A survey on control schemes for distributed solar collector ... - CiteSeerX

Solar Energy 81 (2007) 1240–1251 www.elsevier.com/locate/solener

A survey on control schemes for distributed solar collector fields. Part I: Modeling and basic control approaches E.F. Camacho a, F.R. Rubio a, M. Berenguel

b,*

, L. Valenzuela

c

a

Universidad de Sevilla, Escuela Superior de Ingenieros, Departamento de Ingenierıá de Sistemas y Automa´tica, Camino de Los Descubrimientos s/n, E-41092, Sevilla, Spain b Universidad de Almerıá, Departamento de Lenguajes y Computacioń, A´rea de Ingenierıá de Sistemas y Automa´tica, Carretera Sacramento s/n, E-04120 La Canãda, Almerıá, Spain c Plataforma Solar de Almerıá – CIEMAT, Carretera Sene´s s/n, P.O. Box 22, E-04200 Tabernas, Almerıá, Spain Received 9 August 2006; received in revised form 20 December 2006; accepted 8 January 2007 Available online 7 February 2007 Communicated by: Associate Editor B. Norton

Abstract This article presents a survey of the different automatic control techniques that have been applied to control the outlet temperature of solar plants with distributed collectors during the last 25 years. Different aspects of the control problem involved in this kind of plants are treated, from modeling and simulation approaches to the different basic control schemes developed and successfully applied in real solar plants. A classification of the modeling and control approaches is used to explain the main features of each strategy. 2007 Elsevier Ltd. All rights reserved. Keywords: Solar thermal energy; Temperature control; Automatic control

1. Introduction When the crisis of 1973, during which oil prices roses dramatically, real interest in renewable sources of energy was rekindled. Attention turned to application of solar power for the generation of electricity and really interesting initiatives appeared. The programs initiated included a 200 kWe rated plant constructed at Coolidge, Arizona in 1979 (Larsen, 1987) and 500 kWe plant built in 1981 at the Plataforma Solar de Almerıá (PSA), Spain (Schraub and Dehne, 1983). The plant constructed in Spain was part of the International Energy Agency (IEA) project entitled Small Solar Power Systems (SSPS). In this plant two types of collecting systems were considered. One was a central receiver system (CRS) and other was a distributed collector system (DCS) using parabolic troughs.

*

Corresponding author. Tel.: +34 950 015683; fax: +34 950 015129. E-mail address: [email protected] (M. Berenguel).

0038-092X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2007.01.002

Parabolic trough systems concentrate sunlight onto a receiver pipe located along the focal line of a trough collector. A heat transfer fluid (HTF), typically synthetic oil or water, is heated as it flows along the receiver pipe and is routed either to a heat exchanger, when this fluid is oil, to produce steam that feeds an industrial process (for instance a turbine), to a flash tank, when the fluid is pressurized water, to produce steam up to 200 C for an industrial process, or to a turbine when superheated and pressurized steam is produced directly in the solar field (Zarza et al., 2001, 2002a,b). In order to provide viable power production they have to achieve their task despite fluctuations in energy input, i.e. the sunlight. An effective control scheme is needed to provide operating requirements of a solar power plant. Most of the plants that are operational currently, such as the SEGS plants in California (Price et al., 1990), provide this energy in the form of oil heated by a field of parabolic trough collectors. However, the processes usually connected to such fields for electricity generation (Wettermark, 1988; Price et al.,

E.F. Camacho et al. / Solar Energy 81 (2007) 1240–1251

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Nomenclature AC adaptive control ANN artificial neural network CC cascade control CRS central receiver system DCS distributed collector system DISS direct solar steam DSG direct steam generation FF feedforward FLC fuzzy logic control GS gain scheduling HTF heat transfer fluid IEA International Energy Agency IHP Improving Human Potential EU Programme IMC internal model control LQG linear quadratic Gaussian control MLP multilayer perceptron MPC model (based) predictive control MUSMAR multivariable self-tuning multipredictor adaptive regulator

