Modelling the behaviour of controllers in an HVAC system - a case study -

Transcription

1 Department of the Built Environment Unit Building Physics and Services Masterproject 2 Author T.J. Baas BSc Modelling the behaviour of controllers in an HVAC system - a case study - Supervisors Ir. R.P. Kramer Dr. ir. A.W.M. van Schijndel Date April 2015 Place Eindhoven

2 Masterproject 2 Modelling the behaviour of controllers in an HVAC system - a case study - A research of Eindhoven University of Technology In collaboration with Strukton Worksphere bv Masterproject 2 Eindhoven, April 2015 Author: T.J. Baas BSc ID Supervisors: Ir. R.P. Kramer Dr. ir. A.W.M. van Schijndel Eindhoven University of Technology Den Dolech AZ Eindhoven The Netherlands Tel: +31 (0) cec@tue.nl All rights reserved. Nothing out this paper may be copied, multiplied and/or may be published by print, photocopy, microfilm or any other way without prior permission of the Eindhoven University of Technology. Copyright 2015 Eindhoven University of Technology

3 Abstract At Eindhoven University of Technology (TU/e), practical buildings and systems are often modelled for research purposes. These simulations are often based on Matlab oriented software. With the HAMBase building model, developed by the university itself, one is able to model the heat and vapour flow in a building very accurate. Because HAMBase is based on Matlab, system models can easily be imported from Simulink. One is also able to build accurate system models with Simulink, but many difficulties are experienced while modelling the control behaviour in the systems. Therefore, a new research project was set up, which focusses solely on the modelling of the control behaviour in HVAC systems. A research is set up in collaboration with Strukton Worksphere bv. Strukton can offer a large amount of measurement data from HVAC systems and is always interested in potential energy savings within HVAC systems. The HVAC system of the Strukton office itself is used as case-system for the simulation study. This case system is, like most HVAC systems in the Netherlands, controlled by the Priva building management system (BMS). The simulation study focusses on the modelling of the controllers in this BMS. With the combination of these controller models and a system model of the AHU, a test model for control strategy studies can be created. Conventional PID controllers are widely applied for the control of HVAC systems. Although the basic structure of a PID controller is rather simple, a lot of different configurations exist. With different PID structures and features as anti-windup, many different configurations can be created. Eventually, the exact algorithm of the controller in Priva is found and a model could be built. The controller model, built in Simulink, shows very accurate simulation results compared to the measurement data. With the controller model available, a sensitivity study is performed in order to test the influence of some controller specifications on the model output. It was found that, based on stationary feedback signals, the influence of the data logfrequency and the anti-windup method is significantly large. The performance of the different controllers in the case system is evaluated using the measurement history of Performance indicators on long term performance and smoothness are calculated for each controller and compared afterwards. It was found that the controllers of the heating- and cooling coil performed significantly worse compared to the heat exchanger controller. This is probably caused by the dead time in the system, but further research may conclude if energy savings can be achieved by loop tuning. With this research, a model is built which can accurately simulate the control behaviour in an HVAC system. Further research is proposed to link the controller model to a process model, in order to allow studies on the robustness of the controller. With the model of the controller, also a starting point for control strategy studies is made. When the controller models are linked to simulation models of the components in the case system, a perfect case model for control strategy studies is created. This model can be used for studies on performance tuning and energy consumption reduction of HVAC systems. The modelling of the system components and linking to a control loop model is therefore highly recommended.

4 Table of contents Title Modelling the behaviour of controllers in an HVAC system Abstract 3 1 Introduction Background Previous research of the TU/e Research setup 6 2 Theory PID controllers PID algorithms Integrator windup Control loop performance tuning Control loop performance evaluation 11 3 Method Case building Measurement data Controller modelling Sensitivity and performance evaluation 14 4 Results Controller configuration Model sensitivity Controller performance 20 5 Discussion and recommendations Controller model Sensitivity study Performance evaluation Recommendations 21 6 Conclusions 23 7 References Literature Software Model references 25

5 Table of contents Title Modelling the behaviour of controllers in an HVAC system Appendices: I. System diagrams Strukton Son 26 II. Control schemes 28 III. Monitoring overview 30 IV. Specifications air handling unit 31

6 1 Introduction In the first part of this chapter, some relevant background information is given, followed by the problem definition and research setup in the second part. 1.1 Background At Eindhoven University of Technology (TU/e), practical problems in buildings are often modelled for research purposes. For the modelling, different software tools are used. Heat and vapour flows within the building are modelled with HAMBase. HAMBase is a multi-zone building model based on Matlab and is developed by the TU/e itself. Using HAMBase, one is able to perform accurate simulations on practical issues. In addition to the building model, Simulink is often used to simulate the (HVAC) systems in the building. Both HAMBase and Simulink are based on Matlab, which makes it easy to integrate a Simulink model into a HAMBase model. Using Simulink, one is able to build an accurate model of the building s systems. However, many difficulties are experienced during simulation of the controllers in the system. A lack of knowledge on the exact algorithm and behaviour of the controllers makes it hard to perform an accurate simulation. Besides the lack of knowledge, time is also a limiting factor while simulating the control systems. Therefore, specific research on the modelling of such controllers is needed. As designing-, developing- and exploitation firm in building services, Strukton Worksphere manages about 300 buildings within the Netherlands. The systems managed by Strukton are all controlled by a third party building management system (BMS). Control signals sent by the controllers in the software are shown by the BMS, but the actual control strategy of the controllers itself is often shielded. Knowledge on the actual behaviour of the controllers provides the key access to performance studies for the company. Most of the monitored data of the buildings managed by Strukton Worksphere is stored by the building management system. Therefore, appropriate data to validate a software model is largely available. Priva is an international developing and supplying firm of control systems for the built environment and horticulture. Priva is a world leading company in control systems for horticulture and is with its Top-Control building management system also market leading company in the Netherlands, with a market share of about 50%. From the buildings managed by Strukton Worksphere, is 85% equipped with Priva Top-Control. All these management systems of Priva are built up with the same (PID) controllers. Simulating control systems like Priva Top-Control are a big issue for the TU/e in performance studies on for example museums. Understanding the control behaviour of the BMS is also very important for ATES balancing studies, which are major issues in the Netherlands nowadays (Hoving, 2015). 1.2 Previous research of the TU/e Previous to this research project, another research of the TU/e is performed on controllers in HVAC systems. The master s student M. Niesen built up a Simulink model of a test setup HVAC system (Niesen, 2010), built at the Colorado State University. The test setup was part of an academic research on the Colorado State University (Anderson, et al., 2007). The objective of the research project of Niesen was to build up a model of an Air-Handling-Unit (AHU), in order to analyse different controllers and controlling strategies. The model build by Niesen consisted of multiple SISO (Single Input Single Output) PI controllers. The Simulink-model of the AHU can be used as reference model to test and analyse different controllers and control strategies in further research. 1.3 Research setup As explained in section 1.1, research on the behaviour of controllers in an HVAC system is needed. A research project is started in order to get insight in the actual behaviour of controllers in such system. The simulation model is also sufficient for future work control strategy studies. For this research, a case building of Strukton is used to validate the simulation model. As case building, the office building of Strukton Worksphere in Son is used. The air-handling-unit (AHU) of the building is modelled using the Simulink software and validated with real-time monitored data of the BMS. 6 Modelling the behaviour of controllers in an HVAC system

