MODEL BASED OPTIMAL CONTROL FOR INTEGRATED BUILDING SYSTEMS

Transcription

1 MODEL BASED OPTIMAL CONTROL FOR INTEGRATED BUILDING SYSTEMS A. Yahiaoui 1, J. Hensen 1, L.Soethout 2, D. van Paassen 3 1 Center for Buildg & Systems TNO-TU/e, 56MB Edhoven, Netherlands 2 TNO Built Environment and Geosciences, 26AA Delft, Netherlands 3 Department of Mechanical Engeerg, TU Delft, 2628CD Delft, Netherlands a.yahiaoui@bwk.tue.nl ABSTRACT: Buildg performance simulation has traditionally concentrated on the use of basic and conventional control methods, which are of limited use sce they cannot solve all the challenges encountered. With this regard, there is a great terest the concept of modern control strategies for tegrated buildg systems. To explore this potential, the paper focuses maly on the application of model-based optimal control to buildgs. In this case, a performance criterion mimized by lear programmg is proposed order to mata the temperature of door environment comfortable while mimizg energy consumption. Particularly, this paper is concerned with the relevance and reliability of tegratg control and buildg performance simulation environments by run-time couplg, over TCP/IP protocol suite. In addition, this paper volves a case-study with two important steps; the first step consists of experiments obtaed a test-cell that demonstrate the potential ability of advanced control strategies buildgs, and then simulation results are obtaed with the use of distributed control and buildg performance simulation software by run-time couplg. Keywords Buildg performance simulation, run-time couplg, model-based optimal control, and energy consumption. 1. INTRODUCTION Modern control theory is an emergent disciple that has been maly applied to large-scale projects and complex systems, used broadly aeronautic, automobile and space dustry sce early sixties. For the buildg doma, there is still a need for developg optimal control strategies for rapid response of HVAC (Heatg, Ventilation and Air-Conditiong) and lightg systems of buildgs to achieve the desired comfort (cludg its effect on satisfaction and productivity) while mimizg energy consumption and cost. Especially the advent of computer-based Buildg Automation Systems (BAS) has fueled the vestigation of buildg equipment and components, order to atta optimal control and management of their functions an efficient and rational way while reducg fossil fuel consumption and green house gas emissions (see e.g. IEA, 22). Modern control methods are fact an efficient way for handlg emergency issues buildgs, as a central computer of a BAS can turn devise an optimal control strategy for specific urgent situations. As an example, Lute J. P. (et al., 1995) attended to fd a cost-effective optimum to supply heat to the buildg usg a predictor for the door temperature, while matag a comfortable temperature the buildg with a certa range of variation. Furthermore, the control of the temperature heatg or coolg mode is kept between two predefed limits, stead of matag a process variable, as long as possible, constant at its set-pot. As mentioned by e.g. Galata (et al., 1996), multivariable control systems are an efficient and consistent way to control buildg energy services as a whole, with a potential of energy savgs around 18% for the HVAC systems over the year, and around 52% for lightg. Integrated control strategies for heatg, coolg and artificial/natural lightg are regulated simultaneously by one multi-controller rather than dividually by various control strategies. Besides this important potential, many additional perspectives may exist, like stability of comfort aspects buildgs and steady-state concepts used generally as a basis for