1990) or seawater desalination (Zarza, 1991) are most efficient when operated continuously. To do this they must be provided with a constant supply of hot oil at some prespecified temperature despite variations in the ambient temperature, the inlet temperature and the direct solar radiation. This requirement prompted the use of a storage tank as a buffer between solar collection and the industrial process on early plants such as the SSPS system at the PSA, Spain (Wettermark, 1988) and SEGS I in California. For this purpose, later plants, SEGS II–IX, operated a gas fired boiler running in parallel to the solar field in order to make up any shortfalls in the solar produced steam (Price et al., 1990). Whilst these facilities enable the overall plant power output to be maintained during shortfalls, they do not remove the requirement for a fixed quality energy output from the field, in the form of tight outlet temperature control (Meaburn and Hughes, 1996). The purpose of this control is not to maintain a constant supply of solar produced thermal energy in the face of disturbances because this is not a cost effective strategy; in theory, oversized collector fields could be used with parts only operating during periods of low solar radiation. Rather, the aim of a control scheme should be to regulate the outlet temperature of the collector field by suitably adjusting the oil flow rate (Wettermark, 1988). This is beneficial in a number of ways. Firstly, it furnishes any available thermal energy in a usable form, i.e., at the desired operating temperature, which improves the overall systems efficiency and reduces the demands placed on auxiliary equipment such as the storage tank. Secondly, the solar field is maintained in a state of readiness for the resumption of full scale operation when the intensity of sunlight rises once again; the alternative is unnecessary shutdowns and startup procedures which

NARX nonlinear autoregressive models with exogenous inputs NC nonlinear control NNC neural network controllers PDE partial differential equation PID proportional-integral-derivative PRBS pseudo random binary sequence PSA Plataforma Solar de Almerıá (Spain) RBF radial basis function RC robust control SEGS solar electricity generating system SISO single input single output SSPS small solar power systems TDC time delay compensation TMR Training and Mobility of Researchers EU Programme

are both wasteful and time consuming. Finally, if the control is good, i.e., fast and well damped, the plant can be operated close to design limits, thereby improving the productivity (Meaburn and Hughes, 1996). During the last 25 years considerable effort has been devoted by many researchers to improve the efficiency of solar thermal power plants with distributed collectors from the control and optimization viewpoints. Most of the work done and summarized in this paper has been devoted to improve the operation of the Acurex field of the SSPS plant located in the PSA, Spain, which uses a parabolic trough systems using oil as heat transfer medium because commercial plants for electricity production (Pilkington Solar International, 1996) and facilities available to tests automatic controllers are using this fluid. But there are also some recent experiences controlling parabolic trough systems using water/steam as heat transfer fluid (Zarza et al., 2001, 2004; Leoń and Valenzuela, 2002; Leoń et al., 2002; Eck et al., 2003; Valenzuela et al., 2003, 2004). Currently the SSPS plant is composed of a distributed collector field, a thermal storage system and the power block (Fig. 1). The distributed collector field has constituted an ideal test-bed plant for control schema implementation as it presents complex dynamics and strong disturbances acting on the plant during the daily operation. The distributed collector field consists of 480 east–west aligned single axis tracking collectors made by the Acurex Corporation in the United States forming 10 parallel loops with a total aperture mirrors area of 2672 m2. Each of the loops is formed by four twelve-module collectors, suitably connected in series. The loop is 172 m long, the active part of the loop measuring 142 m and the passive part 30 m. The heat transfer fluid used is Santotherm 55 thermal oil,

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T

OIL STORAGE TANK

TO STEAM GENERATOR OR DESALINATION PLANT

T

SOLAR COLLECTORS FIELD

T

T

Temperature measurement

F

Flow measurement

TIC

Temperature control

FIC

Flow control

TIC

F

T

FIC

Fig. 1. Schematic diagram of the Acurex solar collector field.

