Optimal sensor network design for multirate systems q Sachin C. Kadu a,b , Mani Bhushan a, * , Ravindra Gudi a a Department of Chemical Engineering, IIT Bombay, Mumbai 400 076, India b Reactor Projects Division, BARC, Mumbai 400 085, India Received 4 April 2007; received in revised form 21 September 2007; accepted 7 October 2007 Abstract A methodology for generating optimal sensor network design for multirate systems is presented. Location of sensors, cost of mea- surement and frequency of sampling are important factors that have been incorporated in the sensor network design formulation. The proposed methodology is based on evaluating trade-off (Pareto optimal) solutions between the quality of state estimation and the total measurement cost associated with the sensor network. To accommodate different sampling frequencies and evaluate their effect on state estimation accuracy, a generic multirate extension of the traditional Kalman filter is used. In general, higher accuracies of the state estimates are realizable at expense of higher measurement cost. Incorporation of these conflicting objectives of minimizing measure- ment cost and maximizing estimation accuracy results in a combinatorial, implicit multiobjective optimization problem, which is solved using the well-known non-dominated sorting genetic algorithm-II. The resulting solutions can be then analyzed by the process designer for determining an appropriate sensor network. The methodology is demonstrated by generating optimal sensor network design for the benchmark quadruple tank set up [K.H. Johansson, The quadruple-tank process: a multivariable laboratory process with an adjustable zero, IEEE Trans. Control Syst. Tech. 8 (3) (2000) 456–465] and the Tennessee Eastman challenge process [J.J. Downs, E.F. Vogel, A plant-wide industrial process control problem, Comput. Chem. Eng. 17 (3) (1993) 245–255]. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Multirate Kalman filter; Sensor network design; Multiobjective optimization 1. Introduction In the process industry, measurements of different pro- cess variables are often obtained at different sampling rates. Such multirate measurement scenarios are encountered frequently in chemical and biochemical processes, for e.g. secondary variables (such as temperature, pressure) are measured at a higher frequency while some quality vari- ables (such as molecular weight, concentration) are mea- sured relatively slowly. In such situations, for monitoring and control, it is possible to generate estimates of the qual- ity variables and secondary variables at frequent rates using (inferential) observer-based schemes that rely on both fast and slow measurements, as well as the process model. State space models are widely used in process con- trol and estimation literature for representing process dynamics. Kalman filtering techniques are preferred tech- niques to infer process variables (states) using incomplete or partial measurements and a first-principles based state space model. The performance, as characterized by the uncertainty in the estimated states in Kalman filtering strategy, can be improved by formally incorporating the infrequently available measurements. The accuracy of the estimated states depends on the total number of sensors (and their noise characteristics), their location (in terms of which variables they sense) and their sampling frequen- cies. The quality of estimates (in terms of their variance) generally increases with the number of sensors and their sampling frequencies, but this also increases the associated measurement cost. Hence, there is a trade-off between the 0959-1524/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jprocont.2007.10.002 q A preliminary version of this manuscript was published in Proceedings of 8th International conference on dynamics and control of process systems (DYCOPS 2007), Cancun, Mexico, vol. 3, 2007, pp. 193–198. * Corresponding author. Tel.: +91 22 2576 7214; fax: +91 22 2572 6895. E-mail address: mbhushan@iitb.ac.in (M. Bhushan). www.elsevier.com/locate/jprocont Available online at www.sciencedirect.com Journal of Process Control 18 (2008) 594–609