Jiří Cigler

Role of MPC in Building Climate Control

Low energy buildings have attracted a lot of attention in past decades. Recent research is dedicated mainly to optimization of building construction and alternative energy sources. We provide a different approach to the energy-consumption and energy-cost optimization. A generic concept of minimizing energy consumption using current energy sources making use of advanced control techniques is presented. Model Predictive Controller (MPC) presented in this article makes use of both weather forecast and thermal model of a building to control inside temperature. This, by sharp contrast to conventional control strategies such as heating-curve (HC) or rule-based controllers (RBC), enables utilization of thermal capacity of the building. The inside temperature can be maintained at desired levels independent of the outside weather conditions using modified formulation of MPC.

Optimal control systems with prescribed eigenvalues

The eigenvalues of a linear and time-invariant control system can be located at desired positions either directly, using eigenvalue assignment techniques, or indirectly, using, for example, a linear-quadratic optimal control. The optimal control induces a certain eigenvalue pattern, depending on the performance index. It is shown in the paper that prescribed eigenvalue locations can be achieved using linear-quadratic optimal control methods.

Nonquadratic stochastic model predictive control: A tractable approach

This paper deals with the finite horizon stochastic optimal control problem with the expectation of the p-norm as the objective function and jointly Gaussian, although not necessarily independent, additive disturbance process. We develop an approximation strategy that solves the problem in a certain class of nonlinear feedback policies while ensuring satisfaction of hard input constraints. A bound on suboptimality of the proposed strategy in this class of nonlinear feedback policies is given for the special case of p=1. We also develop a recursively feasible receding horizon policy with respect to state chance constraints and/or hard control input constraints in the presence of bounded disturbances. The performance of the proposed policies is examined in two numerical examples.

Incorporation of system steady state properties into subspace identification algorithm

Most of the industrial applications are multiple-input multiple-output (MIMO) systems that can be identified using the knowledge of the system’s physics or from measured data employing statistical methods. Currently, there is the only class of statistical identification methods capable of handling the issue of the vast MIMO systems – subspace identification methods. These methods, however, as all the statistical methods, need data of a certain quality, i.e., excitation of the corresponding order, no data corruption, etc. Nevertheless, combination of the statistical methods and a physical knowledge of the system could significantly improve system identification. This paper presents a new algorithm which provides remedy to the insufficient data quality of a certain kind through incorporation of the prior information, namely a known static gain and an input-output feed-through. The presented algorithm naturally extends classical subspace identification algorithms, that is, it adds extra equations into the computation of the system matrices. The performance of the algorithm is shown on a case study and compared to the current methods, where the model is used for an MPC control of a large building heating system.

On 1-norm stochastic optimal control with bounded control inputs

This paper deals with the finite horizon stochastic optimal control problem with the expectation of the 1-norm as the objective function and jointly Gaussian, although not necessarily independent, disturbances. We develop an approximation strategy that solves the problem in a certain class of nonlinear feedback policies, while ensuring satisfaction of hard input constraints. A bound on suboptimality of the proposed strategy in the class of aforementioned nonlinear feedback policies is given as well as a simple proof of mean-square stability of a receding horizon implementation provided that the system matrix is Schur stable.

System identification using wavelet analysis

Abstract System identification (SID) plays a central role in any activity associated with process operations. With control being done on different levels, different models are required for the same plant each for a different range of dynamics. Besides that most identification methods apply to the linear models, they also do not allow for selecting a frequency range. Wavelet methods have the ability to select the time and frequency windows and are also applicable to the nonlinear processes. The paper presents an approach, in which wavelet transform is used for SID enabling selection of the particular frequency range. Even though, the wavelet transform as a tool is known for a long time and has a number of desirable properties, it is not frequently used in the applications.

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.