able to support temperatures up to 300 C, which is pumped from the bottom of a storage tank through the solar field, where picks up the heat transferred through the receiver tube walls, till the top of the tank. The heated oil stored in the tank is used to boil water that is utilized in a steam turbine to drive an electricity generator or to feed a heat exchanger of a desalination plant. The storage tank was included in order to allow flexible electricity production and to provide a buffer between the electricity generation and the fluctuating solar input (Kalt et al., 1982). For the initial startup of the plant, the system is provided with a three-way valve which allows the oil to be circulated in the field until the outlet temperature is adequate to enter the storage tank. The operation limits for the oil pump are between 2.0 and 12.0 l s1. The minimum value is there for safety and mainly to reduce the risk of the oil being decomposed, which happens when the oil temperature exceeds 305 C. The consequence of exceeding the maximum oil temperature is that all the oil may have to be changed. Another important restricting element in this system is the difference between the field’s inlet and outlet oil temperatures. A suitable or normal difference is around or less than 70 C. If the difference is higher than 100 C, then there is a significant risk of causing oil leakage due to high oil pressure in the pipe system. The paper is organized as follows: in Section 2, the main features of the DCS from the control point of view are outlined. Section 3 summarizes the fundamental modeling and simulation approaches taken by most of the authors, while Section 4 is devoted to explain the basic control strategies used to control DCS during the last 25 years. Finally, some conclusions are included. 2. Main features of the DCS from the control point of view The main difference between a conventional power plant and a solar plant is that the primary energy source, while being variable, cannot be manipulated. The intensity of the solar radiation, in addition to its seasonal and daily cyclical variations, also depends on atmospheric conditions

such as cloud cover, humidity and air transparency. Due to this fact, a solar plant is required to cope with some problems that are not encountered in other thermal power plants. The objective of the control system in a distributed collector field is to maintain the outlet oil temperature of the loop (or the highest outlet oil temperature reached by one of the collectors each sampling time) at a desired level in spite of disturbances such as changes in the solar irradiance level (caused by clouds), mirror reflectivity or inlet oil temperature. The means available for achieving this is via the adjustment of the fluid flow and the daily solar power cycle characteristics are such that the oil flow has to change substantially during operation. This leads to significant variations in the dynamic characteristics of the field, such as the response rate and the dead time, which cause difficulties in obtaining adequate performance over the operating range with a fixed parameter controller. Thus this plant presents some characteristics that make it difficult to control: • Nonlinearity, complexity, requiring modeling simplifications, changing dynamics and changing environmental conditions: (i) The solar radiation acts as a fast disturbance with respect to the dominant time constant of the process; (ii) time varying input/output transport delay, since the delay in action depends on the manipulated variable (oil flow rate); this type of delay appears both in the field and in the pipe connecting the loops to the storage tank; (iii) when modeling simplifications are done, there are strong unmodeled dynamics and the linearized dynamics vary with the operating point; indeed, the plant is best modeled as a distributed parameter system and, further, there are antiresonance modes (frequencies at which the magnitude of the frequency response changes abruptly) in the frequency response of the collector field within the control bandwidth, in such a way that when the system is excited with a signal (oil flow or solar radiation) with principal frequency components corresponding to those of the antiresonance modes, variations at the system output are very small.


• Solar systems are in general expensive in terms of the energy produced and so any improvements in performance that could be gained through the use of advanced control techniques would help to present them as a viable alternative to conventional energy sources. • A solar collector is essentially a very large heat exchanger and these types of systems are quite common in process industry, then most of the experience gained with the control of solar collector fields can be used for other, more common, industrial processes. These aspects render the control problem at hand a difficult one and call for the use of carefully designed control algorithms, presenting enough robustness to cope with the high levels of uncertainty present in the plant. The activities performed by the control groups related to this field cover modeling, identification and simulation, classical proportional-integral-derivative control (PID), feedforward control (FF), model based predictive control (MPC), adaptive control (AC), gain-scheduled control (GS), cascade control (CC), internal model control (IMC), time delay compensation (TDC), optimal control (LQG), nonlinear control (NC), robust control (RC), fuzzy logic control (FLC) and neural network controllers (NNC). The basic control approaches (PID, CC and FF) are briefly commented in this paper within the scope of the control of DCS, while the rest are described in the second part of this survey. 3. Modeling and simulation approaches Several classifications of modeling approaches can be found in the literature, having a wide acceptance as presented by Brosilow and Joseph (2002). The hierarchy of process models has been used for different purposes in this type of solar plants: control models, simulation models, setpoint optimization models, fault tolerance, etc. Models for control purposes range from the simplest ones, based on steady-state relationships or in linear low-order approaches, to nonlinear empirical or first principles-based ones. In practice, the DCS has been modeled both by using first principles or empirically by conducted practical tests. In this second case, when introducing a step input signal in the oil flow in an open loop configuration (reaction curve method) while the rest of disturbances do not experience changes, the response can be approximated by that of a first order system or overdamped second order system with a delay depending on the fluid velocity (Camacho et al., 1997). This kind of step response suggests the use of low order linear descriptions of the plant (as is usually done in the process industry) to model the system and to design diverse control strategies. When using persistent excitation signals (e.g. random binary sequences) or by analytically examining the dynamics of the system (Meaburn and Hugues, 1993b, 1995) it can be seen that the plant exhibits a number of antiresonance modes (frequencies at which the

