Selection of best wavelet for discrete wavelet transform based PID controller connected with liquid level system and its performances analysis

In this paper, the performance of discrete wavelet transform (DWT) based PID controller is compared to the conventional proportional-integral-derivative (PID) controller applied to Liquid level system (LLS). Here, DWT is used to decompose the actuating signal into different scales. The high scale gives the approximate or low frequency information and low scale gives the detail or high frequency information contained in the actuating signal. Based on this frequency information, the decomposed coefficients of each level are scaled by their respective gains and then added together to generate the final control signal. The choice of wavelet to decompose the error signal is an important factor because the wavelet affects the reconstructed signal quality and the design of the system as a whole. The minimum description length criterion permits to select not only the suitable wavelet filter but also the optimum number of wavelet coefficients retained for the signal reconstruction. Simulation results show that the proposed controller has faster transient response and more satisfactory operation under steady-state conditions with respect to PID controller. Simulation is done in National Instruments LabVIEW software.