(t+k))         for k = 0 .. N
subject to forecast, physical limits, power budget, spill penalty, ...
```

The *command* that's emitted at time `t` is merely the first step of that plan; next tick the forecast shifts and the optimiser re-runs. There's no fixed `demand = f(level)` curve — the curve is remade every tick.

That's why Tier-3 modes get **block diagrams + scenario time-series**, not transfer functions.

## At a glance

| Item | Value |
|---|---|
| Tier | 3 — optimisation-based |
| Signal driving demand | full state (level, flow, power) + **forecasts** (inflow, grid price, weather) |
| Secondary inputs | cost weights, horizon length, solver config |
| Output | demand + planned trajectory over horizon |
| Thresholds adjusted at runtime? | Effectively yes — the optimiser treats them as soft constraints |
| Use when | Available forecasts beat reactive control, or multi-objective optimisation is needed |

## Diagram 1 — signal flow (block diagram)

```
Placeholder image — replace with:
  diagrams/modes/mpc-block.drawio.svg

Blocks:

  [sensors]   [inflow forecast]   [grid price]   [weather API]
      │             │                  │              │
      └─────────────┴──────────────────┴──────────────┘
                             │
                       ┌─────▼──────┐
                       │ state +    │
                       │ forecast   │
                       │ bundle     │
                       └─────┬──────┘
                             │
                       ┌─────▼───────────────────┐
                       │ MPC solver              │
                       │  • horizon N            │
                       │  • cost weights w       │
                       │  • constraints C        │
                       │  • linearised model     │
                       └─────┬───────────────────┘
                             │
                       ┌─────▼───────┐
                       │ command[0]  │ ── the step we act on now
                       │ command[1]  │
                       │   ...       │
                       │ command[N]  │ ── re-planned next tick
                       └─────┬───────┘
                             │
                   ┌─────────▼─────────┐
                   │ safety layer clip │ ← dryRun / overflow always apply
                   └─────────┬─────────┘
                             │
                          demand  →  MGC
```

## Diagram 2 — scenario time-series

A much more useful way to evaluate MPC is to plot *what it did* over a simulated scenario: level, planned vs actual demand, the cost function breakdown, the active constraints. The [simulations harness](../../simulations/README.md) is built for exactly this — MPC will need a dedicated scenario like `mpc-storm-with-forecast.js`.

```
Placeholder — replace with:
  diagrams/modes/mpc-scenario.drawio.svg

Stacked time-series showing:
  1. basin level over time (with forecast shadow and horizon)
  2. demand over time (with the re-planning edges visible)
  3. cost breakdown: energy vs spill-penalty vs ramp-penalty
  4. active constraints over time (colored bands)
```

## Inputs

| Signal | Where from | Role |
|---|---|---|
| current state | `measurements` container | initial condition for optimiser |
| inflow forecast | external — sewer model / weather API | drives the cost integral |
| grid-price forecast | external — market feed / schedule | weights energy cost |
| cost weights `w` | config | trades off spill vs energy vs ramp |
| horizon `N` | config | 15–60 minutes typical |
| model parameters | config / learned | basin dynamics, pump curves |

## Threshold policy

Levels appear in the optimiser as **soft constraints** (penalties in the cost function):

| Threshold | Role in MPC |
|---|---|
| `dryRunLevel`, `overflowLevel` | hard constraints — if the optimiser's plan crosses them, safety layer clips |
| `minLevel`, `maxLevel` | soft constraints — penalty weight `w_level` applied to excursions |
| `startLevel` | advisory only — optimiser doesn't inherently care, but may be used in cost weights for rule-of-thumb alignment with human expectations |

So unlike Tier-1/2 where thresholds directly gate the action, here they shape the objective.

## Demand formula

Not a formula — an optimisation problem:

```text
state, forecast, constraints = gather_inputs()
plan = mpc_solver.solve(
    state0         = state,
    forecast       = forecast,
    horizon        = N,
    model          = basin_dynamics + pump_curves,
    cost           = w_energy × Σ power(k)
                   + w_spill  × Σ max(0, level(k) − overflowLevel)²
                   + w_undercut × Σ max(0, minLevel − level(k))²
                   + w_ramp   × Σ (command(k) − command(k-1))²,
    constraints    = pump_limits + power_budget + rate_limits,
)
demand = plan.command[0]
```

## Edge cases

- **Solver timeout.** Fall back to the previous plan's step, or to a levelbased curve as a safe default. Log.
- **Bad forecast (persistent bias).** Optimiser can chase a wrong prediction for many ticks. Adaptive forecast bias correction, or a watchdog comparing forecast-vs-realised, is essential.
- **Infeasibility.** If constraints can't be satisfied (e.g. power budget and maxLevel simultaneously during a severe storm), relax soft constraints in priority order (ramp first, then maxLevel, then energy) — never relax dryRun/overflow.
- **Safety takeover.** The safety layer still overrides. MPC should *anticipate* safety trips in its cost function (big penalty for trajectories that invoke them), not hit them.

## Related

- [Functional description](../functional-description.md) — basin model + safety layer
- [modes/levelbased.md](levelbased.md) — Tier 1 — the "default" MPC falls back to
- [modes/powerbased.md](powerbased.md) — Tier 2 — MPC generalises the clip idea into full optimisation
- [simulations/README.md](../../simulations/README.md) — where MPC simulation scenarios will live