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magnitude of the frequency response changes abruptly) within the control bandwidth. Thus, nonlinear models (both mechanistic and empirical ones) or high order linear models around different operating points should have to be used (Camacho et al., 1997). 3.1. Fundamental models A distributed solar collector field, under general assumptions and hypotheses, may be described by a distributed parameter model of the temperature (Klein et al., 1974; Rorres et al., 1980; Orbach et al., 1981; Carotenuto et al., 1985, 1986; Carmona, 1985; Camacho et al., 1988, 1997; Berenguel et al., 1994). The dynamics of the distributed solar collector field are described by the following system of partial differential equations (PDE) describing the energy balance: oT m ðt; xÞ ¼ g0 GIðtÞ P rc Di pH t ðT m ðt; xÞ T f ðt; xÞÞ ot oT f oT f ðt; xÞ þ qf cf qðtÞ ðt; xÞ ¼ Di pH t ðT m ðt; xÞ T f ðt; xÞÞ qf cf Af ot ox ð1Þ

qm cm Am

where the subindex m refers to the metal and that of f to the fluid and all the parameters and variables are described in Table 1. Prc represents the sum of radiative and conductive thermal losses, that usually are modelled as a linear conductive relation of the form Hl(Tm(t, x) Ta(t)). A simplified energy balance neglecting heat losses has been also used by several authors (e.g. Johansen and Storaa, 2002a,b; Farkas and Vajk, 2002a,b,c, 2003; Silva et al., 2003a,b; Willigenburg et al., 2004a,b; etc.), described by: A

oT oT gG ðt; xÞ þ qðtÞ ðt; xÞ ¼ 0 IðtÞ ot ox qc

ð2Þ

Table 1 DCS model variables and parameters Symbol

Description

Units

t x q c A T(t, x) q(t) I(t) g0 G Ta(t) Hl

Time Space Density Specific heat capacity Cross-sectional area Temperature Oil pump volumetric flow rate Solar radiation Mirror optical efficiency Mirror optical aperture Ambient temperature Global coefficient of thermal losses

s m kg m3 J K1 kg1 m2 K, C m3 s1 W m2

Ht

Coefficient of metal–fluid transmission Inner diameter of the pipe line Tube length Inlet fluid temperature Outlet fluid temperature

Di l Tin(t) Tout(t)

m K, C W m1 C1, W m1 K1 W m2 C1, W m2 K1 m m K, C K, C

1244


where T(t, x) is the oil temperature at position x along the tube, with boundary condition T(t, 0) = Tin(t), Tin(t) being the inlet oil temperature to the distributed solar collector field. The objective is to control the variable Tout(t) = T(t, l) to its specified setpoint. The incoming energy depends on the peak optical efficiency of the collectors, on the mirrors reflectivity, on the effective reflecting surface and on the effective irradiance onto the collector. These two last variables depend on the incidence angle between solar rays and the vector normal to the collector surface, this angle being a function of the solar hour and date. Both lumped and distributed parameter versions of the models obtained from Eqs. (1) and (2) have been used both for control and simulation purposes, based in general hypotheses. Depending on the applications the properties of the oil are considered constant or functions of the temperature. The development of numerical simulation models of the plant has played an important role in the design of different control strategies avoiding a number of expensive and time consuming controller tuning tests at the solar power plant. Based on Eq. (1), a distributed parameter model of the Acurex field was developed (Carmona, 1985; Camacho et al., 1988) and implemented (Berenguel et al., 1994; Camacho et al., 1997) and has been used for simulation purposes by many researchers. Some authors have modified this original simulation model or performed different implementations to use other numerical methods or to account for the dynamics of the tubes connecting the outlet of the DCS with the storage tank. As shown in Rato et al. (1997a), the dynamic characteristics of a tube joining the output of the loops with the top of the storage tank are given by a gain less than one, a time constant and a variable delay. This approximation has been adopted in order to modify the basic formulation of the nonlinear model to account for dynamic characteristics introduced by the tube. The modified model has been validated with data obtained at the plant in closed-loop operation (Rato et al., 1997a). In Normey-Rico et al. (1998) a modification was performed to this nonlinear model of parabolic trough collectors in Berenguel et al. (1994) and Camacho et al. (1997) to include varying transport delay. In Meaburn (1995), a modification of the original model was also developed, as it suffered from the limitation of not being able to adequately represent transport delay effects and the inconvenience of not having a steady state finder. When using the model for transient studies, the initial conditions are found by simply running the model over a time to permit initial transients to decay. To overcome this, the discrete model equations were reformulated to provide the capability of direct calculation of steady-state conditions using an implicit trapezoidal approximation, instead of a 2-step Euler approximation as that used by Berenguel et al. (1994) and Camacho et al. (1997). All the mentioned models are based on standard fluid flow and thermodynamic considerations, but considering uncompressible fluid. The effort is nowadays placed in