7 Objective The objective of this research is to build up a Simulink-model of an HVAC system, including its controllers, and being able to perform accurate simulations on the behaviour of the system and its controllers. In order to validate the model, detailed measurement data of a case-building is used. The following research question is used as guidance for the research project: Can the actual behaviour of an HVAC system, determined by its controllers, be accurately simulated, according to data from real-time measurements? Figure 1.1 shows the structure of the research project used to answer the research question. All stages in the structure could, unfortunately, not be accomplished in this project. This is mainly due to drawbacks in controller simulation and a limited amount of time available for the project. Further research is needed for the remaining stages in the structure. The grey-hatched boxes in the structure represent the stages accomplished in this research project. Further research is proposed to fulfil the remaining part of the research structure. These research proposals can be found in chapter 5.4. This first part of the research project provides answers to the following research questions: 1. What are the state of the art techniques used in PID-control of HVAC components? 2. Can the behaviour of individual controllers in an appropriate case system be accurately modelled with Simulink? 3. Which tuning methods for PID controllers can be used for the controllers in the case system? 4. What is the sensitivity of the controller s simulation model to the different components of the controller? 5. Is it possible to give an indication of the performance of the controllers in the case system? Figure 1.1; Structure of the research The report is build up as follows: Chapter one describes the problem definition, the research setup and some background information of the project. In the second chapter, a brief overview is given of the some relevant theory found during the literature review. Chapter three describes the research method, followed by the results in chapter four. The results are discussed and further research is proposed in chapter five. The conclusions are drawn in chapter six and the references to literature and corresponding modelling files can be found in chapter seven. Finally, some additional relevant information can be found in the appendices. 7 Modelling the behaviour of controllers in an HVAC system

8 2 Theory Below, a brief overview is given of the theory on PID controllers, controller algorithms, anti-windup schemes, control loop tuning and finally on evaluation techniques. 2.1 PID controllers Automatic controllers are a key issue in most automatic processes. The controllers can be used to regulate for example flow rates, temperatures, pressures etc. in automated processes. The most common controller used in (industrial) processes is the PID-controller. This controller is named after the Proportional, Integral and Derivative mode in the controller. The controller is based on feedback-control, it compares the measured process variable with its setpoint. The calculated difference between the measured value and the setpoint is called the error. Based on the error and the input settings, the PID controller sends an output to keep the process variable at its setpoint. Proportional control The proportional mode in the controller changes the controller output in proportion to the input, the error. The proportional factor is called the controller gain or proportional gain. By increasing the proportional gain, the controller will react faster to an error. However, when the proportional gain is set too high, the system will begin oscillating. If the proportional gain is set too low, the controller won t react adequately on errors. A major drawback when applying proportional control only is offset. When for example the load on a heating system suddenly changes, an error will occur. The control signal will respond proportional to this error. However, at one point the control signal will become equal to the error. The measured error will then become zero and the control signal will stay constant. Therefore, using proportional control only will always lead to an offset. Integral control One way to eliminate the offset due to proportional control is implementing integral control. The integral mode integrates the error over time. Therefore, it will increase or decrease the control signal as long as there is an error present. The speed of the integral action depends on the magnitude of the error and the integral time, which is an input setting for the integral control mode. The integral mode of a PID controller is switched off by selecting an integral time of zero. Derivative control The third control mode in PID controllers is the derivative control. By differentiation of the error, the control signal will respond more rapid on increments and decrements of the error. However, derivative control is rarely used for HVAC systems, mostly since such quick response is not really necessary for HVAC systems and derivative control makes the tuning of the controller more complex. By setting the derivative time to zero, the derivative mode in the PID controller is switched off. Figure 2.1 shows the recovery of the heating temperature after a sudden change in load. The recovery is shown for proportional (P), proportional-integral (PI) and proportional-integral-derivative (PID) control. Figure 2.1; System recovery for P, PI and PID control (Smuts J., PID Controllers Explained, 2011) 8 Modelling the behaviour of controllers in an HVAC system

9 2.2 PID algorithms In total, three different PID algorithms are arranged by manufacturers (Smuts J., 2010). The three algorithms are called interactive algorithm, non-interactive algorithm and parallel algorithm. Figure 2.2 shows a schematic diagram of the different algorithms. The oldest PID algorithm is the interactive algorithm, also known as series algorithm. It is represented by equation 2.1. Interactive u(t) = K c (e(t) + 1 τ i e(t) dt) (1 + τ d d dt ) [2.1] The second algorithm shown in figure 2.2 is the non-interactive algorithm, also known as ideal algorithm. If no derivative control is used (τ d = 0), the non-interactive algorithm will be equal to the interactive algorithm. The noninteractive algorithm is represented by: Non-interactive u(t) = K c (e(t) + 1 τ i e(t) dt + τ d de(t) dt ) [2.2] The last PID algorithm is the parallel algorithm. This is the only algorithm using a proportional gain (K p ) instead of a controller gain (K c ). The proportional gain doesn t influence the integral and derivative control, where the controller gain does. The parallel form of the algorithm makes tuning of the controller much more complex. This algorithm is therefore rarely applied. Equation 2.3 gives a representation of the algorithm. u(t) = K p e(t) + K i e(t) dt + K d de(t) dt [2.3] Parallel Figure 2.2; Schematic diagram different PID algorithms 2.3 Integrator windup A major drawback of PID controllers is integrator windup. This occurs when the actuator saturates, which causes an error in the feedback signal. The integrator will continue integrating while the actuator is fully saturated and the integral value will become very large. Even when the error decreases the actuator still saturates, which leads to large overshoots and settling times. This integration error is known as integrator windup. A lot of PID-configurations exist to avoid integrator windup. In a document by Warsaw University of Technology alone, thirteen different configurations were shown (Warsaw University of Technology). The configurations can basically be divided in two different approaches, conditional integration and back calculation. Also combinations of the two different approaches exist. Back calculation Back calculation is an approach which is used to avoid integrator windup. Back calculation is first proposed by Fertik and Ross, already in The approach is based on tracking. Basically, a controller provided with back calculation knows two different operation modes. In case the actuator is not saturated, the controller acts as an ordinary controller. Once the actuator saturates the integral is recomputed so its new value gives an output at the saturation level. Figure 2.3 shows a block diagram of a PID controller provided with back calculation. The rate of resetting the integral can be adjusted by the so called tracking time constant τ t. Figure 2.3; Block diagram of a PID controller provided with back calculation 9 Modelling the behaviour of controllers in an HVAC system