2 multivariable systems. Most buildg components (e.g. valves) are basically characterized with saturations constrats. This limited factor must be prioritized by means of state space methods, which are not only useful analysis and design of lear systems, but are also an important startg pot for advanced optimal and nonlear control buildgs. However, these previous studies do not take to account all buildg material and construction properties plus system components and performance aspects cludg requirements imposed by occupants and environmental conditions. In most cases, this necessitates appropriate methods to control comfort and energetic aspects volvg one or more limited factors (like for stance, the measured variable must rendezvous with the setpot before the required time is accumulated). To tackle these problems, an approach to distributed control and buildg performance simulation environments by run-time couplg has been developed and implemented. The run-time couplg uses Internet sockets order to exchange data to each other durg simulation. In this approach, the buildg model and the control system, separated different environments, work together through run-time couplg. The models can be located on different kds of hosts where performance simulation is much faster than usg a sgle computer. To deal with the door temperature controller under constrats that avoid undesirable operation regimes, a model is developed usg the notion of the block diagram representation of the temperature control process of a space, modeled by a contuous-time transfer function of different elements formg the feedback control system. This paper describes a modelbased optimal control strategy that suitably regulates the door temperature a buildg. In this case, a performance criterion mimized by lear programmg is proposed order to optimize the comfort aspects with the mimum use of energy cost. This model-based optimal control is terms of a reduced steady state form, derived from experimental studies with a test-cell, located at Delft Technical University (TU Delft). Then, through a run-time couplg between doma dependent buildg environments and doma specific buildg performance simulation software, the same proposed model is used to obta simulation results with respect to the same material proprieties and climate data used for experiments. The first part of this paper presents a brief description of distributed control and buildg performance simulation. The next part elaborates the concept behd our idea concerng the tegrated performance assessment by identifyg the overall effect of novative control strategies for tegrated buildg systems. Then, a mathematical formulation for heatg mode is described that proposes a performance dex for the optimization of the comfort and energetic aspects. The fourth section consists of the synthesis relevant to the control feedback structure for tegrated buildg systems. The last essential part of this paper is a case study resultg on a balance between theoretical aspects and practical applications. 2. DISTRIBUTED CONTROL AND BUILING PERFORMANCE SIMULATION One key of the issues facg us when we want to simulate a buildg modelg plus environmental control systems is that frequently certa system components and/or control features can be modeled one simulation environment while models for other components and/or control features are only available other simulation software. In other words, there is doma specific software for buildg performance simulation (BPS) is usually relatively basic terms of control modelg and simulation capabilities (e.g. ESP-r, TRNSYS). On the other hand, there exists doma dependent control modelg environments (CME), which are very advanced control modelg and simulation features (e.g. Matlab/Simulk). To alleviate the restricted issue mentioned above, it is essential to reason behd our hypothesis that marryg the two approaches by run-time couplg would potentially enable tegrated

3 performance assessment by predictg the overall effect of novative control strategies for tegrated buildg systems. Previous ( Yahiaoui et al., 23 and Yahiaoui et al., 25), it has been described that a promisg approach to run-time couplg between ESP-r and Matlab/simulk is an IPC (Inter-process Communication) usg Internet sockets. This approach performs distributed simulation by a network protocol order to exchange data between buildg model and its controller, as it relatively happens a real situation. Both buildg model and its controller which are separated and work together through run-time couplg can be located on different kds of hosts which the performance simulation is much faster than usg a sgle computer. Consequently, the development of this new advent would potentially enable new flexible functionalities of buildg control strategies that are not yet possible. Durg the simulation, commands and data are transmitted between ESP-r and Matlab/Simulk. If for stance the buildg model (i.e. ESP-r) has to send its current measured process to its controller (i.e. Matlab/ Simulk) with TCP/IP-stream, a method called encodes them and transmits them with a defed control sequence via TCP/IP to a method received. This then receives the control sequence, decodes data from TCP/IP-stream format and sends data to the recipient (Matlab/ Simulk). When the controller has to send back the actuated process to its buildg model via TCP/IP, the same procedure is this fact repeated, as shown on figure 1. Fig. 1. Distributed control and buildg performance simulation environments In the current implemented approach of run-time couplg between ESP-r and Matlab, it is ESP-r which starts simulation. Indeed, Matlab is launched at every ESP-r time-step as a separate process. If the connection between ESP-r and Matlab breaks down the data to be exchanged cannot be transferred until the communication between them is reconnected. More detail about distributed buildg doma specific and doma dependent software tools by run-time couplg can be found (Yahiaoui et al., 24 and Yahiaoui et al., 25). 3. OPTIMAL CONTROL CONCEPTS FOR INTEGRATED BUILDING SYSTEMS The design process of optimal control uses a sequence of high-level steps similar to those of pole placement design. In optimal control, it necessitates first to develop optimality criterion for the controller ga. Then, mathematical algorithms compute this ga to produce a compensation factor that satisfies the proposed criterion.