modeling DCS with direct steam generation. In Yebra et al. (2001, 2005) and Yebra (2006) a model is being developed using the Modelica thermohydraulic library Thermofluid. The dynamic validation of the models has been done in various ways. Most of the authors have used typical stepresponse test performed at the plant. In Meaburn and Hughes (1997) dynamic validation was conducted by making a comparison between the plant and model in the frequency domain. The frequency response of the plant was obtained by a Fourier analysis of measured input and output data during transients. The method of excitation used was the simple pulse test. This was chosen in preference to periodic signals such as the common pseudo random binary sequence (PRBS) simply because it extracts the dynamic information very quickly. In comparison, a PRBS signal needs to be well over an hour long to extract the relevant data with sufficient accuracy, suffering from the influence of solar radiation drifts. In order to use PRBS type signals, computer models have to be used, as done in Camacho et al. (1994b). Eqs. (1) and (2) have also been used for control purposes (Camacho et al., 1997), in the development of feedforward controllers (Rorres et al., 1980; Carotenuto et al., 1986; Rubio, 1985; Rubio et al., 1986, 2006; Camacho et al., 1992, 1997; Berenguel et al., 1994; Meaburn and Hughes, 1997; Silva et al., 1998; Valenzuela and Balsa, 1998; Johansen and Storaa, 2002a,b), nonlinear PID controllers including a real-time numerical integration of the distributed plant model (Johansen and Storaa, 2002a,b), nonlinear model-based predictive controllers (Camacho and Berenguel, 1994b; Berenguel, 1996; Arahal et al., 1997, 1998a,b; Berenguel et al., 1997b, 1998, Pickhardt and Silva, 1998; Berenguel, 1998; Pickhardt, 1999, 2000a), internal model control (Farkas and Vajk, 2002a,b,c, 2003), time delay compensation (Normey-Rico et al., 1998), feedback linearizing controllers (Carotenuto et al., 1985; Barao et al., 2002; Silva et al., 2002b; Igreja et al., 2003; Cirre et al., 2005), multirate controllers (Silva et al., 2002a, 2003b) etc. (all these strategies treated in other sections) and for setpoint optimization purposes. Rorres et al. (1980) and Orbach et al. (1981) suggested an optimal control formulation where the objective is to maximize net produced power when the pumping power is taken into consideration. In Cirre et al. (2004a,b) a compensator was introduced to automatically compute setpoints for the whole range of operating conditions of the Acurex distributed solar collector field, looking for the maximum achievable temperature taking into account operational constraints, such as the maximum constructive temperature (305 C), the saturation of the control signal (oil flow between 2 and 12 l s1), the maximum temperature gradient between the inlet and outlet oil temperature (80 C) and accounting for the actual values of the disturbances (mainly in solar radiation, inlet oil temperature and mirrors reflectivity). An enthalpy balance is used for setpoint optimization purposes taking into account the mentioned aspects. The


advantages of using this kind of setpoint optimization strategy are evident in the starting phase of the operation, when the largest variations in the inlet oil temperature occurs due to the existence of cold oil within the tubes and the recirculation using the three-way valve till reaching the minimum temperature to be entered at the top of the storage tank.

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nection of ten neural networks is built, while for the passive part a white box model and a neural network black box model are developed. All models are identified and validated using measurement data. In Ionescu et al. (2004) a model of the overall solar power plant is also developed using neural networks, to avoid overhead generated by training each one of the networks presented in the work of Sbarciog et al. (2004) and Wyns et al. (2004).