10 Conditional integration Another approach to avoid integrator windup is conditional integration, also called integrator clamping. With this approach the integral action is only used when certain conditions are met (no saturation for example). Visioli defined four different forms of conditional integration (Visioli, 2003): 1. The integral term is limited to selected limits. 2. The integration is stopped when the system error is large, i.e. when e > ē, where ē is a selected value. 3. The integration is stopped when the controller saturates, i.e. when u u s. 4. The integration is stopped when the controller saturates and the system error and the manipulated variable have the same sign, i.e. when u u s and e u >0. Also an alternate version of scheme 3 exists, where the integral term is kept at a prescribed value during controller saturation. This approach is also called preloading. Previous research has shown that scheme 4 performs best (Hansson, Gruber, & Tödtli, 1994) (Rundqwist, 1991). Combination of approaches Several researches have proposed new anti-windup configurations, based on a combination of the two approaches mentioned. Configurations proposed can for example be found in (Bohn & Atherton, 1995), (Hodel & Hall, 2001) and (Visioli, 2003). 2.4 Control loop performance tuning In order to optimize control loop performance, several hundreds of tuning methods exist for the PID parameters, most of them recorded since 1992 (O'Dwyer, PI and PID controller tuning rules: an overview and personal perspective, 2006). The most well-known and widely applied tuning rules are the Ziegler- Nichols rules, recorded already in 1942 (Ziegler & Nichols, 1942). Eleven years after the Ziegler-Nichols tuning rules were published, Cohen and Coon published their tuning rules. The Cohen-Coon rules are based on the same tuning objective as the Ziegler-Nichols rules, but are applicable for a wider variety of processes and therefore also widely applied. The Cohen-Coon rules work well for processes with L<2τ, while the Ziegler-Nichols rules work well for processes with L<0.5τ (where L is the dead time and τ is the time constant of the process) (Smuts J., Cohen-Coon Tuning Rules, 2011). Finally, the IMC tuning rules (also known as Lambda rules) are also widely used (Rivera, Morari, & Skogestad, 1986). The IMC rules are more based on robustness instead of fast step response, in contradiction to the Ziegler-Nichols and Cohen-Coon rules. But as mentioned before, there are many different tuning methods for PID controllers. Tuning objectives In order to find the most suitable tuning rules for a process, it is important to define the tuning objective. O Dwyer defined five different classifications of tuning rules (O'Dwyer, PI and PID controller tuning rules: an overview and personal perspective, 2006): Tuning rules based on a measured step response Tuning rules based on minimising an appropriate performance criterion Tuning rules that give a specified closed loop response Robust tuning rules, with an explicit robust stability and robust performance criterion built in to the design process Tuning rules based on recording appropriate parameters at the ultimate frequency One of the tuning objectives based on step response is called Quarter Amplitude Decay (QAD). QAD is based on fast step response, which leads to relatively large overshoots. Like the name of the objective suggests, the amplitude of the oscillation cycles decays with factor 4. Ziegler-Nichols, Cohen-Coon and many other tuning rules are based on QAD. The IMC tuning rules are robust tuning rules, giving good response on setpoint changes but give bad performances for integrating processes (Horn, Arulandu, Gombas, VanAntwerp, & Braatz, 1996). Many other tuning rules are based on error-integral, for eample minimising the Integral of Absolute Error (IAE) (O'Dwyer, Handbook of PI and PID Controller Tuning Rules (2nd Edition), 2006). 10 Modelling the behaviour of controllers in an HVAC system

11 Adaptive techniques Adaptive tuning techniques are developed in order to maintain the optimal PID settings throughout dynamic processes. Adaptive techniques were first introduced in 1983 and can generally be divided in three categories (Äström, Hägglund, Hang, & Ho, 1993): Automatic tuning Gain scheduling Adaptive control With automatic tuning (auto-tuning), a controller is tuned automatically. This tuning is however on demand of the user, which can be manually or pre-programmed. Using gain scheduling, the parameters are changed depending on a measured value (for example the system input or system output). Strategies where the parameters are continuously adjusted on the process dynamics and disturbances are called adaptive control. The on/off and traditional PID control techniques are still used in many HVAC systems (Afram & Janabi- Sharifi, 2014). Although it is multiple times shown that adaptive PI control has superior performance to that of classical PI control (Seem, 1998) (Zhang & Bai, 2007). Also research projects on combinations of PID control with Fuzzy control or neuron control for HVAC-control have proven to be successful, for example (Bai, 2013) (Soyguder, Karakose, & Alli, 2009) (Wang & Jing, 2006). 2.5 Control loop performance evaluation The feedback control loop of an HVAC system can be described by the schematic diagram shown in figure 2.4. Several indicators exist to evaluate the performance of control loops in general. One of the most commonly used performance evaluation techniques is the sensitivity function (Rivera, Morari, & Skogestad, 1986): S = e y s d [2.4] Figure 2.4; Feedback control loop HVAC system The variable d in the sensitivity function refers to the load disturbances, which are often hard to measure. Using the sensitivity function, it is preferable to keep the function as small as possible over a broad errorfrequency range. In order to evaluate step responses and the effect of load disturbances changes, Rivera et al. introduced the Integral Absolute Error (IAE) and the Integral Squared Error (ISE): ISE = (y y s ) 2 dt 0 IAE = y y s dt 0 [2.5] [2.6] In order to evaluate the input performance, Skogestad introduced the Total Variation (TV) of the input (Skogestad, 2003), which is a good indicator for the smoothness of the process. The total variation is the sum of all the increments and decrements of the process input u(t), assuming a discretized signal: TV = i=1 u i+1 u i [2.7] 11 Modelling the behaviour of controllers in an HVAC system

