Online Estimation and Control in Delta Domain Using Time Moments

Abstract

The present thesis is concerned with controller design of linear discrete-time systems modeled in the delta domain. Time moment method, a tool so far used for model order reduction is applied to compute online time moments from the input-output response of the plant and reference model to estimate the controller parameters adaptively. Traditionally, discrete-time sampled data systems are represented using shift-operator parameterization. Such parameterizations are not suitable at fast sampling rates. An alternative parameterization using the so-called delta operator maintains a close correspondence to its continuous-time counterpart at fast sampling rate. Using delta operator parameterization it is possible to unify both discrete-time and continuous-time theory. The coefficients of the discrete-time transfer function are similar to the corresponding ones in continuous-time and it becomes easier to tune controller parameters for improved dynamic performance. The thesis addresses a novel method to compute the time moments in delta domain. At fast sampling limit, the delta operator model tends to the analog dynamic system model. The  - operator model can be applied to a wide range of discrete-time systems, from sampled-data systems with coarse sampling intervals to rapidly sample near continuous-time systems. Moreover, it has certain numerical advantages compared to the shift operator parameterization. It therefore provides a unified framework for system studies, where continuous-time results can be achieved from the discrete-time description of the system. In the first part of the thesis, computation of the first three moments in the delta domain k0,k1 and 2 k are carried out. Numerical computation of these time moments has been carried out using MATLAB code. In the second part of the thesis, time moments obtained in the first part are used in different control schemes like PCMS, PTCS, and PTCFS to match the time moments of the compensated plant with the desired response. At the end, the different control schemes give the same results in continuous domain as well as in delta domain.