3.2. Data-driven models Linear black-box models have been obtained from parameter identification by many authors for control purposes. Low order linear models have been commonly used for adaptive control purposes (Camacho et al., 1992, 1994a; Camacho and Berenguel, 1997; Normey-Rico et al., 1998; Pe´rez de la Parte et al., 2007; Rubio et al., 2006), while high order linear models are employed for gain scheduled controllers (Camacho and Berenguel, 1993, 1994a,b; Camacho et al., 1994b, 1997; Pickhardt, 1998, 2000b; Rato et al., 1997b; Nenciari and Mosca, 1998; Johansen et al., 2000), all these treated in part II of this survey. Regarding nonlinear models, several methodologies, among which numerous types of artificial neural networks (ANN), have been proposed for building a nonlinear model of the solar power plant, which consequently was used for simulation purposes or as a core element in various model based prediction schemes. In Kalogirou (2000, 2001) a comprehensive review of applications of ANN in renewable energy systems is performed. Within the scope of solar plants with distributed collectors, in Arahal et al. (1997, 1998b) the application of the general identification methodology to obtain neural predictors for use in a nonlinear predictive control scheme is shown. Every step of the methodology is explained. Nonlinear autoregressive models with exogenous inputs (NARX) models are used in this work, where several algorithms for selecting past signal values as inputs are developed. Multilayer perceptrons (MLP) and radial basis functions (RBF) networks are used in this work, while in Arahal et al. (1998a) a comparison is done between different types of RBF neural networks for the same plant. Berenguel et al. (1998) used a static neural network in an autoregressive configuration and proposed a selection method based on the reduction of the estimated gradient for determining the past values that the network needs to construct the prediction. Pereira and Dourado (2002a,b) suggested a neuro-fuzzy system based on a radial basis function network with support vector learning, while Henriques et al. (2002c) used a recurrent network in combination with an on-line learning strategy to update both the weights of the network and the current state. In Sbarciog et al. (2004) and Wyns et al. (2004), the identification of a DCS is performed both using neural networks and physical models. The nonlinear identification problem is tackled by decomposing the complex system in two main components: an active part and a passive part. For the active part of the solar power plant a model based on the parallel con-

4. Basic control algorithms The control theory for linear processes has for some time been considered a well established scientific discipline with powerful techniques for analyzing and designing controllers. The main problems in process control when applying the linear control theory are caused by the fact that (Seborg, 1994, 1999): (i) a linear mathematical model of the plant is needed and finding one is not a trivial problem in many cases; (ii) mathematical models of real processes cannot take all aspect of reality into account and simplifying assumptions have to be made where models are only approximations of reality, (iii) most processes are nonlinear and (iv) because of changing environmental conditions most processes are not time invariant. While in other power generating processes, the main source of energy (the fuel) can be manipulated as it is used as the main control variable, in solar energy systems, the main source of power which is solar radiation cannot be manipulated, acting as a disturbance when considering it from a control point of view. Although these types of plants have all the characteristics needed for using advanced control strategies able to cope with changing dynamics, (nonlinearities and uncertainties) most of them are controlled by traditional PID controllers. As fixed PID controllers cannot cope with some of the mentioned problems, they have to be detuned with low gain, producing sluggish responses or if they are tightly tuned they may produce high oscillations when the dynamics of the process vary, due to environmental and/or operating conditions changes. This is the case of distributed solar collector fields, where the use of more efficient control strategies resulting in better responses would increase the number of operational hours of the field. Thus, when the control specifications are very tight and the control system makes the process work at high frequencies, where uncertainties are higher, or for some systems with complex dynamics that cannot be approximated by simple linear low order models, more sophisticated or advanced control techniques are needed, as those included in Table 2 proposed by Seborg (1994, 1999) according to their use in industry, where most of the techniques are addressed in this article. Category I, treated in the first part of this survey, consists of standard control strategies that have been widely used for several decades. The vast majority of automatic control loops in the process industries (about 90%) still relay on various forms of the ubiquitous PID controller, which has been