12 3 Method In this chapter the case building is described, as well as its HVAC system and the monitoring techniques of the system. Further, the research methods used for controller modelling and evaluation are discussed. 3.1 Case building As mentioned in chapter 1, the office building of Strukton Worksphere in Son is used as case building for the research project. The building has six floors and is provided with a parking lot, a restaurant and a total of 7500 square meter offices. The building is equipped with two air-handling-units, one providing the restaurant of fresh conditioned air, the other supplying fresh air for the offices. Since the AHU s are quite different, only the unit supplying air to the offices is modelled. The building is provided with a Priva Top-Control building management system. The volume- and energy flows in the HVAC system are broadly monitored by the building management system and additional sensors placed by the company itself. Figure 3.1 shows a schematic diagram of the AHU, detailed schematic diagrams of the building s services are enclosed as appendix I. Figure 3.1; Schematic diagram air-handling-unit case building The upper section of the AHU in figure 3.1 represents the flow of extracted air from the building (from right to left). The air is extracted by a fixed speed fan and flows through the rotary heat exchanger to the ambient. At the bottom section of the AHU, ambient air is extracted by a similar fixed speed fan. The supply air flows through respectively the rotary heat exchanger, heating coil and cooling coil. Reversible heatpumps are installed to supply conditioned water for the heating- and cooling coil and for additional space heating. The HVAC system is controlled by the BMS. The system control is built up from a master-slave control with four PI-controllers. The master loop controls the required temperature of the supply air and the activation of the different components in the system. The amount of power supplied by the heat exchanger, heating coil and cooling coil is controlled by individual PI-controllers. Figure 3.2 below gives a schematic overview of the control system. Detailed process control schemes are enclosed as appendix II. Figure 3.2; Control loop air handling unit 12 Modelling the behaviour of controllers in an HVAC system

13 3.2 Measurement data The AHU from the case building is broadly measured, both by the BMS and by external transmitters. The data from the BMS and the external transmitters is logged respectively per 4 and per 1 minute. Figure 3.3 gives an indication of the type and position of the measurements in the AHU (orange and purple circles). The orange circles in the figure indicate measurement point (Moisture [%RH] and Temperature [ C]), the purple circles indicate calculated values of the BMS (PI control signal [-] and Temperature [ C]). Figure 3.3; Schematic diagram AHU monitoring The data important for the modelling of the controller is the error signal (input of the controller) and the control signal (output of the controller). The input of the controller is the difference between the air supply temperature reached (T 9 ) and the air supply temperature calculated (T 10 ). The different control signals (PI 1, PI 2, PI 3, and PI 4 ) are outputs of the controllers and these values are used for validation of the simulation model. Remaining measurement points in the AHU are not directly of influence for the controller s behaviour, they are mostly relevant for the validation of the process models. An overview of all sensors in the AHU with its description is enclosed as appendix III. 3.3 Controller modelling To get insight in the behaviour of (PI-) controllers, a simulation model of the PI-controllers in the case system is built with Matlab/Simulink. The R2013a version of Mathworks Matlab/Simulink was used for the simulation study. The simulation model is fully built up in Simulink, using blocks from the basic Simulink library in the software. As explained in chapter 2, many different algorithms of PID controllers exist (different anti-windup schemes etc.). Knowledge on the algorithm of the controller is therefore essential when building a simulation model of the controller. Initially, the algorithm is tried to be found by trial and error and using the BMS-data for validation. Using trial and error, an approximation of the controller s behaviour could be made in Simulink. It was however not possible to reproduce the measured control signal of the validation data. Eventually, a meeting with the manufacturer of the BMS was set up, in order to trace the exact algorithm of the PIcontroller. 13 Modelling the behaviour of controllers in an HVAC system

14 3.4 Sensitivity and performance evaluation With the configuration of the controller known, a sensitivity study can be performed. Besides the sensitivity, also the performance of the controllers in the case system is evaluated. This chapter describes the method used for both evaluation studies. Sensitivity A sensitivity study shows the required knowledge level on the controller s specifications, when a controller is modelled. The influence on the controller s output is calculated for variations in: Integrator method (Backward Euler, Forward Euler and Trapezoidal) Sample time (1 second, 10 seconds and 60 seconds) Data frequency (1 second, 4 minutes and 10 minutes) Anti-windup approach (Back-calculation and without anti-windup) For each variation mentioned above, the simulation is performed and the controller s output logged. In order to compare the different sensitivities, agreements are calculated in mean values of the relative deviations, compared to the measurement data. Performance evaluation With the large amount of measurement data available, a performance evaluation of the controllers in the case system can be made. The controllers are evaluated based on their control hours, the hours the temperature is controlled by that specific controller. As performance indicator, the Integral Absolute Error and Total variation (equations 2.6 and 2.7) are used. After each performance is calculated, they are compared with each other for evaluation. 14 Modelling the behaviour of controllers in an HVAC system

15 4 Results The results of the simulation study on the PID controller of the case building are presented below. The plots that can be found in this chapter are results of the simulations with Matlab and Simulink. A list with the corresponding simulation files for each figure can be found in chapter 7.3. The used Matlab- and Simulink files are digitally enclosed with this report. 4.1 Controller configuration In order to trace the exact algorithm of the controller, a meeting was set up with the manufacturing firm of the BMS. This meeting provided more knowledge on the configuration of the controller, a practical approximation of the controller s configuration could be defined. This configuration is shown in figure 4.1. Figure 4.1; Schematic diagram PI-controller with clamping The configuration of the controller, according to Priva, has the interactive PID-form as main structure. For the case building, this form is similar to the non-interactive form, since no derivative control is used. The interactive PI-form is extended with a conditional integration anti windup feature. The anti-windup scheme used is the fourth form mentioned by Visoli: The integration is stopped when the controller saturates and the system error and the manipulated variable have the same sign, i.e. when u u s and e u >0. The values of K c, T i and the saturation limits of the controller can be defined by the user in the Priva software. Besides these variables, also an offset, dead time and T d can be defined in the software, but these are all set at zero for the case building. However, simulation results of a back-calculation type show better agreement with the validation data. The PID controller with back calculation used for the simulations is similar to the one discussed in chapter 2.3, but without derivative control and a tracking time constant τ t of 1. A schematic diagram of the PI controller with back-calculation which shows good agreement is shown in figure 4.2. The values of K c, T i and the saturation limits of the controller are similar to that used for the controller equipped with clamping control. Figure 4.2; Schematic diagram PI-controller with back-calculation 15 Modelling the behaviour of controllers in an HVAC system

