Eva Žáčeková

From Linear to Nonlinear Model Predictive Control of a Building

Abstract In the building climate control area, the linear model predictive control (LMPC)—nowadays considered a mature technique—benefits from the fact that the resulting optimization task is convex (thus easily and quickly solvable). On the other hand, while nonlinear model predictive control (NMPC) using a more detailed nonlinear model of a building takes advantage of its more accurate predictions and the fact that it attacks the optimization task more directly, it requires more involved ways of solving the non-convex optimization problem. In this paper, the gap between LMPC and NMPC is bridged by introducing several variants of linear time-varying model predictive controller (LTVMPC). Making use of linear time-varying model of the controlled building, LTVMPC obtains predictions which are closer to reality than those of linear time invariant model while still keeping the optimization task convex and less computationally demanding than in the case of NMPC. The concept of LTVMPC is verified on a set of numerical experiments performed using a high fidelity model created in a building simulation environment and compared to the previously mentioned alternatives (LMPC and NMPC) looking at both the control performance and the computational requirements.

On Satisfaction of the Persistent Excitation Condition for the Zone MPC: Numerical Approach

Abstract In recent years, advanced control techniques such as Model Predictive Control based on optimization and making use of a model providing the predictions of the future behavior of the controlled system have been massively developed. These model-based controllers rely heavily on the accuracy of the available model (predictor of the controlled system behavior) which is crucial for their proper functioning. However, as the current operating conditions can be shifted away from those under which the model has been identified, the model sometimes happens to lose its prediction properties and needs to be re-identified. Unlike the theoretical assumptions, the data from the real operation suffer from undesired phenomena accompanying the closed-loop data. In the current paper, we focus on developing an algorithm which would serve as an alternative to the (often costly or even unrealizable) open loop excitation experiment. The requirements such an algorithm should meet are: low computational complexity, low level of original MPC performance degradation and ability to provide sufficiently informative data when necessary. Unlike to the currently available approaches which solve this problem for the classical MPC formulation (tracking error penalization), in this paper we propose an algorithm which works well also for the zone MPC formulation (penalization of output zone violation), however, it is versatile enough and can be extended considering wider variety of the optimization formulations.

Building modeling: on selection of the model complexity for predictive control

Abstract Model Predictive Control has become a wide-spread solution in many industrial applications and is gaining ground in the field of energy management of the buildings. A model with good prediction properties is an ultimate condition for good performance of the predictive controller. In this paper grey box modeling and model predictive control relevant identification are used for construction of candidate models of a building. We introduce a two-stage iterative procedure for model selection: in the first stage a minimum set of disturbance inputs is formed such that the resulting model is the best with respect to defined criterion; then the second stage comprises addition of states to obtain a final minimum parameter set maximizing the model quality. The procedure stops when it makes no sense to select more complex model as it brings no more quality improvements. Finally a case study is provided where all the above mentioned approaches are investigated.

Dual control within MPC framework

Abstract Model predictive controller (MPC) is a successful in control of the buildings environment. The inherent part of the MPC is a systems model which is the bottleneck of this control approach. Data collected for the system identification very often comes from the closed-loop operation which often leads to a failure of classical identification approaches. A new algorithm is presented here when a persistent excitation (PE) condition is incorporated into a control criterion. The controller ensures sufficiently excited data, which makes the system re-identification possible. The algorithm uses the maximization of the minimal eigenvalue of the information matrix to achieve a richer identification data. As a result, the data used for re-identification are sufficiently excited and the estimate of the system parameters is better.