ASHRAE LV-11-C006-2011 Proportional-Integral-Plus (PIP) Control System for Individual Thermal Zones in a Small Ventilated Space.pdf

1、Ali Youssef, Vasileios Exadaktylos, Sezin E. zcan, Daniel Berckmans M3-BIORES: Measure, Model 27.56”25.60”15.75”) were used. Step inputs in ventilation rate and inlet air temperature are applied and temperature responses at 30 sensor locations are recorded. First order transfer function data-based m

2、odels are identified for modeling the dynamic behavior of temperature in each of the 20 cells. A Proportional-Integral-Plus PIP control system is designed based on the identified models to control the temperature in each of the 20 cells individually. INTRODUCTION An imperfectly mixed fluid is charac

3、terized by spatio-temporal distributions in environmental variables (temperature, humidity, gas concentrations, dust concentrations, etc.) of which the values and the evolution are influenced by the flow pattern of the fluid and the interaction with the living organisms (Barber and Ogilvie, 1982; Be

4、rckmans, 1986). It is recognized that these spatio-temporal distributions in the micro-environmental variables are a serious limitation for improving both the quality of the life or the living organisms and the quality of the products and the energy efficiency of the production process (e.g. De Moor

5、 and Berckmans, 1993). On a macro-scale level, a lot of energy is lost in the inefficient control of the imperfectly mixed indoor environment. Barber and Ogilvie (1982) suggest that multiple flow regions, stagnant zones and short-circuiting of air to the exhaust outlet are the major causes of incomp

6、lete mixing. Therefore, the development of models for advanced control system design must account adequately for these imperfect mixing processes (Price et al., 1999). In applications where the ventilated process is supposed to be homogeneous, one strives to achieve a spatially homogeneous distribut

7、ion of heat and mass. On the other hand, if the ventilated process is supposed to be heterogeneous, a spatially heterogeneous distribution of heat and mass is desired. For example, in ventilated rooms which are not entirely LV-11-C00648 ASHRAE Transactions2011. American Society of Heating, Refrigera

8、ting and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAES prior written permission.Figure 1. Schemati

9、c 3D diagram of the test installation Heater occupied, it is important to achieve good air conditions and thermal comfort in the occupied zone, without providing too large amounts of fresh air and heat in those parts of the room where it is not required (Sandberg, 1981; Van Brecht, 2004). In the pre

10、sent paper, the data-based modeling approach (e.g. Young, 1993; Young et al, 1998) is applied to the problem of modeling and controlling imperfect mixing in ventilated air space. Modeling is applied to data obtained from ventilation/heating experiment carried out on a small scale instrumented chambe

11、r. One advantage of the data-based model is its simplicity and ability to characterize the dominant model behavior of a dynamic system. This makes such a model an ideal basis for model-based control system design (Taylor et al, 1996; Price et al, 1999; Taylor et al, 2004). In this study, it is propo

12、sed that a data-based model for temperature in fixed spatial zones will be used in the design of Proportional-Integral-Plus (PIP) control system. TEST INSTALLATION AND EXPERIMENTS The research work presented in this paper is based on the analysis of data from planned experiments in a small scale tes

13、ted instrumented chamber in the Laboratory of Measure, Model and Manage Bioresponses (M3-BIORES) at the Katholieke Universiteit Leuven. The test chamber represented in the figure 1, has an inner dimension of length = 0.70 m (27.56”), width = 0.65 m (25.60”), and height = 0.4 m (15.75”) and is equipp

14、ed with an electrical heater with maximum capacity of 224 W. Two axial fans are installed, one in the inlet, which forced the incoming air over the heater before the air enters the chamber, while the second fan (exhaust fan) in the outlet to force out the air from the chamber. The chamber wall was c

15、onstructed with Plexiglas, wood with aluminum framing. The ceiling of the chamber was constructed with Plexiglas of 0.008 m (0.315”) thickness rested on aluminum framing. The inlet of the system composed of two series of ducting system first a circular ducting of 0.1055 m (4.15”) inner diameter, whe

16、re inlet fan was installed followed by a square ducting of outer dimension of 0.12 0.12 m (4.72” 4.72”) of made up of 0.018 m (0.71”) thick wooden wall, inside this section the heater was fixed. The temperature inside the test chamber could be changed by changing the inlet temperature which is regul

17、ated by the in/outlet fans and the heater voltages.A 2D grid of 30 calibrated temperature sensors (Semiconductors LM35) with and accuracy of 0.1 oC were arranged uniformly in 6 5 matrix of with a total dimension of length = 0.55 m and width = 0.44 m. The 2D grid of sensors were lowered 0.16 m downwa