16 The model of the PI controller is validated for two controllers of the case system, the heating coil (HC) and the heat exchanger in heating mode (HEH). Only differences between these controllers are the values of K c and T i, and the fact that the output of the HC-controller is rounded to integers. Figure 4.3 shows the control signals of the heat exchanger and the heating coil for Tuesday 31 th of April. Figure 4.3; Control signals April 31 th 2015 The control signal for the heat exchanger directly increases to 100% when the air handling units starts up. Additional heating power is provided by the heating coil in the morning, this signal is then also used to control the air temperature. In the afternoon, obviously less heating power is required. The control signal of the heating coil decreases to zero and the control signal of the heat exchanger is used to adequately control the air temperature. During start-up of the system, the control signal of the heating coil directly rises at 6:00 AM, while the signal of the heat exchanger starts rising a few minutes after 6:00 AM. This can be explained by the starting procedure of the system, as entered in the BMS. This standard starting-sequence of the BMS seems however not very convenient. During the project, it became clear that the interval of the measurement data is very important. The measurement data in the database of the case system has a measurement frequency of 4 minutes. This data was interpolated to seconds for the simulations. It however became clear that with measurement data of a higher frequency (measurements per second), much better agreement can be obtained for the simulation. But since all data was logged per 4 minutes, the data in the database of the case building became useless for further simulation purposes. The validation of the proposed controller model is therefore limited. The controller is validated for 3 days of measurement data, only the heating coil (HC) and the heat exchanger heating (HEH) were active during these days. Examples on the sensitivity of the data frequency can be found in chapter 4.2 and proposals on further research are given in chapter 5.4. The Simulink model with back calculation shows good agreement with the validation data, as can be seen in figure 4.3. Providing the model with clamping (conditional integrating) instead of back-calculation shows less agreement, the same holds for the standard PID-controller block in the Simulink library. In the meeting, Priva indicated that the controller may react inaccurate to errors of low magnitude (± 0.1 C). However, validation of the model, without considering inaccuracies for small errors, shows good agreement. Further validation of the controller is needed to investigate the accuracy for small errors and to determine the actual anti-windup method in the controller (clamping or back-calculation). 16 Modelling the behaviour of controllers in an HVAC system

17 4.2 Model sensitivity Chapter 4.2 shows the sensitivity of some relevant factors to the simulation agreement. Very important to note is that the controller model is not connected to a dynamic process, the feedback signal of the validation data is used as input of the controller model. This means that when the simulated signal deviates, the model will continue calculating from that deviation in the control signal instead of correcting itself. The sensitivities presented below will therefore only apply for cases where the feedback signal from the measurements is used. Integrator method The integration loop in the controller can be performed by use of different integration methods. The standard Simulink integrator block provides three different approaches: Forward-Euler, Backward-Euler and Trapezoidal integration. The model-configuration used for the plot in figure 4.3 makes use of Backward-Euler integration. This integration approach shows thus good agreement with the measurement data. Figures 4.4 and 4.5, show the model output for respectively the Forward-Euler and Trapezoidal integration approach. These both approaches show also good agreement with the measurements. Figure 4.4; Control signal April 31 th Forward Euler integration Figure 4.5; Control signal April 31th Trapezoidal integration Sample time Besides integration method, also the sensitivity to sample time is tested. The only distinction between the two different controllers in Priva is the sample time (1 and 10 seconds). The controller used in the case building works on a sample time of 10 seconds. The model used for figure 4.3 is also based on a 10 seconds sample time. Figures 4.6 and 4.7 show the output signal for sample times of respectively 1 and 60 seconds. Only for the 60 seconds sample time, shown in figure 4.7, a slightly divergent control signal can be obtained. This deviation is however very small. 17 Modelling the behaviour of controllers in an HVAC system

18 Figure 4.6; Control signal April 31 th second sample time Figure 4.7; Control signal April 31 th seconds sample time Data frequency As mentioned in chapter 4.1, the frequency of the measurement data is very important. For the output signal in figure 4.3, a data interval of 1 second was used. Mainly since the interval of 4 minutes had shown bad performance earlier. Figure 4.8 shows output of the same simulation model, but now based on a data interval of 4 minutes. As expected, a significant deviation in output signal can be obtained. The deviation also increases over time, this is because the controller continues calculating from the deviated output signal, as explained before. Figure 4.9 shows the simulated control signal for a 10 minutes data interval, which obviously amplifies the effect. Figure 4.8; Control signal April 31 th minutes data interval 18 Modelling the behaviour of controllers in an HVAC system

19 Figure 4.9; Control signal April 31 th minutes data interval Anti-windup method The final sensitivity discussed is that of the anti-windup method. As mentioned before, an anti-windup method is applied in the controller model. Figure 4.10 shows the importance of taking the anti-windup feature into account when building the simulation model. The figure shows a comparison between the measurement data, and the output signal of the model without the anti-windup feature for April 20 th. It shows a significantly large difference, which is again mainly caused by the fact that the controller continues calculating with a wrong input signal. Figure 4.10; Control signal April 20th Without anti-windup Sensitivity overview The differences between the measurement data and the different model outputs are converted to percentages mean absolute deviation. This deviation during operation hours is calculated in percentages for both the heating coil and the heat exchanger. These percentages are shown in table 4.1, to make a comparison between the sensitivities easier. Looking at the percentages, it can be seen that the controller is especially sensitive for the data frequency and the antiwindup approach. From experiments with the measurement data, a squared valve curve was found for the heating and cooling coil. This means that the deviation of % for the heating coil, can lead to a deviation of 443% (!) in energy consumption for this particular example. Sensitivity overview controller Mean abs Controller features deviation HEH HC Backward Euler 0,26% 6,49% Integration method Forward Euler 0,38% 6,67% Trapezoidal 0,28% 6,57% 1 second 0,35% 18,70% Sample time 10 seconds 0,26% 6,49% 60 seconds 0,87% 17,90% Data log frequency Anti-windup approach Table 4.1; Sensitivity overview controller 1 second 0,26% 6,49% 4 minutes 2,61% 37,82% 10 minutes 5,03% 52,59% Back-calculation 0,26% 6,49% None 0,00% 129,15% 19 Modelling the behaviour of controllers in an HVAC system

