Simultaneous identification of linear building dynamic model and disturbance using sparsity-promoting optimization

Abstract

We propose a method that simultaneously identifies a dynamic model of a building's temperature in the presence of large, unmeasured disturbances, and a transformed version of the unmeasured disturbance. Our method uses 1-regularization to encourage the identified disturbance to be approximately sparse, which is motivated by the piecewise constant nature of occupancy that determines the disturbance. We test our method using both open-loop and closed-loop simulation data. Results show that the identified model can accurately identify the transfer functions in both scenarios, even in the presence of large disturbances, and even when the disturbance does not satisfy the piecewise constant property.

An autonomous MPC scheme for energy-efficient control of building HVAC systems

“…Identifying a linear black box model directly from data is also not straightforward (we discuss this later in Section 3). Recent progress in this direction is made in [21,16], which identifies a linear model in which the input is the heat gain due to the HVAC system. However, the model is still not linear with respect to the control commands such as air flow rate.…”

“…where w is the transformed version of the internal heat load q int (kW); see [16] for details. It captures the effect of q int on the zone temperature T z .…”

“…The system identification algorithm used here is the SPIDR method proposed in our earlier work [16]. Fix i as the current time when system identification is to be carried out.…”

“…Specifically, the plant is simulated in SIMULINK © . The system identification problem from [16] for estimating model and disturbance is solved using CVX © [40] package. For control computation, the nominal non-convex problem (7) is solved using Ipopt © [41] package, and the proposed convex problem (13) is solved using CVX © [40] package.…”

“…1, that is capable of operating autonomously for long periods of time without intervention of a human expert. The "ID + prediction" block uses an algorithm proposed in our prior work [16] to identify the plant model and the unmeasured internal disturbance from easily measured input-output data. This algorithm involves solving an optimization problem that is always feasible and convex, and the model it identifies ( M ) is guaranteed to be stable and possess properties that are consistent with properties of a building HVAC system.…”