4 Integrated buildg systems volve all the physical elements and user requirements that affect the design of buildgs, cludg structural systems like mechanical, electrical and so on. Those elements can consist of HVAC (Heatg, Ventilation and Air-Conditiong), lightg, power and energy, fire and safety, and water supply systems. Besides, most process control problems buildgs are related to the control of flow, pressure, temperature, and level (e.g. light, daylight, etc), which it is not suitable to use traditional or conventional control methods. Optimal control theory is the powerful tool to solve closed set constraed variation problems. Although design of such control systems, it is sometimes necessary to design controllers that are not only effectively regulate the behavior of a system, but also mimize or maximize some user defed criteria such as energy or time conservation, or obey other physical or time constrats imposed by the environment. Hence, the advantage of usg this technique consists of fdg a feasible control law (model) so as the system startg from the given itial condition transfers its state to the objective set, and mimizes a performance criterion. 3.1 Optimization for Modern Control The ma purpose of the automatic control systems can be formulated as multi-objective optimization tasks (Andersson, 2 and Coello et al., 22), which a buildg system must focus more on numerous distct goals: Optimization of comfort aspects (thermal and visual); Safety of occupants; Satisfyg occupants wishes; and Mimization of energy consumption. Each of these objectives may conflict with others- for stance, attemptg to maximize conflictg thermal comfort requirements of different occupants can be expected to result creased energy consumption if not well optimized at the system level. Nevertheless the literature, several methods have been proposed to address multi-objective optimization tasks (e.g. Lute et al., 1995). In fact, optimization is a very useful technique for conductg realistic studies when the cause and effect relationship between objectives and outcomes can be specified mathematically or through simulation. Optimization seeks to mathematically mimize (or maximize) an objective functional of many parameters the presence of one or more constrat functions. Although, the optimal control of buildg processes and plants under dynamics conditions, i.e. the concerned variables are changg with respect to time and this time is volved system description that needs dynamic optimization techniques to be solved, differential equations are used as good means to describe their processes and plants. 3.2 State Space Based Modelg Procedure The traditional and conventional control theory and methods (for stance root-locus) that have been used buildgs so far are based on simple-put and simple-output description (SISO) of buildg plants, usually expressed as a transfer function. These methods do not use any knowledge of the terior structure of the buildg equipment and components, which it means that those methods do not capture all buildg dynamics and disturbances that affect its components. In fact, those methods allow only limited control of the closed loop behavior when the feedback path is used. Modern control techniques, for stance optimal control theory, can solve such limitations by usg a much richer description of the buildg plant dynamics (such as valve actuators).

5 The so-called, the state-space representation provide the dynamics as a set of coupled firstorder differential equations a set of ternal variables known as state variables, together with a set of algebraic equations that combe that state variables to physical output variables. With this description, the Multi-put Multi-output (MIMO) plants are formed through a complete buildg model. For time variant systems, mathematical model for buildg plants are based on physical laws normally results a state space model of the followg form: x& = f( x, u) (1) y = h( x, u) where f () and h() are nonlear functions of their arguments: x() t is the ternal sate vector, ut () is the control put vector, yt () is the measured output vector and x& () t represents the differentiation with respect to the time t. The first equation, called the state equation, is used to capture the physical dynamics of the system and has memory herent the n tegrators. The second equation, called the output, or the measurement equation, is used to represent the way on how the measurements of system variables are performed, which the results depend on the type of sensors used. 3.3 Lear Quadratic Regulator Design The purpose of lear quadratic regulator (LQR) design is to realize a buildg system with practical components that will provide the desired operatg performance. The desired performance can be readily stated terms of time-doma dices. In this steady state and transient periods, the performance dices are normally specified time doma and therefore it is obvious to enlighten some of those practical aspects, which should be considered when designg controllers for real applications. Optimal control theory provides the mathematical tools for solvg problems, either analytically or through computer iterative methods, by formulatg the user criteria to a cost function (e.g. Burns, 21). This control theory consists then of fdg a control function u, either an open-loop form ut () or a feedback (a closed-loop) form uxt (, ), which can drive a system from the state x1 at the time t 1 to the state x2 at the time t 2 such a way to mimize or maximize the performance dex J ( U ), as follow: t2 m JU ( ) = ( xqx + uru ) dt, Q, R>, (2) u U t1 where Q is a state weight matrix which its choice may lead to a control system that requires the state x larger than desired and R is a control weight matrix which its choice may lead to the controller ga k such that the feedback control law is: where xref ut () = xref Kxt. () (3) is the desired state, called set-pot. 3.4 Indoor Thermal Comfort Previous research reported (Bloomfield et al., 1977) has described that termittent conditiong can save the energy used buildgs. Then (lute et al. 1995) mentioned that it is also possible to save energy by a certa variation from the temperature set-pot. But neither of those studies tried to mimize energy by keepg the door temperature as long as around the set-pot. In the current case, a mathematical performance criterion is proposed order to