20 4.3 Controller performance Using the measurement data of 2014, a comparison can be made of the controller s performance. Table 4.2 shows the operation hours of each controller in However, when multiple controllers are active (for instance HEH and HC), only one controller is actively controlling the temperature and the second one is at a fixed level. The control hours in table 4.2 denote the hours the controller is actively controlling the air temperature. A comparison in share of the control hours between the four controllers in the system is shown in figure To evaluate the controller s performance, the Integral Absolute Error (IAE) and Total Variation (TV) of each controller are calculated over In addition to the IAE and TV, also the mean IAE and mean TV are calculated to make a performance-comparison of the different controllers easier. Results of these performance indicators are shown in table 4.3. Figure 4.12 shows a comparison between the performance indicators of each controller. The control hours of the HEC are zero over 2014, which means the performance indicators (IAE and TV) are also zero and are therefore left out of the plots. It can be noticed from the results that the heat exchanger (HEH) performs clearly better on IAE, compared to the coils (HC and CC). This is probably caused by the large dead time in the coilsystem, compared to the heat exchanger. The heat exchanger performs also better on the process smoothness, expressed in TV, but for TV the differences are smaller. Table 4.2; Operation hours 2014 Operation hours 2014 Operation Control Controller hours hours PID HEH PID HEC PID HC PID CC Figure 4.11; Control hour distribution Table 4.3; Performance evaluation per controller Performance criteria Performance evaluation per controller Different PID controllers PID HEH PID HEC PID HC PIC CC Operation hours [h] Control hours [h] IAE total [ C] IAE mean [ C] TV total [ C] TV mean [ C] Figure 4.12; Performance evaluation 2014: IAE and TV 20 Modelling the behaviour of controllers in an HVAC system

21 5 Discussion and recommendations In the first part of this chapter, results of the project are discussed (5.1 t/m 5.3). In the last section of the chapter, section 5.4, recommendations are given for further research. 5.1 Controller model A model of the controller is built in Simulink, based on the measurement data from the case building. Although a large amount of data-history is available, only few could be used for validation, due to the low frequency of data-logging. The final controller model is therefore based on little validation data (3 days), validation with additional data may be useful to guarantee its accuracy. 5.2 Sensitivity study With the final configuration of the controller known, a sensitivity study is performed. The sensitivity study showed the influence of individual controller specifications on the simulation outcome. The influences shown are however only valid for cases without a process-model, like this project. In process-modelling and in practical appliances, with interaction between controller and process, the controller would correct itself since it will receive a different feedback signal. But the results of the sensitivity study can be used for controlleronly modelling. 5.3 Performance evaluation For the performance evaluation, described in chapter 3.4 and 4.3, the data-history of 2014 is used. But like also mentioned before, the log frequency of this data is of significant influence on the modelling accuracy. The results of the performance evaluation have therefore to be taken with care. The results show however a clear pattern, which is most important to know. 5.4 Recommendations The model of the PI-controller is, as mentioned in section 5.1, based on relatively few validation data. Further research should determine if the proposed algorithm gives accurate results for a larger set of measurement data. Focus for these tests have to be on the anti-windup approach which is applied and the possible inaccuracy for small errors (±0.1 K). Further research is also needed to model the dead time, offset and derivative control functions of the Priva controller. This however, requires measurement data of a different case system, since the specific case system of the Strukton building doesn t use these functions. Within this project, the sensitivity of the Priva controller to different factors is tested. This sensitivity study shows the sensitivity of the controller model when the feedback control signal of the measurement data is used. This however doesn t show the dynamic behaviour of the controller. Further research is needed to combine the controller model with a process model. Such combined model would allow studies on the sensitivity, robustness and performance of the controller in dynamic situations. The performance evaluation study on the controller in the case study showed a significant difference in performance, between the controllers for the heat exchanger and the coils. This difference is probably caused by the larger amount of dead time for the coils. But the behaviour of the heating and cooling coil has high influence on the energy consumption, in contradiction to the heat exchanger. Further research on the performance of the controllers may therefore lead to improvements on energy consumption and thermal comfort. During the project was found that the data log-frequency of the case building was too low for accurate modelling. The large database, containing measurement data of multiple years, became more or less useless. It is therefore recommended for Strukton to start logging the important variables of the system per second, or per ten seconds, in order to build up a new database. Such database is preferable for the recommended further research. 21 Modelling the behaviour of controllers in an HVAC system

22 Control strategy studies With this research on the behaviour of controllers in an HVAC system, a solid start is made towards control strategy studies. The behaviour of the controllers can successfully be simulated, but the coupling with a system model is needed to get insight in the dynamic behaviour and performance of the control loop. Figure 5.1 shows the project stages needed to accomplish before control strategy studies can be performed. Within this project, a Simulink-model is built which can perform accurate dynamic simulations on the behaviour of the separate PI-controllers in the case-system. With this model, each slave control-loop (see figure 3.2) can be simulated. Further research is needed to build up an interactive control model which can be used to communicate between the separate PI-controllers and simulate the master control loop. Besides the control loop modelling, also system modelling is needed to build up an appropriate test model for control strategy studies. The AHU of the Strukton office in Son can be used as case-system for the system modelling. Further research is needed to build up accurate models of each component in the system, which can thereafter be combined into one single system model of the AHU (the track on the left side in figure 5.1). When both the control- and the system-model are built, they can be merged into one single Simulink model. With this model, a perfect test environment is created for control strategy studies on HVAC systems. Figure 5.1; Research structure Within this current project, a lot of background research is already performed on the system components and its monitoring. The monitoring overview and the specifications of the system s components which are already found are enclosed as respectively appendix III and IV. 22 Modelling the behaviour of controllers in an HVAC system

23 6 Conclusions This chapter evaluates the results of the research project, based on the research questions which are defined in chapter 1. The main research question for this project is: Can the actual behaviour of an HVAC system, determined by its controllers, be accurately simulated, according to data from real-time measurements? The answer on the main research question of the project is given in the last section of this chapter. First, answers are provided to the subquestions defined for the project. What are the state of the art techniques used in PID-control of HVAC components? The most widely applied control techniques in HVAC control are the conventional PID control strategies, often applied with for example anti-windup techniques. Research has shown potentials for automatic PIDtuning and adaptive control. More recent research also shows potentials for combinations of PID- and Fuzzyor Neuron control for HVAC systems. Such control techniques are however still rarely applied within the field of HVAC control. Can the behaviour of individual controllers in an appropriate case system be accurately modelled with Simulink? For this project, an accurate controller model is built for the PID controller used in leading building management software in the Netherlands. It is thus possible to accurately model the behaviour of individual controllers in an HVAC system. Important to note is that data with a high log frequency is needed for validation of the model. Which tuning methods for PID controllers can be used for the controllers in the case system? Practically, all tuning rules designed for PID controllers with the interactive and non-interactive form can be applied at the PI controllers in the case system. Defining a tuning objective would help selecting the best applicable tuning method. Looking at HVAC control, minimising error-integral based tuning could be a suitable objective. Besides manual tuning methods, also automatic- and adaptive tuning can be applied to the controllers in the case system. What is the sensitivity of the controller s simulation model to the different components of the controller? A sensitivity study was performed, in order to get an indication of the sensitivity of different controller components. Results of this study showed that the model can significantly be influenced by the data log frequency and the appliance of an anti-windup approach. It was also showed that the sensitivity to integration methods was low and the sensitivity to the controller s sample time was in between. If have to be noted that the sensitivity study is based on a non-dynamic feedback signal. Is it possible to give an indication of the performance of the controllers in the case system? With the large database of the case system available, a performance evaluation could be made of the different controllers in the case system. This performance evaluation showed that the performance of the controllers which are controlling the heating- and cooling coil was significantly lower than that of the controller controlling the heat exchanger. This difference in performance is probably caused by the dead time in the coil-system, further research is proposed to examine possible performance improvements. Based on the answers to the subquestions above, an answer can be derived for the main research question. With this project, a model of the Priva controller is built in Simulink. This model is shown to be very accurate, looking at the plots in chapter 4. In order to model the total (control) behaviour of the HVAC system, the master loop has to be modelled to connect the different controllers. First tests of the interaction between two controllers have proven to be successful and schematic diagrams of the master loop are made as well. So in answer to the research question, it is possible to build accurate simulation models for the actual control behaviour in an HVAC system. This project is a start towards detailed HVAC behaviour simulations and performance optimization studies. 23 Modelling the behaviour of controllers in an HVAC system

