Estimation and control of temperature profile over a sheet in thermoforming process using non-equidistant temperature sensor

Fourier transform is a very popular technique for the estimation and reconstruction of signal and image. This technique can be used for the estimation of the temperature profile over the sheet. But one of the drawbacks of this method is in order to use this method for the estimation of the temperature profile of the sheet; the sensors have to be placed at equidistant position over the sheet. This placement may not be optimum position for the prediction of the temperature profile of the sheet. The temperature sensors usually placed at the optimum position of the sheet for the best estimation of surface temperature of a sheet with least number of sensors. The proposed method for the estimation of temperature is can be used for the arrangement of sensor with non-equidistant. The proposed method is developed in such a way that it can do a high-quality estimation of the temperature profile over the entire sheet through its harmonics and the spatial harmonic controller can control the harmonics to obtain the desired temperature profile. Computational cost is also considered during the development of the proposed method. The computational cost of computing Non-Uniform Fast Fourier Transform (NUFFT) to estimate the temperature profile is reduced to make the technique more computational efficient. The performance of the proposed estimator and controller is tested in simulation at different operating conditions to compare with the conventional method of the estimation of temperature profile which is based on the weighted average of the temperature of the sensors surrounding the point. The superiority of the proposed method for the estimation of temperature and hence the accuracy of the developed controller and its prospective real-time application is evidenced by the results.