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A new controller based on discrete wavelet packet transform (DWPT) for liquid level system (LLS) has been presented here. This controller generates control signal using node coefficients of the error signal which interprets many implicit phenomena such as process dynamics, measurement noise and effect of external disturbances. Through simulation results on LLS problem, this controller is shown to perform faster than both the discrete wavelet transform based controller and conventional proportional integral controller. Also, it is more efficient in terms of its ability to provide better noise rejection. To overcome the wind up phenomenon by considering the saturation due to presence of actuator, anti-wind up technique is applied to the conventional PI controller and compared to the wavelet packet transform based controller. In this case also, packet controller is found better than the other ones. This similar work has been extended for analogous first order RC plant as well as second order plant also.

A new controller based on discrete wavelet packet transform (DWPT) for liquid level system (LLS) has been presented here. In this proposed controller, packet transform is used to decompose the error signal into different frequency nodes at various scales which represents many underlying phenomena such as process dynamics, noise and disturbances. These coefficients are scaled by their respective gains and then added together to generate the control signal. NI DAQ device is used to interface between the PC based controllers simulated in NI LABVIEW software to the real time RC plant analogous to LLS and a second order RLC plant. The performance of this controller has been studied and compared to the PI controller. From hardware results, this controller is shown to perform better than both the discrete wavelet transform (DWT) based proportional integral controller and PI controller. Also, it can handle noise more efficiently.

The presented work explored the possibility of developing a discrete wavelet transform-based repetitive control (DWTRC) strategy along with a proportional controller for a liquid level system (LLS) to track a periodic reference signal. The modified DWTRC with a P control system is a type of servo mechanism, effective for periodic reference input. The entire effort derives from two distinct parts. First, the tracking performance and stability measure of the system with inclusion of a repetitive controller (RC) in presence of P controller that has been studied and compared with conventional P and PI controllers in both time and frequency domains, subjected to periodic command to establish the usefulness of the former. The most obvious disadvantage of the RC with P control is the requirement of large memory for the presence of RC, and the memory requirement linearly increases with both repetition time and sampling frequency. Second, to overcome this difficulty, deployment of the discrete wavelet transform (DWT) in the RC loop is done to reduce the problem of memory requirement, and ensures efficient and high-speed computation due to the filtering and data reduction property of DWT. Finally, the effectiveness of DWTRC is validated through saving memory and optimizing the tracking error with variation of the wavelet order and its decomposition level.

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.

This paper deals with an identification problem of modeling a nonlinear dynamic system of multivariable glucose-insulin process in an IDDM patient. Out of many model structures that can represent a nonlinear process effectively; the Hammerstein-Wiener model has attracted a lot of attention. The present work proposes a generalized identification method of Hammer stein-Wiener model from the input-output data of multivariable nonlinear glucose-insulin process. The present algorithm consists of a three-block (LNL) realization. For the multivariable system, the first and third blocks are standard impulse response filter (TRF) realization applied to an equivalent linear system using adaptive recursive least square (ARLS) algorithms. In the second block, i.e. the nonlinear part, ARLS algorithms have been used to solve up to second order kernels of Volterra equations with extended input vector consisting of cross components as well. The input-output data taken from the simulated nonlinear process have been used to identify the system with a filter memory length of M=3 and the validation results have shown good fit and in concordance with predicted output.

In this paper wavelet transform is used to determine the state and trajectory sensitivity of homogeneous and non-homogeneous systems. The differential-algebraic equation describing a system is converted via wavelet transform to an algebraic generalized Lyapunov equation which is solved for the coefficients of the state variables in terms of Haar basis. Further, problems of trajectory sensitivity analysis for singular as well as nonsingular systems have also been explored using the same orthogonal basis. Finally, using Kronecker product method, a generalized program is developed to determine the state and sensitivity for any number of basis function in Haar domain.