Hamid Reza Shaker

Frequency-Interval Model Reduction of Bilinear Systems

In this technical note, a new method for model reduction of bilinear systems is presented. The method is developed in particular for many applications in which one is interested to approximate a system in a given frequency-interval. To this end, new generalized frequency-interval gramians are introduced for bilinear systems. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. The conditions for these equations to be solvable are derived and an algorithm is proposed to solve such equations iteratively. The method is further illustrated with the help of an illustrative example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.

Generalised gramian framework for model/controller order reduction of switched systems

In this article, a general method for model/controller order reduction of switched linear dynamical systems is presented. The proposed technique is based on the generalised gramian framework for model reduction. It is shown that different classical reduction methods can be developed into a generalised gramian framework. Balanced reduction within a specified frequency bound is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, generalised gramian‐based Petrov–Galerkin projection is constructed instead of the similarity transform approach for reduction. The framework is developed for switched controller reduction. To the best of our knowledge, there is no other reported result on switched controller reduction in the literature. The method preserves the stability under an arbitrary switching signal for both model and controller reduction. Furthermore, it is applicable to both continuous and discrete time systems for different classical gramian‐based reduction methods. The performance of the proposed method is illustrated by numerical examples.

Optimal Sensor and Actuator Location for Unstable Systems

Accurate and reliable process measurements play a key role in the success of process control. In addition to selecting the instrumentation hardware, it is important to determine which variables should be measured in a process. Therefore it is important to study techniques for placing sensors on the processes. Dually the problem of placing actuators on the processes is equally important. In this paper, the problem of determining optimal sensor and actuator locations for the linear systems is addressed. The problem of the sensor locations is viewed as the problem of maximizing the output energy generated by a given state and for the actuator locations is viewed as the problem of minimizing the input energy required to reach a given state. Such design problems occur in many applications, and therefore have been studied extensively. Unfortunately, the results in this context, which have been proposed so far, only support stable systems. However, in industrial practices it is often the case that the system, which is needed to be controlled, is not stable. The method which is proposed in this paper is a general method in the sense that it supports both stable and unstable systems. The technique is successfully used for determining the optimal sensor locations of the linearized Continuous Stirred-Tank Reactor unstable model.

Control configuration selection for bilinear systems via generalised Hankel interaction index array

Decentralised and partially decentralised control strategies are very popular in practice. To come up with a suitable decentralised or partially decentralised control structure, it is important to select the appropriate input and output pairs for control design. This procedure is called control configuration selection. It is well known that a suitable control configuration selection is an important prerequisite for a successful industrial control. In this paper the problem of control configuration selection for multiple-input and multiple-output (MIMO) bilinear processes is addressed. First, the concept of the cross-gramian is developed for bilinear systems. The conditions for the existence of generalised cross-gramian are derived. It is shown that if the cross-gramian exists it is the solution to the generalised Sylvester equation. To obtain the cross-gramian in a more computationally efficient way, an iterative method for solving the generalised Sylvester equation is proposed. The generalised cross-gramian is used to form the generalised Hankel interaction index array. The generalised Hankel interaction index array is used for control configuration selection of MIMO bilinear processes. Most of the results on control configuration selection, which have been proposed so far, can only support linear systems. The proposed method supports bilinear processes, takes the effects of dynamics of the process into account and can be used to propose a richer (sparse or block diagonal) controller structure. More importantly, since for each element of generalised Hankel interaction index array just one generalised Sylvester equation is needed to be solved, the proposed control configuration selection method is computationally more efficient than its gramian-based counterparts.

Time-interval model reduction of bilinear systems

In this paper, a new method for model reduction of bilinear systems is presented. The proposed technique is from the family of gramian-based model reduction methods. The method uses time-interval generalised gramians in the reduction procedure rather than the ordinary generalised gramians and in such a way that it improves the accuracy of the approximation within the time-interval for which the method is applied. The time-interval generalised gramians are the solutions to the generalised time-interval Lyapunov equations. The conditions for these equations to be solvable are derived and an algorithm is proposed to solve these equations iteratively. The method is further illustrated with the help of two illustrative examples. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.

Model reduction via time-interval balanced stochastic truncation for linear time invariant systems

In this article, a new method for model reduction of linear dynamical systems is presented. The proposed technique is from the family of gramian-based relative error model reduction methods. The method uses time-interval gramians in the reduction procedure rather than ordinary gramians and in such a way it improves the accuracy of the approximation within the time interval which is applied. It is proven that the reduced order model is stable when the proposed method applies to a stable system. The method uses a recently proposed inner–outer factorisation algorithm which enhances the numerical accuracy and efficiency. In order to avoid numerical instability and also to further increase the numerical efficiency, projector matrices are constructed instead of the similarity transform approach for reduction. The method is illustrated by a numerical example and finally it is applied to a practical CD player example. The numerical results show that the method is more accurate than ordinary balanced stochastic truncation.

Stability analysis for a class of discrete-time two-dimensional nonlinear systems

Stability analysis for a class of discrete-time two-dimensional nonlinear systems is addressed in this paper. A linear matrix inequality based sufficient condition for asymptotic stability is proposed. This condition is an analogous counterpart for two-dimensional linear systems which is shown to be easily verifiable and suitable for design problems. The result is illustrated by a numerical example.

Fault detection and diagnosis for smart buildings: State of the art, trends and challenges

Worldwide, buildings account for ca. 40% of the total energy consumption and ca. 20% of the total CO2 emissions. While most of the energy goes into primary building use, a significant amount of energy is wasted due to malfunctioning building system equipment and wrongly configured Building Management Systems (BMS). For example, wrongly configured setpoints or building equipment, or misplaced sensors and actuators, can contribute to deviations of the real energy consumption from the predicted one. Our paper is motivated by these posed challenges and aims at pinpointing the types of problems in the BMS components that can affect the energy efficiency of a building, as well as review the methods that can be utilized for their discovery and diagnosis. The goal of the paper is to highlight the challenges that lie in this problem domain, as well as provide a strategy how to counterfeit them.

Challenge: Advancing Energy Informatics to Enable Assessable Improvements of Energy Performance in Buildings

Within the emerging discipline of Energy Informatics people are researching, developing and applying information and communication technologies, energy engineering and computer science to address energy challenges. In this paper we discuss the challenge of advancing energy informatics to enable assessable improvements of energy performance in buildings. This challenge follows a long-standing goal within the built environment to develop processes that enable predictable outcomes. Implementing this goal in the research framework of energy informatics creates a need for establishing a new underlying assumption, which states that the impact of energy informatics solutions should be assessable. This assumption applies to particular building contexts and when solutions act simultaneously. Research based on this assumption will enable new sound processes for the built environment facilitating informed decision for adding intelligent solutions to buildings compared to only favoring passive building improvements.

Commercial buildings energy performance within context occupants in spotlight

Existing commercial buildings represent a challenge in the energy efficiency domain. Energy efficiency of a building, very often equalized to a building;s performance should not be observed as a standalone issue. For commercial buildings, energy efficiency needs to be observed and assessed within the context of performance of resident businesses. We examine both business performance and energy performance and how they relate to one another to conclude that building occupants, who are also employees, hold the key to optimizing both metrics in one of the most cost-efficient ways. Finally, the goal of our contribution is twofold: 1) to re-scope the concept of building performance to and show the importance to consider, hand-in-hand, both energy performance and performance of resident businesses, and 2) re-state the importance of the potential that lies in the active involvement of building occupants in optimizing overall building performance.