Tomasz Larkowski

Modelling of an Air Handling Unit: A Hammerstein-bilinear Model Identification Approach

The paper focuses on modelling and system identification of an air handling unit (AHU), which is part of larger heating ventilation and air conditioning (HVAC) system dedicated for clean room manufacturing. The aim is to use the model for subsequent control optimisation and further for control system design. The underlying physical relations of an AHU are investigated through a white-box model. Based on the white-box model considerations a discrete-time bilinear black-box model is proposed. The AHU cooling/heating capacity is altered by means of water valves. The valve introduces a Hammerstein nonlinearity on the system input, which needs to be additionally identified together with the dynamic bilinear model representing the heating/cooling coil of the AHU. The discrete-time model coefficients are then estimated based on real measurements.

Frisch scheme identification for dynamic diagonal bilinear models

The article addresses the problem of dynamic system identification in the errors-in-variables framework for a class of discrete-time time-invariant input–output bilinear models when subjected to a white input signal. The proposed algorithm is based on an extension of the bias-compensated least squares method and utilises the Frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences. The appropriateness of the approach is analysed and its performance evaluated when compared to other errors-in-variables identification techniques by means of a Monte Carlo simulation. The results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed.

Algorithms for recursive/semi-recursive bias-compensating least squares system identification within the errors-in-variables framework

Algorithms for the recursive/semi-recursive estimation of the system parameters as well as the measurement noise variances for linear single-input single-output errors-in-variables systems are considered. Approaches based on three offline techniques are presented: namely, the bias eliminating least squares, the Frisch scheme and the extended bias compensating the least squares method. Whilst the underlying equations used within these approaches are identical under certain design choices, the performances of the recursive/semi-recursive algorithms are investigated via simulation, in order to determine the most suitable technique for practical applications.

Design of Unknown Input Reconstruction Filter Based on Parity Equations for Errors-in-Variables Case

Abstract This paper presents a novel approach to the problem of unknown input estimation in the presence of measurement noise. The observer developed here is based on the parity equations concept, hence, in contrast to the Kalman filter-based approaches, it is orthogonal (independent) to the system state vector. Therefore, due to the reduction of the number of estimated signals, an increased accuracy of the input estimation is achieved. This makes the scheme advantageous in cases when the accuracy of the unknown input estimate is crucial and knowledge about the system states is not required. By increasing the order of the parity space, which is a tuning parameter of the proposed algorithm, the influence of measurement noise can be reduced. An errors-in-variables case is considered, i.e. both measured input and output signals are affected by noise. A Lagrange multiplier method is used to obtain an analytical solution for the filter parameters. The proposed technique is suitable for both minimum-phase and nonminimum-phase systems.

Energy Consumption Analysis of HVAC System with Respect to Zone Temperature and Humidity Set-Point

Abstract The general aim is to increase the energy efficiency of heating ventilation and air conditioning (HVAC) systems by achieving highly stable control performance allowing for operation close to the specification limits, where the highest profitability can be obtained. Considering the nonlinear behaviour of HVAC systems the use of advanced control techniques is a necessity in achieving this goal. One of the key questions arises here: are the economical benefits gained from the implementation of advanced control techniques higher than the installation costs? In this paper, the steady state characteristics between control set-points and HVAC system energy usage are estimated, in order to help to answer this question.

Temperature Model of an Industrial Air Handling Unit and Manufacturing Zone

Abstract The paper focuses on system identification of a temperature model of an industrial air handling unit in connection with an air conditioned manufacturing zone. The models obtained are intended to be used for a subsequent control analysis and tuning of the presently installed temperature control system. Model structures are predetermined based on simplified first principles modelling approach. A bilinear parametrisation method in tandem with a simplified instrumental variable technique is applied for the parameter estimation of a discrete-time Hammerstein-bilinear model representing the air handling unit. Whilst a simplified instrumental variable method for continuous-time system identification is utilised for estimating the parameters of the linear manufacturing zone model.

Control Optimisation of a Domestic Heating System

The paper presents various control techniques for optimization and energy efficiency for domestic heating systems. A description of the heating system model, its behaviour and underpinning processes are presented. The model of the heating system, which is inherently nonlinear, is formulated either as a linear time varying (LTV) system or a bilinear time varying (BTV) system or bilinear time invariant (BTI) system. For each model representation various formulations of generalised predictive control (GPC) are investigated. The original GPC, in its non-incremental and modified forms are implemented and tested for these systems. Depending on the model structure, i.e whether the model is LTV, BTV or BTI, the GPC is formulated as a linear self tuning control (LSTC) GPC, bilinear self tuning control (BSTC) GPC and fixed bilinear (FB) GPC, respectively. It is shown that depending on the adopted model representation various degrees of improvement are possible when using different formulations for GPC.

Unknown Input Reconstruction Observer for Hammerstein-Wiener Systems in the Errors-in-Variables Framework

Abstract In this paper an approach for reconstructing an unknown input in the case when input and output signals are both subject to measurement uncertainties, i.e. errors-in-variables framework, is presented. The algorithm is applicable to Hammerstein-Wiener systems, i.e. systems composed from a dynamic linear system followed and preceded by a memoryless nonlinearity. It is based on a parity equations concept and forms an extension of the idea developed previously by the authors for linear systems. The only requirement is that the function used to describe the component static output nonlinearity must be strictly monotonic. The order of the parity space can be treated as a tuning parameter allowing for a trade-off between the smoothness of the reconstructed unknown input and a phase lag to be obtained. An analytical solution of the overall problem is obtained by using a Lagrange multiplier method.

Design of Parity Equations Using Right Eigenstructure Assignment

System uncertainties, such as modelling errors, external disturbances etc. can impede the fault detection process. Therefore a need arises for robust fault diagnosis, where complete disturbance decoupling can be achieved. The main contribution of this paper is the design of a parity relation for robust fault detection using right eigenstructure assignment. Up to date the left eigenstructure assignment technique has been used for the design of first order disturbance decoupled parity relations. In many cases complete disturbance decoupling is not possible when using left eigenstructure assignment. Therefore, the proposed method utilises the right eigenstructure assignment technique for the purpose of robust fault detection. The novelty of the developed scheme is to replace the traditional asymptotically convergent state observer by a state observer, which converges in a predefined time. The proposed method is demonstrated to be equivalent to a parity relation of a user predefined order.

Regularized Structured Total Least Norm for the Identification of Bilinear Systems in the Errors-in-Variables Framework

The paper addresses the identification of time-invariant bilinear system (BS) models in the errors-in-variables (EIV) framework. The proposed scheme is based on the structured total least norm (STLN) technique extended here to handle BS. The performance of the presented approach, i.e. the bilinear STLN (BSTLN) with its further extension incorporating the Tikhonov regularization is compared to several other EIV identification techniques via an extensive Monte-Carlo simulation study. The results obtained demonstrate a considerable noise robustness and therefore the applicability of the BSTLN algorithm in the EIV framework.