18、rd from the ceiling to make a horizontal 2D grid of sensors suspending on the empty space of the chamber. The velocity of the exhaust air was measured by velocity sensor, which was installed inside the circular outlet ducting. A measurement and data collection unit with programmable measurement freq

19、uency was used for the data acquisition. All measurements were recorded every second and logged in the computer. 2011 ASHRAE 49During the course of the initial research reported in this paper, experiments have been carried out with step increases in both ventilation rate (over the range 9-40 m3.h-15

20、.30-23.5 cfm) and heating power (over the range 40-170 W; 136.5-580 Btu.h-1). A typical example of these step experiments is given in figure 2. The figure shows inlet temperature response (third graph) during and experiment with steps increase in inlet ventilation rate (top graph) from 9 to 27 and t

21、o 40 m3.h-1(5.30, 15.9, and 23.5 cfm), and with steps up in heating power from 40 to 100 and to 170 W (136.5, 341, and 580 Btu.h-1)and down in reveres sequence. The step experiments are designed in such way that all the steps up and down in heating power are repeated with each step in ventilation ra

22、te with time period of 20 minutes for each step in heating power. 2D TEMPERATURE DISTRIBUTION AND SPATIAL CLASSIFICATION In this study a grid system that involves 5265 cells (8165) is built based on two-dimensional interpolation between the 30 temperature measurements points (65 sensors grid). Figur

23、e 3a shows a typical example for the 2D temperature spatial distribution using the (8165) grid system at ventilation rate of 9 m3.h-1(5.3 cfm) and 100 W (341.21 Btu.h-1) heating power. In order to have spatially fixed zones for control purposes the horizontal area of the test chamber is divided into

24、 20 equal squared cells (54) and the average temperature of each cell is calculated at each time instance null. The cell Figure 2. Measured steps in ventilation rate (top graph), steps in heating power (second graph), and the inlet temperature (third graph) Step.(3) Step. (2) Step. (1) 50 ASHRAE Tra

25、nsactionstemperatures are classified into predefined classes with a threshold of 0.3 oC (Figure 3b). In which a 20 nullmatrix contains nullsamples of the chamber inside temperatures nullnull, where null =1,2,.,20, is formed. Figure 3b illustrates the spatial temperature distribution over the 20 cell

26、s at ventilation rate of 9 m3.h-1(5.30 cfm) and 100 W (341.21 Btu.h-1) heating power. Some adjacent cells with same temperature are forming together larger zones such as the 6 adjacent cells with temperature 24.2 oC (Figure 3b). The temperature in each of these zones is considered to be uniform with

27、 temperature difference of 0.3 oC. It is observed that the number of these uniform zones is depending on both ventilation rate and inlet temperature. The number of uniform zones at 100 W heating power and ventilation rates of 9, 27, and 40 m3.h-1(Step.1, Step.2, and Step.3) are 7, 4, and 3, respecti

28、vely. DATA-BASED MODELS IDENTIFICATION AND PARAMETERS ESTIMATION In order to identify and model the temperature dynamics of each of the 20 defined cells in the test chamber, it would be preferable to perform experiments in which the inlet temperature nullnullnullis changing fast in a sufficiently ex

29、citing manner. In other words, the input should be chosen to induce changes in the output variables that are sufficiently informative to allow for the unambiguous estimation of the dominant dynamic characteristics. However, since the mechanism for generating such input perturbations in temperature i

30、s currently unavailable on the test chamber system, an alternative approach of applying step changes in ventilation rate and heating power was used. A typical example of which is shown in figure 2. Then the temperature response at the inlet, for given ventilation and heating power changes (steps), i

31、s used as an input nullnullnullto the system. The discrete-time Simplified Refined Instrumental Variable (SRIV) algorithm (Young et al., 1992) is used to identify the linear discrete-time Transfer Function (TF) model between nullnullnulland cell temperature nullnull(where null=1,2,.,20). Coefficient

32、 of Determination nullnullnulland the Young Identification Criterion nullnullnullare employed as mode structure identification criteria (see e.g. Young, 1989). For the first step (Step. 1) in Table 1, namely the response of cell temperature nullnullto steps increases in heating power from 40 up to 1

33、00 and 170 W and steps down in inverse sequence, and at ventilation rate of 9 m3.h-1(Figure 2). The identified TF model for the response of temperature nullnull(e.g. at cell null=16) to the changes in inlet temperature nullnullnulltakes the Figure 3. (a) 2D spatial distribution of the temperature in

34、 the test chamber visualised using the 5265 cells at ventilation rate of 9 m3.h-1(5.30 cfm) and 100W (341.21 Btu.h-1) heating power. (b) 20cells temperature distribution showing 8 thermal zones. a b IO24.2 oC 24.5 24.8 oC 24.5 oC 25.1 25.4 oC 24.8 oC 25.7 oC IO 2011 ASHRAE 51first order form, nullnu