6 mimize the energy consumption so that the temperature of buildg stays as close as possible to the set-pot. The control is designed to mata an door temperature with the adaptive optimum comfort temperature used wter for buildgs with natural ventilation, which it can be deduced from the ASHRAE 55 standard (see e.g. Hensen et al., 21). For the period of non-occupied of an office buildg, the door temperature can float library and sometimes it cannot be certa safe boundaries. Though the energy is saved, i.e. the heater is completely switched-down; the performance of controller can be tested to see how long the controller takes to get the door temperature to the set-pot. Durg the occupied period of an office buildg, the controller is designed order to mimize the energy consumption and to optimize the door temperature together with the Predicted Mean Vote (PMV) by choosg an appropriate weightg state matrix of the controller. In addition, PMV is a measure used to predict a comfortable situation buildgs. 4. MATHEMATICAL STATEMENT OF THE PROBLEM As a heatg system for Delft test-cell is sealed up a buildg model shown schematically figure 2. A simple model of its plant is represented as the rate change of the temperature difference the heat flow Q supplied by the heater, and the heat rate Q loss lost through the wall sulation, related by the followg equation: d mc ( T T ) = Q Q (4) out loss dt where m is the buildg mass ( Kg ), c is the average specific heat ( J Kg. K ), Q are heat flow rates ( J s or W ), and T and Tout are temperatures ( o C ). Qloss and Q Q loss T out T Heater Q Fig. 2. TU Delft test-cell case study When the outside temperature Tout is constant (or very slowly varyg), the relation given by 2 d V equation (4) can became, mc ( T ) h = Q R loss (5) dt where Vh is the heater voltage, and R is the electric resistance of the heater. Qloss The rate of heat lost through the wall sulation is proportional to the temperature difference across the sulation, which it is given by Q = U ( ) T T (6) i out

7 where U is a heat loss coefficient (W K ) Submittg from equation (6) to equation (5) gives a relation form of the state-space representation, which is as follow: d U 1 U T = T + Q + T out (7) dt m. c m. c r. c U where the Tout factor is the effect of the disturbance put. rc. Accordg to state-space form represented (1), the notation of the equation (7), used U 1 U this paper becomes, x & = x u mc. + mc. + rc. ξ (8) The value of c for this example consisted of usg common proprieties for air temperature which it is taken from table with respect to the average temperature of the buildg wter time, as mentioned (ETB, 25). On the basis of this table, c is somethg like 1.5 ( kj. / KgK. ). The value of m is also calculated with respect to density ρ, which is 3 the order of 1.25 ( Kg m ). The heat loss coefficient U is calculated relation of U-value defed by each area relation with all areas of the room model. Sensors are stalled more or less all over different places the room to provide timely detection of potential temperature changes where the door temperature is the average of all measures collected by those sensors. An optimal controller strategy needs to be designed order to optimize the thermal comfort the room and to mimize the energy consumption with the cost function that satisfies the requirements imposed by occupants. The answer to that issue depends on the satisfaction of thermal environment an office buildg and the energy savg. The mathematical formulation is proposed as follows: Performance dex, mimize the total expression over time period t 1 to t 2 : t q1 m J ( U ) = ( q1x + R. u + q2.(1 PMV ) ) dt, with Q = u U q (9) t 2 1 Constrats on energy ut () and on comfort PMV are: um () t u() t umax () t (1) PMVm PMV PMVmax In the performance dex defed by the relation (9) three terms contribute to the tegrated cost of control: the quadratic form xq 1 x which represents a penalty on the deviation of the state x from the itial (which is the desired state), the term uru which 2 represents the performance of the controller and the last term q.(1 ) 2 PMV signifies the optimum comfort temperature the room. 5. CONTROLLER SYNTHESIS The purpose of optimal control theory is to give a systematic method to synthesize control laws with proprieties specified to optimize a performance dex (or criterion) or a cost function. The remag problem is to obta the control ga K. In consequence to do so, the control feedback structure for an tegrated buildg model, shown figure 3 is performed order to assign the control system with the parameters required for optimization. But to obta the simulated results, the controller realized for experiments is the same carriedout Matlab side and the extensive buildg model is entirely implemented ESP-r side.

