自动化专业外文文献

ISSN: 1991-8763
967
Issue 11, Volume 3, November 2008
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
Fotis N. Koumboulis, Nikolaos D. Kouvakas, Paraskevas N. Paraskevopoulos
Abstract: - In the present paper, the analytic mathematical model of a test case central heating system is developed in the form of a nonlinear neutral time delay model with time varying delay which in turn is simplified to a neutral time delay model with constant time delay. In the process it is shown that the influence of the delay is significant, thus its incorporation to the model is of high importance while the constant delay approximation imposes only small error. A PID controller is derived to control the temperature of a room, which is modeled as a first order differential equation. The controller parameters are evaluated using a metaheuristic algorithm. Key-Words: central heating, modeling, neutral time delay system, PID controller, metaheuristic time delay model with constant time delay. It will be 1 Introduction shown that the influence of the delay is significant, The problem of modeling and control of central thus its incorporation to the model is of high heating systems has attracted significant attention importance while the constant delay approximation during the last years (see f.e. [1]-[15]). In particular, imposes only a small error to the system. Finally, a significant attention has been given to the modeling, PID controller will be derived to control the construction and optimization of core components of temperature of a room, which will be modeled as a central heating systems, such as pipe networks and first order differential equation. The controller piping elements (see f.e. [4]-[8] and the references parameters will be evaluated using a metaheuristic therein), radiators and other heating systems (see f.e. approach whose efficiency will be investigated. The [9]-[10]), boilers (see [11]-[12]) etc. Furthermore, resulting closed loop response will be compared to different control techniques have been applied to the response produced by the same controller for the such systems in order to regulate the ambient air case where the parameters are evaluated using the temperature in heated areas (see f.e. [13]-[17]). first Ziegler Nichols method and the open loop The present paper is an extended version of [16] response of the system applying appropriate constant where the dynamic model of the system is briefly actuatable inputs. presented while the room temperature is controlled via a PI controller. In the present paper the mathematical model of the test case central heating 2 Dynamic Model of a Test Case system will analytically be presented in the form of a Central Heating System nonlinear neutral time delay model. In particular, In what follows, the general dynamic model of a test separate models will be presented for the core case central heating system will be produced. The components of the system, i.e. pipe network, radiator system consists of the piping network, a radiator and and boiler. The separate models will be combined to a boiler (see Figure 1). The radiator heats up a room, a nonlinear neutral time delay system (with time thus the performance output of the system is the varying delay) which will be simplified to a neutral
FOTIS N. KOUMBOULIS Dep. of Automation Halkis Institute of Technology 34400, Psahna, Evoia GREECE koumboulis@teihal.gr NIKOLAOS D. KOUVAKAS Dep. of Electrical & Computer Engineering National Technical University of Athens 15780, Zographou, Athens GREECE kouvakas@teihal.gr
Φ + (2ϕ − 1)Tj − ϕTj +1 ⎤⎥ − 0 ⎦ N
⎛T − T ⎟ ⎞1 ⎜ j a ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎝ ΔTma ,0 ⎟ ⎠
n
n
while the last section is given as
Φ C dTN = H qq (TN −1 − TN ) − 0 N dt N
power emitted by the radiator which is directly related to the temperature of the ambient air.
Ta
radiator, N is the number of sections the radiator is partitioned and Tj is the radiator temperature in the jth section. The temperature difference ΔTj is given by
WSEAS TRANSACTIONS on SYSTEMS and CONTROL
Fotis N. Koumboulis, Nikolaos D. Kouvakas, Paraskevas N. Paraskevopoulos

Analytic Modeling and Metaheuristic PID Control of a Neutral Time Delay Test Case Central Heating System
C dT1 = H qq ⎡⎢Ti − (1 − ϕ )T1 − ϕT2 ⎤⎥ − ⎣ ⎦ N dt
1 Φ0 ⎛ T1 − Ta ⎞ ⎟ ⎜ ⎟ ⎜ − ⎜ ⎟ ⎟ N ⎜ ⎟ ⎝ ΔTma ,0 ⎠