Matej Pcolka

Economical nonlinear model predictive control for building climate control

In this paper, two alternatives approaches to model predictive control (MPC) are compared and contrasted for the role of zone temperature controller - the commonly used linear formulation (LMPC) and rather unconventional nonlinear formulation (NMPC). The economical focus is reflected by the performance criterion being a combination of the comfort requirements and the monetary cost penalties (price of the consumed hot water and the electricity needed to deliver the water to the building) of the controlled inputs. With this formulation, the optimal controller drives toward minimization of the real price rather than minimization of abstract quantities. It turns out that the NMPC is able to attack the cost minimization directly while retaining a compact optimization formulation as opposed to the suboptimal linear alternative. A considerable part of the superiority of the NMPC can be owed also to the use of a nonlinear model that captures the nonlinear building dynamics much more accurately than the linear models. Thanks to an enhanced search step choice introduced in this paper, the NMPC outperforms both the LMPC and the conventional controller significantly even under severe computational restrictions which demonstrates its strong practical applicability.

Gradient method optimization of penicillin production

A fermentation process is generally defined as a biological process containing the growth of the biomass (bacteria, yeasts) resulting from the consumption of essential substrate supplies (source of carbon, nitrogen, oxygen, etc.). The biomass growth is usually followed by the production of various products from which especially the variety of antibiotics makes the fermentation processes attractive for the industrial utilization. However, the complicated dynamics, high level of uncertainty and nonlinearity and difficult online measurement of the process variables come hand in hand with the attractivity and turn the attempts on optimal control of the fermentation process into a very delicate challenge. To tackle it, the theory of the gradient projection method has been partially adapted and fully implemented by the authors of this paper. Numerical experiments show its significantly better performance than for other known methods. Moreover, these experiments reveal an interesting “superprofile” visible for long cultivation times.

Gradient method optimization of penicillin production: New strategies

Since their discovery, fermentation processes have gone along not only with the industrial beverages production and breweries but since the times of Alexander Fleming they have become a crucial part of the health care due to antibiotics production (from which the overwhelming majority of 90% is produced during a fermentation process). However, complicated dynamics and strong nonlinearities cause that the production with the use of linear control methods achieves only suboptimal yields. From the variety of nonlinear approaches, gradient method has proved the ability to handle these issues - nevertheless, its potential in the field of fermentation processes has not been revealed completely. In this paper, two fresh control strategies are introduced and compared - both of them are based on a double-input optimization approach, yet a successful reduction to a single-input optimization task is proposed. To accomplish this, model structure used in the previous work has been modified so that it corresponds with the new optimization strategies which together with the model stands for the main contribution of this paper.

Multiple-input cultivation model based optimization of penicillin production

Unlike prevailing contemporary approach considering the influx feed flow as the only crucial input influencing the final product concentration in bioprocess cultivation, the current paper considers other (non-nutritional) inputs as well. Among them, the volume withdrawal is an important option. Two types of control strategies employing this second input are considered here, each of them using it in a different way. First, the so-called quasi-double-input strategies exploit the broth withdrawal to follow a pre-determined volume profile. Second, the true-double-input strategies consider the second input as a completely independent optimization variable. Main analysis tool here is the gradient optimization numerical algorithm and its adaptations. All resulting strategies are summarized and formulated in the context of optimization, those introduced earlier (i.e., the quasi-double-input) are unified into a common general strategy. Practical complication (inadmissible volume decrease) related to withdrawal introduction is successfully addressed and the summary results show indisputable improvement gained by the non-nutrient input introduction.

Identification and energy efficient control for a building: Getting inspired by MPC

This paper deals with identification of a building model based on real-life data and subsequent temperature controller design. For the identification, advanced identification technique - namely MPC Relevant Identification method - is used. This approach has the capability of providing models with better prediction performance compared to the commonly used methods. Regarding the controller part, several alternatives are proposed. First, both linear and nonlinear MPC controlling the zone temperature are designed. Although highly attractive due to promising energetic savings and thermal comfort satisfaction, MPCs demand high computational power. To overcome this issue and preserve the attractive properties of the MPC, two MPC-learned feedback controllers are proposed, one learned from LMPC and the other learned from NMPC. While remaining computationally low-cost, they improve the performance of the classical controllers towards the high-performance MPC standards. The results exploiting data from real operation of an office equipped with air handling unit situated in Lakeshore building, Michigan Tech, are presented and discussed.

Enhancement of practical applicability of optimal control of a nonlinear process

This paper makes a step towards practical applicability of the optimal control for industrial penicillin production. Using the nonlinear gradient method as the key optimization tool, two ways of measurement feedback incorporation into the optimization procedure are proposed. Firstly, the receding horizon approach (whose linear variant is widely spreading in the field of operation of various industrial processes) is investigated considering different lengths of optimization horizon. Secondly, the shrinking horizon approach inspired by the character of the solved task with terminal criterion is examined. In order to make the latter comparable to the receding horizon approach, various sampling periods of the input signal are considered. Utilization of the nonlinear continuous time model of the controlled process clearly distinguishes this paper from the earlier publications. The behavior of both approaches is tested on a set of numerical experiments with the focus on performance under constrained computational resources. The obtained results demonstrate the superiority of shrinking horizon approach and its strong computational restriction resistance.

Semi-receding horizon algorithm for “sufficiently exciting” MPC with adaptive search step

In this paper, the task of finding an algorithm providing sufficiently excited data within the MPC framework is tackled. Such algorithm is expected to take action only when the re-identification is needed and it shall be used as the “least costly” closed loop identification experiment for MPC. The already existing approach based on maximization of the smallest eigenvalue of the information matrix increase is revised and an adaptation by introducing a semi-receding horizon principle is performed. Further, the optimization algorithm used for the maximization of the provided information is adapted such that the constraints on the maximal allowed control performance deterioration are handled more carefully and are incorporated directly into the process instead of using them just as a termination condition. The effect of the performed adaptations is inspected using a numerical example. The example shows that the employment of the semi-receding horizon brings major improvement of the identification properties of the obtained data and the proposed adaptive-search step algorithm used for the “informativeness” optimization brings further significant increase of the contained information while the aggravation of the economical and tracking aspects of the control are kept at acceptable level.

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.

Toward a Smart Car: Hybrid Nonlinear Predictive Controller With Adaptive Horizon

This paper focuses on the development of an optimization algorithm for car motion predictive control that addresses both hybrid car dynamics and hybrid minimization criterion. Instead of solving computationally demanding nonlinear mixed-integer programming task or approximating the hybrid dynamics/criterion, the Hamiltonian-switching hybrid nonlinear predictive control algorithm developed in this paper incorporates the information about hybridity directly into the optimization routine. To decrease the time complexity, several adaptive prediction horizon approaches are proposed, and for some of them, it is shown that they preserve maneuverability-related properties of the car. All developed alternatives are verified on an example of a motion control of a racing car and compared with the approximation-based nonlinear predictive control and a commercial product. Moreover, a sensitivity analysis examining robustness of the algorithm is included as well.