8 Fig. 3. Control feedback structure for tegrated buildg model 5. 1 Solvg Control Problem Solvg the control problem with equality constrats is computationally not complex sce it does lead to boundary values. A controller is defed to mimize the performance dex: t with x( t1) = x1, x( t2) x2 t1 m J ( U) = ( q x + Ru. + q.(1 PMV) ) dt, u U = (11) U 1 subject to the dynamic system x& = x+ u, x( t1) = x1 (12) mc. mc. The Hamiltonian for (11) and (12), is V V U 1 H( x, u, ) = ( q1x + Ru. + q2.(1 PMV) ) + ( ) ( x+ u), (13) x x mc. mc. The first-order necessary conditions for optimally (a J mimum) is V H( x, u, ) pt & () = x, pt ( 1) = pt ( 2) (14) u The derivative of the Hamiltonian exists, and control function ut () is found by (14). In H particular when x gets to a set-pot, we have = (15) u 1 1 V and we fd the followg optimal control u = R.( ). (16) mc. x From (15) and (16), the mimization of J leads to the followg nonlear differential equation (the so-called Riccati equation) order to fd the unknown (symmetric matrix) p : U pt &() = R 2.. pt () Q.( ). p(), t pt ( f ) = (17) mc. mc. Solvg (17), the control law is then obtaed with (16) the form of time-varyg. When t =, the optimal controller becomes time-variant. f 6. BUILDING TEST CELL: -CASE STUDY The current case study is illustrated to vestigate an application with two objectives. The first consists of comparg between experiments and simulation results obtaed by usg the same buildg model and the same model-based optimal control with the same time step of 1mn/hour. The second qualifies the importance of the run-time couplg approach when it volves the tegration of advanced control applications buildg performance simulation.

9 6.1 Experiments A test cell of dimensions (3.15*3.85*2.6 m 3 ) is built TU Delft with light construction materials for the purpose to vestigate causes that fluence the door environment of passive solar buildgs. Those causes can clude natural ventilation, radiant or solar heat ga and heat loss coefficient. A model-based optimal control for real-time specification is developed and implemented Matlab/Simulk. This controller actuates the electrical heater of 175 (W ) with proper amount of power needed for the actual situation through a data acquisition located the room. The obtaed experimental results are presented figure : :3 1: 1:3 2: 2:3 3: 3:3 4: 4:3 5: 5:3 6: 6:3 7: 7:3 8: 8:3 9: 9:3 1: 1:3 11: 11:3 12: 12:3 13: 13:3 14: 14:3 15: 15:3 16: 16:3 17: 17:3 18: 18:3 19: 19:3 2: 2:3 21: 21:3 22: 22:3 23: 23:3 : H-power (%) T-side T-set pot T-outside Fig. 4. Experimental results Simulation Results Test-cell buildg model is implemented ESP-r with new databases created to carry out the same material proprieties used practically the construction, as shown figure 2. The climate measurements are also partially tegrated sce ESP-r considers their values on an hourly basis. The simulated results, shown figure 5 are obtaed typically with the same model-based optimal control developed on the same (Matlab/Simulk) environments respectively used for experimental results. Although the run-time couplg approach, described above is used to exchange data between ESP-r and Matlab/Simulk, which is synchronously launched at every ESP-r time step as a separate process durg the occupied period, exactly from 6 to 18 o clock : :3 1: 1:3 2: 2:3 3: 3:3 4: 4:3 5: 5:3 6: 6:3 7: 7:3 8: 8:3 9: 9:3 1: 1:3 11: 11:3 12: 12:3 13: 13:3 14: 14:3 15: 15:3 16: 16:3 17: 17:3 18: 18:3 19: 19:3 2: 2:3 21: 21:3 22: 22:3 23: 23:3 : H-power (%) T-side T-set pot T-outside Fig. 5. Simulation results