24 7 References 7.1 Literature Afram, A., & Janabi-Sharifi, F. (2014). Theory and applications of HVAC control systems - a review of model predictive control (MPC). Building and Environment 72, Anderson, M., Buehner, M., P., Y., Hittle, D., Anderson, C., Tu, J., et al. (2007). An experimental system for advanced heating, ventilating and air conditioning (HVAC) control. Energy and Buildings 39, Äström, K., Hägglund, T., Hang, C., & Ho, W. (1993). Automatic tuning and adaptation for PID controllers - a survey. Control Eng. Practice (Vol.1 No.4), Bai, J. (2013). Development an Adaptive Incremental Fuzzy PI Controller for a HVAC system. INT J Comput Commun 8, Bohn, C., & Atherton, D. (1995). An analysis package comparing PID anti-windup strategies. IEEE Control Systems (Vol. 15), Chen, Y., & Treado, S. (2013). Development of a simulation platform based on dynamic models for HVAC control analysis. Energy and Buildings. Hansson, A., Gruber, P., & Tödtli, J. (1994). Fuzzy anti-reset windup for PID controllers. Control Eng. Practice Vol.2 No.3, Hodel, A., & Hall, C. (2001). Variable-structure PID control to prevent integrator windup. IEEE transactions on industrial electronics (Vol. 48, No. 2), Horn, I., Arulandu, J., Gombas, C., VanAntwerp, J., & Braatz, R. (1996). Improved filter design in Internal Model Control. Ind. Eng. Chem. Res. 35, Hoving, J. (2015). Maintaining ATES balance using continuous commissioning and model predictive control. Eindhoven: Eindhoven University of Technology. Niesen, M. (2010). Optimalisatie regelsystemen. Eindhoven: Eindhoven University of Technology. O'Dwyer, A. (2006). Handbook of PI and PID Controller Tuning Rules (2nd Edition). London: Imperial College Press. O'Dwyer, A. (2006). PI and PID controller tuning rules: an overview and personal perspective. Dublin: Dublin Institute of Technology. Rivera, D., Morari, M., & Skogestad, S. (1986). Internal Model Control. 4. PID Controller Design. Ind. Eng. Chem. Process Des. Dev. 25, Rundqwist, L. (1991). Anti-reset windup for PID controllers (PhD thesis). Lund: Studentlitteratur AB. Seem, J. (1998). A new Pattern Recognition Adaptive Controller with application to HVAC systems. Automatica (Vol.34 No.8), Skogestad, S. (2003). Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control 13, Smuts, J. (2010, March 30). PID Controller Algorithms. Retrieved February 20, 2015, from Opticontrols: Smuts, J. (2011, March 24). Cohen-Coon Tuning Rules. Retrieved March 3, 2015, from Opticontrols: Smuts, J. (2011, March 07). PID Controllers Explained. Retrieved February 20, 2015, from Opticontrols: Soyguder, S., Karakose, M., & Alli, H. (2009). Design and simulation of self-tuning PID-type fuzzy adaptive control for an expert HVAC system. Expert Systems with Applications 36, Visioli, A. (2003). Modified anti-windup scheme for PID controllers. IEE Proc.-Control Theory Appl. Vol. 150, Wang, J., & Jing, Y. (2006). Study of neuron adaptive PID controller in a single-zone HVAC system. Conference of: Innovative Computing, Information and Control, Warsaw University of Technology, I. (n.d.). Integral Anti-Windup for PI Controllers. Retrieved February 13, 2015, from Warsaw University of Technology: Zhang, X., & Bai, J. (2007). A new adaptive PI controller and its application in HVAC systems. Energy Conversion and Management 48, Ziegler, J., & Nichols, N. (1942). Optimum settings for automatic controllers. Transactions of the A.S.M.E. (November 1942), Modelling the behaviour of controllers in an HVAC system

25 7.2 Software Simulations were performed, using the following software: - Mathworks MATLAB R2013a - Mathworks Simulink 8.1 (R2013a) 7.3 Model references Some figures in the report contain plots from the Matlab- and/or Simulink simulations. These simulation files used for the project are all digitally enclosed by this report. Below, a reference is made between the figures in the report containing those plots and their corresponding simulation files. Figure nr: Page Figure 4.3; Control signals April 31th Matlab: DATA m Simulink: PI_controller_interaction.slx Figure 4.4; Control signal April 31th Forward Euler integration 17 Matlab: DATA m Simulink: PI_controller_interaction_ForwardEuler.slx Figure 4.5; Control signal April 31th Trapezoidal integration 17 Matlab: DATA m Simulink: PI_controller_interaction_Trapezoidal.slx Figure 4.6; Control signal April 31th second sample time 18 Matlab: DATA _sample1.m Simulink: PI_controller_interaction_sample1.slx Figure 4.7; Control signal April 31th seconds sample time 18 Matlab: DATA _sample60.m Simulink: PI_controller_interaction_sample60.slx Figure 4.8; Control signal April 31th minutes data interval 18 Matlab: DATA _data4min.m Simulink: PI_controller_interaction.slx Figure 4.9; Control signal April 31th minutes data interval 19 Matlab: DATA _data10min.m Simulink: PI_controller_interaction.slx Figure 4.10; Control signal April 20th Without anti-windup 19 Matlab: DATA m Simulink: PI_controller_interaction_withoutantiwindup.slx Figure 4.11; Control hour distribution 20 Matlab: Performance_2014.m Figure 4.12; Performance evaluation 2014: IAE and TV 20 Matlab: Performance_2014.m 25 Modelling the behaviour of controllers in an HVAC system

