Enrrgv Vol. 15, No. 6, pp. 467-477, 1990 0360-5442/90 $3.00 + 0.00 Printed in Great Britain. All tights reserved Copyright 0 1990 Pergamon Pressplc zyxwvu A NONLINEAR DYNAMIC THERMAL REGULATOR FOR A PARABOLOIDAL SOLAR COLLECTOR G. STAvRA&%Ist, G. BITSORIS$, and M. SANTAMOURIS§,~ tProduction Engineering Department, Technical University of Crete, Agiou Titou Square, 73100 Chania, Crete, *Automatic Control Laboratory, Electrical Engineering Department, University of Patras, Patras 26110 and QSociety for Appropriate Technologies Ltd. Themistokleous 87, 10683 Athens, Greece zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ (Received 6 July 1989; received for publication 27 November 1989) Ah&act-This paper deals with the problem of the identification and the thermal regulation of a solar paraboloidal collector. First, a short description of the experimental process is given and former modelling results are presented. Then, using experimental data, a bilinear model for the receiver of the collector is derived. Based on this model, a nonlinear dynamic regulator is established. The role of this regulator is to define an equilibrium point for the output temperature of the heat-transfer fluid and, in addition, to eliminate deviations which are due to external perturbations. Finally, simulation results are presented in order to evaluate the performance of the proposed technique. A microprocessor-based system is recommended for implementation of the control algorithm. 1. INTRODUCTION Two pairs of paraboloidal solar concentrators have been built on the experimental field of Saint-Chamas in Marseille, France. These THEK concentrators (for THErmal-Kilowatt) are thermal concentrating solar collectors intended for operation up to a mean output temperature of 300°C and for delivering a power of 30 kW.’ The THEK collector concentrates solar energy on a receiver in which circulates a heat-transfer fluid. The operation of the THEK collector is perturbed by the variations of the solar flux, the ambient temperature and the wind speed. Thus, the problem of the design of a regulator of the output temperature of the heat-transfer fluid is essential. The THEK collector is shown in Fig. 1 and is designed around a revolving paraboloid reflector which is permanently pointed towards the sun and concentrates direct solar radiation on a receiver. The receiver is a steel, spirally-wound tube placed on the focal plane of the reflector. In the receiver, shown in Fig. 2, the concentrated solar energy is transformed to thermal energy transported by a heat-transfer fluid (Gilothermoil) which circulates in the boiler. Measurement devices (flow-meter, thermocouples, solar-flux sensor, etc.) are directly connected to a data-acquisition system coupled to a computer which controls the process. The measurements are performed every 3.3 sec.lV5 The receiver is considered to be a thermal process and is a distributed-parameter system. An exact dynamical model would be provided by a set of partial differential equations. Since such a model requires complicated computations, it is not suitable for real-time control. In order to establish a control law which can be easily implemented, a set of linear ordinary differential equations has been proposed in Refs. 3 and 4 as a model of the system. The assumptions made there normally produce a model consisting of nonlinear differential equations. A linear model has been developed in Refs. 3 and 4 by linearizing these equations. Such a model is, however, valid only in a small neighborhood of the working point. After a detailed thermal analysis, a bilinear model has been proposed in Ref. 6 as a more rational approximation to the general nonlinear model. Also, a procedure for estimation of bilinear model parameters using real data has been described. In this case, physical considerations have not been taken into account and the matrices of the bilinear model are considered to be completely unknown. This approach (ITo whom all correspondence should be addressed. 467