Case study on the identification of a multivariable cooling system with time-varying delay

Abstract

This Case Study illustrates the application of uncorrelated multisine signals for the identification of a multivariable cooling system with time-varying delay. The system has two inputs, one associated with the flow control system and the other with the Peltier system, and a temperature output. The suppression of harmonic multiples of two and three in the signals confirms that the system is largely linear. The application of several periods of the perturbation signals leads to the identification of a time-invariant model for the channel from the Peltier system to the temperature output and the detection of a time-varying component for the channel from the flow control system to the temperature output. A delay reconciliation technique is applied to remove the relative delays between individual periods of the output so that the averaged period becomes more representative of the individual periods. Continuous-time modelling of the time-invariant part of the time-varying channel is further carried out as it facilitates online adaptive identification of the variable delay using a gridding approach which accommodates fractional delay values.