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resonance modes, but good results have been achieved in the reported literature both in terms of setpoint tracking and disturbance response when restricting the bandwidth of such controllers. Practically all the tested PID-based control schemes incorporate a feedforward term in the control loop to account for the effect of measurable disturbances (Camacho et al., 1992, 1997; Berenguel, 1996; Rubio et al., 2006). In Cirre et al. (2004a,b) a class of PID structure combined with a feedforward term and a block for automatic generation of setpoint has been satisfactory tested at the plant. Adaptive or gain scheduling PI controllers (Camacho et al., 1992, 1997; Vaz et al., 1998), switching fuzzy logic or neural network based PID controllers (Cardoso et al., 1999; Henriques et al., 1999a,b; Markou and Petropoulakis, 1998), fuzzy logic PID controllers (Berenguel et al., 1997a, 1999; Stirrup et al., 2001) and robust PID controllers (Cirre et al., 2003) are good examples of this philosophy of including a feedforward action and some kind of adaptation to plant dynamics when using PID controllers. In Vaz et al. (1998) a PID controller with gain interpolation is developed, while in Johansen and Storaa (2002a,b) a mixed feedback/feedforward energy based control using PID control is implemented in the form of a PID feedback with time-varying/ nonlinear gain. These control schemes will be explained in the part II of this survey.

Table 2 Classification of process control strategies according to the degree of use in industry Category I: conventional control strategies Manual control PID control Ratio control Cascade control Feedforward control

Acronym PID CC FF

Category II: advanced control: classical techniques Gain scheduling GS Time delay compensation TDC Decoupling control Selective/override controllers Category III: advanced control: widely used techniques Model predictive control MPC Statistical quality control Internal model control IMC Adaptive control AC Category IV: advanced control: newer techniques with some industrial applications Optimal control LQG Nonlinear control NC Robust control RC Neural network controllers NNC Fuzzy logic control FLC Expert systems Category V: advanced control: proposed strategies with few (if any) industrial applications

4.2. Feedforward control (FF) commercially available for over 60 years. The other categories are treated in part II of this survey.

Feedforward controllers are extensively used in industry to correct the effect caused by external and measurable disturbances. The disturbances are sensed and used to calculate the value of the manipulated variable required to maintain control at the setpoint (using a model of how the disturbances affect the process). The offset resulting from modeling errors can be eliminated by adding feedback. DCS suffer from changes in the received energy which can be slow, as daily radiation variations, mirror reflectivity changes due to accumulation of dust, etc.; or fast, mainly due to passing clouds and changes in the inlet oil temperature at the starting phase of the power conversion system. These disturbances force the oil flow to change producing a variable residence time of the fluid within the field. Feedforward has been widely used in the control of DCS (Rorres et al., 1980; Carotenuto et al., 1986; Camacho et al., 1992, 1997; Berenguel et al., 1994; Meaburn and

4.1. PID control (PID) Due to the significant variations in the dynamic characteristics of DCS mentioned in Section 2, it is difficult to obtain a satisfactory performance over the total operating range with a static controller, mostly if well damped responses are required, due to the existence of resonance dynamics. The use of PID controllers (Fig. 2) with fixed parameters has been restricted to safe operation conditions (backup controllers) (Carmona et al., 1987; Camacho et al., 1997), but they cannot cope with nominal operation of the plant without including additional compensators in the control loop (Barao, 2000; Barao et al., 2002). Even in those cases, performance is restricted by the excitation of

r(s) +

e(s)

+

Kp

v(s)

ACTUATOR

+

-

Kp/Ti

+

1/s

+

+

1/Tt

Fig. 2. Basic PID + antiwindup control scheme.

u(s)

PLANT

y(s)


1247

Input fluid Solar temperature radiation

FEEDFORWARD CONTROLLER uFF(t) r(t)

+ +

CONTROLLER

u(t) +

PLANT

y(t)

-

Input fluid Solar temperature radiation

r(t)

+

CONTROLLER

uC(t)

FEEDFORWARD CONTROLLER

u FF(t)

PLANT

y(t)

-

Fig. 3. Basic feedforward control schemes (FF). (a) Parallel configuration, (b) series configuration.