10 A detailed comparison between experiments and simulation results shows that there are small changes both responses of the controller used for the door temperature the test cell. Those changes are due to the climate data that highly fluence the temperature side the test cell. In fact this outside temperature is a disturbance that makes changes over time and the controller designed does not takes action to suppress sensitive put noise, which causes chatterg at short tervals of few seconds only. However, the controller designed can filter noises if an estimator is used to operate the actual causes with negative values. Another pot comparison is that the responded signals both figures (4 and 5) are not very close to each other. This is due to ESP-r, which considers the climate data on an hourly base and probably due to theoretical approximations used sometimes to represent closely practical issues. Nevertheless, the controller designed matas the door temperature controlled with the PMV boundaries of thermal comfort while mimizg energy consumption near optimum. 7. CONCLUSIONS A mathematical formalism of model-based optimal control for heatg mode is proposed by dicatg two ma factors, of energetic and comfort aspects. These factors are then concerned with improvg the door environmental quality of buildgs. In fact, it may be concluded that correspondg model based control algorithms are possible to be tegrated for such purposes. However, the run-time couplg, approach described above can than generates an associated knowledge for wider applicability of advanced control strategies buildgs. Future work cludes a development of LQR control based estimator to filter disturbances. 8. REFERENCES Andersson, J (2) A Survey of Multiobjective Optimization Engeerg Design, Technical Report No. LiTH-IKP-R-197, Depart. of Mech. Eng., Lkpg University. Burns, R. (21) Advanced Control Engeerg, Butter Worth Heemann, Elsevier, UK Brosilow, C.B., Zhao, G.Q. and Rao, K.C. (21) A Lear Programmg Approach to constraed Multi-Variable Control, Proc. American Control Conf, pp Coello, C.A.C., Van Veldhuizen, D.A. and Lamont,G.B. (22) Evolutionary Algorithms for Solvg Multi-Objective Problems, Proc. Kluwer Acad. Publishers, New York ETB, (25) The Engeerg ToolBox s website,inc. < Galata, A. Proietto Batturi, F., and Viadana, R. (1996) A smart control strategy for shadg devices to improve the thermal and visual comfort, Proc. 4th European Conf.: Solar Energy and Urban Planng, Berl IEA, (22) Control Strategies for Hybrid Ventilation New and Retrofitted Office Buildgs (HYBVENT), Annex-35 Report, University of Aalborg, Denmark. Hensen, and Centnerova,L. (21) Energy simulation of traditional vs. adaptive thermal comfort for two moderate climate regions," Proc. Int. Conf. "Movg Thermal Comfort Standards to the 21st Century", Oxford Brookes University, pp Lute, P. and Van Passen, D. (1995) Optimal Indoor Temperature Control Usg a Predictor, Proc. IEEE Control System Journal, pp Yahiaoui. A., Hensen J.L.M. and Soethout L.L. (23) Integration of control and buildg performance simulation software by run-time couplg, Proc. IBPSA Conference and Exhibition 23, Vol. 3, pp , Edhoven, NL. Yahiaoui, A., Hensen, J., and Soethout, L. (24) Developg CORBA-based distributed control and buildg performance environments by run-time couplg, Proc. 1 th ICCCBE, Weimar, Germany. Yahiaoui. A., Hensen J.L.M., Soethout L.L. and Van Paassen, Dolf (25) Interfacg of control and buildg performance simulation software with sockets, Proc. IBPSA Conference and Exhibition 25, Montreal, Canada.