Sigurd Skogestad

David Pérez-Piñeiro, Sigurd Skogestad, Stephen Boyd

We consider the problem of operating a battery in a home connected to the grid to minimize electricity cost, which combines an energy charge and a tiered peak power charge based on the average of the $N$ largest daily peak powers in each billing month. With perfect foresight of loads and prices, the minimum cost is the solution of a mixed-integer linear program (MILP), which provides a lower bound on the cost of any implementable policy. We propose a model predictive control (MPC) policy that uses simple forecasts of loads and prices and solves a small MILP at each time step. Numerical experiments on one year of data from a home in Trondheim, Norway, show that the MPC policy attains a cost within $1.7\%$ of the prescient bound, and saves close to three times as much as the best rule-based policy we consider.

Sigurd Skogestad

Advanced regulatory control (ARC), also known as advanced PID architectures, is a simple and robust way of controlling processes with changing and possibly conflicting constraints, where it previously was believed - at least in academia - that model-based solutions, such as MPC, were the only effective solution. To illustrate this, ARC is applied in two case studies. The first is a gas-liquid separation process, in which selectors and split-parallel control are combined to achieve bidirectional inventory control in which the throughput manipulator moves automatically to the most optimal position. The second case study is on keeping acceptable air quality (CO2-level) and temperature in a room (in this case, a barn for cows). The CO2 and temperature constraints can be conflicting, leading to a hierarchical switching network of PID controllers. Note: this is an extended version (with simulations) of paper at IFAC World Congress, August 2026, Korea.