Hughes, 1997; Silva et al., 1998; Valenzuela and Balsa, 1998). Both dynamic and static feedforward terms (and also white/black box models) have been developed in this scope. The steady state gain of the plant, although a function of the irradiance, ambient temperature, the inlet temperature and the volumetric flow rate, can be predicted using simple static models of the plant (Carmona et al., 1987; Espanã and Rodrı´guez, 1987; Camacho et al., 1992). The most extensively used feedforward compensation, both in parallel (Fig. 3(a)) and series (Fig. 3(b)) configurations, uses a steady-state energy balance from Eq. (1) and experimental data, derived from a correlation for the oil flow as function of the inlet and outlet oil temperatures, solar radiation, mirror reflectivity and ambient temperature (Camacho et al., 1992; Valenzuela and Balsa, 1998). In both cases, the radiation and inlet oil temperature serve to directly adjust the oil flow to the values calculated to maintain the outlet temperature at the desired level. This restricts the outlet temperature excursions, which is desirable from the control viewpoint and ensures that the outlet temperature is predominantly a function of the oil flow, which is the manipulated variable. These feedforward controllers have proved to be effective in many of the tests performed at the plant and have been used by many of the control algorithms tested at the plant (Camacho et al., 1994a,b; Rubio et al., 1995; Camacho and Berenguel, 1997; Ke et al., 1998; Luk et al., 1999; Cardoso et al., 1999; Stirrup et al., 2001; Johansen and Storaa, 2002a,b; etc.). Figs. 4 and 5 show experimental results obtained by Camacho et al. (1997). PID controllers combined with feedforward controllers are also the basis of the new generation of solar plants with direct steam generation (Valenzuela et al., 2004, 2005, 2006).

Fig. 4. Solar plant output using parallel feedforward compensation.

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by accessible disturbances (radiation changes and inlet oil temperature) is used, while in the outer loop a PID is employed. The difference in the dominant time constants of the inner (faster) and outer (slower) control loops is explored by employing different sampling rates in each of them. Cascade control has been recently used in the scope of controlling solar plants with distributed collectors with direct steam generation (Valenzuela et al., 2004). 5. Concluding remarks The main features of the different modeling and basic control approaches used during the last 25 years to control DCS have been outlined. The DCS may be described by a distributed parameter model of the temperature. It is widely recognized that the performance of PI and PID type controllers will be inferior to model based approaches (Camacho et al., 1997; Meaburn and Hughes, 1995). Even when the plant is linearized about some operating point and approximated by a finite dimensional model, the frequency response contains anti-resonance modes near the bandwidth that must be taken into consideration in the controller in order to achieve high performance (Meaburn and Hughes, 1993a, 1995). Thus, the ‘‘ideal’’ controller should be high-order and nonlinear. The control techniques outlined in this paper range from the simplest ones treated in the first part of the survey to others with high complexity studied in the second part, trying to find a trade-off between commissioning time and performance.

Fig. 5. Solar plant output using series feedforward compensation.

4.3. Cascade control Cascade control is a traditional control technique aimed at cancelling the effects of the disturbances on the controlled output by splitting the control problem in two time scales and two control loops: an inner control loop (slave) devoted to compensate for disturbances and the outer control loop (master) controlling the process output (Fig. 6). Few applications of cascade control are reported in the literature and are mainly developed in the scope of the cascade control of a DCS for controlling the average of the temperatures at the outlet of the loops and the temperature of the oil entering the storage tank (Silva et al., 1997; Rato et al., 1997a). In the inner loop an adaptive model based predictive controller exploiting the information conveyed r2(s)

MASTER CONTROLLER

r1(s) TS2(s)

SLAVE CONTROLLER

Acknowledgements The authors thank CICYT and FEDER for partially funding this work under grants DPI2001-2380-CO2, DPI2002-04375, DPI2004-07444-C04-01/04, DPI200406419 and by the Consejerıá de Innovacioń, Ciencia y Empresa de la Junta de Andalucıá. The experiments described in this paper were also performed within the projects ‘‘Enhancement and Development of Industrial Applications of Solar Energy Technologies’’, supported by EEC Program ‘‘Human Capital and Mobility – Large Installations Program’’, EC-DGS XII Program ‘‘Training and Mobility of Researchers’’ and EC-DGS XII program ‘‘Improving Human Potential’’ and promoted by CIEMAT – PSA, Spain. This work has been also performed within the scope of the specific collaboration agreement between the PSA and the Automatic Control, Electronics and Robotics (TEP-197) research group of the Universidad de

TS1(s)

COLLECTOR FIELD TS1(s)

TS2(s)

Fig. 6. Multirate cascade control (CC).

y1(t)

STORAGE TANK INLET

y2(t)


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