35、ll(null) =nullnullnullnullnullnullnull(nullnullnull)nullnullnull(null) =nullnullnullnullnullnullnullnullnullnullnullnullnullnullnull(null) (null = 1,2,20) (1) where the model parameters nullnulland nullnullfor null=16 are -0.9935 and 0.0020, respectively. nullnullnullis the backward shift operator (

36、null.null.nullnullnullnull(null) = null(null 1). Figure 4 shows a comparison between the identified model output and the measured chamber temperature nullnullat cell number 16 (i.e.null=16) and the associated model error (residuals). The whole model estimation results for the three steps (Step.1, St

37、ep.2, and Step.3), namely at the three different ventilation step increases for cell 16 (as an example) are presented in Table 1. First order discrete TF model is a suitable fit to the data in all cases and at the whole 20 cells. The model showed high nullnullnullvalues (0.95 to 0.98) in all cases a

38、nd large negative nullnullnullvalues (-10 to -12), reflecting well defined model parameters estimated with small standard errors (shown in parentheses in Table 1). It is shown in Table 1 that for each ventilation step (Step.1, Step.2, and Step.3) a different first-order TF model is identified. From

39、the time constants null(Table 1), it is clear that the dynamic response of temperature nullnullis faster at high ventilation rate, in which null =47 seconds at ventilation rate of 40 m3.h-1(23.50 cfm) and null =153 seconds at ventilation rate of 9 m3.h-1(5.30 cfm). Table 1. Model estimation results

40、for the three steps Step.1, Step.2, and Step.3 Ventilation rate m3.h-1(cfm) nullnullnullnullnullnullFirst order TF 1,1,1 Model parameter estimates Time constant null(nullnullnull) null(nullnullnull) Step.1 9(5.30) 0.953 -11.1 -0.9935 (0.081) 0.0040 (0.0007) 153 sec Step.2 27(15.90) 0.975 -11.1 -0.98

41、83 (0.090) 0.0093 (0.0010) 85 sec Step.3 40(23.5) 0.976 -11.2 -0.9788 (0.094) 0.0097 (0.0009) 47 sec NON-MINIMAL STATE-SPACE NMSS REPRESENTATION AND PIP DESIGN The methodological approach for PIP control system design is based on earlier research (Young et al., 1987; Taylor et al., 2000), in which i

42、t is necessary to convert the TF model into a suitable NMSS form. Non-Minimal State-Space NMSS form The TF model can be represented by the following NMSS equations: null(null) =nullnull(null1)+nullnull(null1)+nullnullnull(null), null(null) =nullnull(null). (2) The null+nulldimensional non-minimal st

43、ate vector null(null)consists of the present and past sampled values of the output 52 ASHRAE Transactionsvariable null(null)and the past sampled values of the input variable null(null), i.e. null(null) =null(null) null(null1)null(nullnull+1) null(null1) null(null2)null(nullnull+1) null(null)null(3)

44、where null(null)is the integral-of-error between the reference or command input (set-point) nullnull(null)and the sampled output null(null)defined as follows: null(null) =null(null1)+nullnull(null)null(null) (4) The state transition matrix null, input vector null,command input vector null,and out pu

45、t vector nullof the NMSS system can be found in the earlier literatures (e.g. Young et al., 1994; Taylor et al., 2000). Proportional-Integral-Plus PIP control The State Variable Feedback SVF control law (e.g. Taylor et al, 2000) associated with the NMSS form 2 takes the usual form: Figure 4. Inlet t

46、emperature (top graph) and response of the chamber temperature nullnullat cell 16 (measured temperature) together with the identified model (modelled temperature) and model residuals (bottom graph). 2011 ASHRAE 53null(null) =nullnull(null) (5) where nullis the null+nulldimensional SVF control gain v

47、ector null=nullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnull (6) where nullnulland nullnullare the proportional and integral actions, respectively, which are enhanced by higher order input and feedback compensators null(nullnullnull) and nullnull(nullnullnull), respectively. nullnull(

48、nullnullnull) =nullnullnullnullnull+nullnullnullnullnullnull(nullnullnull), null(nullnullnull) =1+nullnullnullnull+nullnullnullnullnullnull(nullnullnull)(7) The closed-loop PIP control system is presented in the block diagram representation illustrated in Figure 5. Simulation example for PIP control From the fist order TF model 1: nullnull(null) =nullnullnullnull(null1)+nullnullnullnullnull(null 1), (8) From equation 3: null(null) =nullnull(null) null(null), (9) and fro