26 I. System diagrams Strukton Son The figure below indicates the schematic diagram of the heating and cooling circuit of the case building. 26 Modelling the behaviour of controllers in an HVAC system

27 The figure below indicates the schematic diagram of the air handling circuit of the case building. 27 Modelling the behaviour of controllers in an HVAC system

28 II. Control schemes Below, a schematic diagram of the starting loop of the AHU at the case building is shown. 28 Modelling the behaviour of controllers in an HVAC system

29 Below, a schematic diagram is shown of the control loop which determines the supply temperature setpoint. 29 Modelling the behaviour of controllers in an HVAC system

30 Not used Not used Technische Universiteit Eindhoven University of Technology III. Monitoring overview Below a schematic diagram is shown which indicates the positions of the sensors used for the project. The sensors are listed in the tables beneath the figure. At the moment of writing, the sensors T4 and M3 are being replaced due to bad performances. Wisensys measurements Nr. ID Code Strukton Description Unit M1 639 Base_ TT_007 - Humidity Measurement - Relative humidity extraction air after HE % RH M Base_ TT_012a - Humidity Measurement - Relative humidity supply air after HE % RH T1 640 Base_ TT_007 - Temperature Measurement - Temperature extraction air after HE C T Base_ TT_012a - Temperature Measurement - Temperature supply air after HE C 1905 Base_ TT_012 - Temperature Measurement - Temperature supply air after HE C 665 Base_5 - dp_cooling_ind - Voltage Measurement - Pressure difference cooling circuit kpa 664 Base_5 - dp_heating_ind - Voltage Measurement - Pressure difference heating circuit kpa 62 Base_5 - pyranometer - Low Voltage Measurement - Solar irradiation W/m² PRIVA History Nr. ID Code Strukton Code Vision Description Unit M2 282 SWS_PAND_OS1_GRFMET_72 357UT1 Measurement - Relative humidity extraction air % RH PI1 294 SWS_PAND_OS1_GRFPID_4 207M1 Calculated value - PID heat exchanger heating % PI2 295 SWS_PAND_OS1_GRFPID_5 207M1 Calculated value - PID heat exchanger cooling % PI3 292 SWS_PAND_OS1_GRFPID_6 329CV1 Calculated value - PID heating coil % PI4 325 SWS_PAND_OS1_GRFPID_8 329CV2 Calculated value - PID cooling coil % T2 281 SWS_PAND_OS1_GRFMET_47 357UT1 Measurement - Temperature extraction air C T3 255 SWS_PAND_OS1_GRFMET_1 310TT1 Measurement - Ambient air temperature C T5 293 SWS_PAND_OS1_GRFMET_36 332TT7 Measurement - Incoming water temperature heating coil C T6 290 SWS_PAND_OS1_GRFMET_37 356TT1 Measurement - Outgoing water temperature heating coil C T7 288 SWS_PAND_OS1_GRFMET_40 356TT2 Measurement - Incoming water temperature cooling coil C T8 289 SWS_PAND_OS1_GRFMET_41 356TT3 Measurement - Outgoing water temperature cooling coil C T9 287 SWS_PAND_OS1_GRFMET_46 356TT4 Calculated value - Temperature air supply C T SWS_PAND_OS1_GRFSYS_79 356TT4 Measurement - Temperature air supply C 283 SWS_PAND_OS1_GRFMET_28 356TT6 Measurement - Room temperature 4th floor C 284 SWS_PAND_OS1_GRFMET_29 356TT7 Measurement - Room temperature 3rd floor C 285 SWS_PAND_OS1_GRFMET_30 356TT8 Measurement - Room temperature 2nd floor C 286 SWS_PAND_OS1_GRFMET_31 357TT1 Measurement - Room temperature 1st floor C 30 Modelling the behaviour of controllers in an HVAC system

31 IV. Specifications air handling unit This document describes the specifications of the AHU which were, during this project, found for modelling purposes. Some specifications, like the flow quantities, may change over time. The product specifications below are based on the product specifications of the AHU-manufacturer (Carrier Airovision 2009). Heat exchanger: Design conditions: Type: Hygroscopic Inlet: -10 C Material rotor: Aluminium 90 % RH Nominal power: kw Outlet: 9.1 C Efficiency latent: 47 % 54 % RH Efficiency dry: 60 % Air flow resistance: 188 Pa Heating coil: Design conditions: Type: Water to air Air inlet: 9 C Nominal power: kw Air outlet: 21 C Air flow resistance: 47 Pa Water inlet: 45 C Water flow resistance: 6 kpa Water outlet: 37 C Tube diameter: mm Air flow rate: m³/s Tube thickness: 0.35 mm Water flow rate: 4.49 l/s Fin distance: 2 mm In-coil air velocity 2.95 m/s Fin thickness: 0.12 mm Cooling coil: Design conditions: Type: Water to air Air inlet (dry): 27 C Nominal power: 235 kw Air inlet (wet): 21.1 C Air flow resistance (wet): 235 Pa 60 % RH Air flow resistance (drip): 27 Pa Air outlet (dry): 15 C Water flow resistance: 15 kpa Air outlet (wet): 14.9 C Tube diameter: 16.5 mm 99 % RH Tube thickness: 0.4 mm Water inlet: 9 C Fin distance: 2 mm Water outlet: 15 C Fin thickness: 0.13 mm Air flow rate: m³/s Water flow rate: 9.36 l/s In-coil air velocity: 2.97 m/s Supply fan: Manufacturer: Nicotra Gebhardt Type: RZR Fixed speed fan Nominal power: kw Efficiency: 82 % Rotational speed (fan): 950 rpm Air flow rate: m³/s Air supply velocity: 8.11 m/s System pressure: 78 Pa External pressure: 300 Pa Dynamic pressure: 39 Pa Total pressure: 1234 Pa 31 Modelling the behaviour of controllers in an HVAC system

32 Extraction fan: Manufacturer: Nicotra Gebhardt Type: RZR Fixed speed fan Nominal power: 11 kw Efficiency: 83 % Rotational speed (fan): 834 rpm Air flow rate: 9.72 m³/s Air supply velocity: 7.67 m/s System pressure: 70 Pa External pressure: 350 Pa Dynamic pressure: 35 Pa Total pressure: 935 Pa Performance curve The figure below shows the performance curve of both the extraction and supply fan. The figure originates from the product specifications of the manufacturer (Nicotra Gehardt Centrifugal Fans RZR, belt driven (2013). 32 Modelling the behaviour of controllers in an HVAC system